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This commit is contained in:
Andrey Pokidov 2025-11-26 22:43:29 +07:00
parent 0dcd9c0d4d
commit 89dfd7644b
32 changed files with 1730 additions and 1719 deletions
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19
basic-geometry-dev/main.c
View file

@ -53,12 +53,12 @@ structure_fp32_t* make_structures(const unsigned int amount)
void print_versor_fp32(const BgcVersorFP32* versor)
{
printf("Versor (s0 = %0.12f, x1 = %0.12f, x2 = %0.12f, x3 = %0.12f)\n", versor->s0, versor->x1, versor->x2, versor->x3);
printf("Versor (s0 = %0.12f, x1 = %0.12f, x2 = %0.12f, x3 = %0.12f)\n", versor->_s0, versor->_x1, versor->_x2, versor->_x3);
}
void print_versor_fp64(const BgcVersorFP64* versor)
{
printf("Versor (s0 = %0.20f, x1 = %0.20f, x2 = %0.20f, x3 = %0.20f)\n", versor->s0, versor->x1, versor->x2, versor->x3);
printf("Versor (s0 = %0.20f, x1 = %0.20f, x2 = %0.20f, x3 = %0.20f)\n", versor->_s0, versor->_x1, versor->_x2, versor->_x3);
}
void print_vector_fp32(const BgcVector3FP32* vector)
@ -469,11 +469,16 @@ void test_basis_difference_fp64()
print_versor_fp64(&turn);
}
typedef union {
int si32;
float fp32;
} uni_number;
int main()
{
//BgcVersorFP32 start = { 1.0f, 0.0f, 0.0f, 0.0f };
//BgcVersorFP32 end = { 0.0f, 1.0f, 0.0f, 0.0f };
/*
BgcVersorFP32 start = { 1.0f, 0.0f, 0.0f, 0.0f };
BgcVersorFP32 end = { 0.9999f, 0.01414f, 0.0f, 0.0f };
BgcSlerpFP32 slerp;
@ -482,8 +487,14 @@ int main()
bgc_slerp_get_turn_for_phase_fp32(&slerp, 0.5f, &result);
print_versor_fp32(&result);
*/
//test_basis_difference_fp64();
uni_number number;
number.fp32 = 2.0f;
printf("%x\n", number.si32);
return 0;
}

77
basic-geometry-test/tests/complex/complex_arithmetics.c
View file

@ -159,35 +159,6 @@ void test_complex_subtract_fp32()
print_testing_success();
}
void test_complex_subtract_scaled_fp32()
{
BgcComplexFP32 vector1, vector2, result;
print_testing_name("bgc_complex_subtract_scaled_fp32");
bgc_complex_set_values_fp32(10.0f, -20.0f, &vector1);
bgc_complex_set_values_fp32(4.0f, 5.0f, &vector2);
bgc_complex_subtract_scaled_fp32(&vector1, &vector2, 2.0f, &result);
if (!bgc_are_close_fp32(result.real, 2.0f) || !bgc_are_close_fp32(result.imaginary, -30.0f)) {
print_testing_error("first test failed");
return;
}
bgc_complex_set_values_fp32(0.36f, 100.4f, &vector1);
bgc_complex_set_values_fp32(1.09f, 0.1f, &vector2);
bgc_complex_subtract_scaled_fp32(&vector1, &vector2, 4.0f, &result);
if (!bgc_are_close_fp32(result.real, -4.0f) || !bgc_are_close_fp32(result.imaginary, 100.0f)) {
print_testing_error("second test failed");
return;
}
print_testing_success();
}
void test_complex_subtract_fp64()
{
BgcComplexFP64 vector1, vector2, result;
@ -217,42 +188,10 @@ void test_complex_subtract_fp64()
print_testing_success();
}
void test_complex_subtract_scaled_fp64()
{
BgcComplexFP64 vector1, vector2, result;
print_testing_name("bgc_complex_subtract_scaled_fp64");
bgc_complex_set_values_fp64(10.0, 20.0, &vector1);
bgc_complex_set_values_fp64(4.0, 5.0, &vector2);
bgc_complex_subtract_scaled_fp64(&vector1, &vector2, 2.5, &result);
if (!bgc_are_close_fp64(result.real, 0.0) || !bgc_are_close_fp64(result.imaginary, 7.5)) {
print_testing_error("first test failed");
return;
}
bgc_complex_set_values_fp64(-0.27, 100.3, &vector1);
bgc_complex_set_values_fp64(-1.29, -0.1, &vector2);
bgc_complex_subtract_scaled_fp64(&vector1, &vector2, 3.0, &result);
if (!bgc_are_close_fp64(result.real, 3.6) || !bgc_are_close_fp64(result.imaginary, 100.6)) {
print_testing_error("second test failed");
return;
}
print_testing_success();
}
void test_complex_subtract()
{
test_complex_subtract_fp32();
test_complex_subtract_fp64();
test_complex_subtract_scaled_fp32();
test_complex_subtract_scaled_fp64();
}
// ================== Multiply ================== //
@ -265,7 +204,7 @@ void test_complex_multiply_fp32()
bgc_complex_set_values_fp32(10.0f, -20.0f, &vector);
bgc_complex_multiply_fp32(&vector, 0.5f, &result);
bgc_complex_multiply_by_number_fp32(&vector, 0.5f, &result);
if (!bgc_are_close_fp32(result.real, 5.0f) || !bgc_are_close_fp32(result.imaginary, -10.0f)) {
print_testing_error("first test failed");
@ -274,7 +213,7 @@ void test_complex_multiply_fp32()
bgc_complex_set_values_fp32(1.78f, -0.1f, &vector);
bgc_complex_multiply_fp32(&vector, 2.0f, &result);
bgc_complex_multiply_by_number_fp32(&vector, 2.0f, &result);
if (!bgc_are_close_fp32(result.real, 3.56f) || !bgc_are_close_fp32(result.imaginary, -0.2f)) {
print_testing_error("second test failed");
@ -292,7 +231,7 @@ void test_complex_multiply_fp64()
bgc_complex_set_values_fp64(30.0, -10.0, &vector);
bgc_complex_multiply_fp64(&vector, 0.3, &result);
bgc_complex_multiply_by_number_fp64(&vector, 0.3, &result);
if (!bgc_are_close_fp64(result.real, 9.0) || !bgc_are_close_fp64(result.imaginary, -3.0)) {
print_testing_error("first test failed");
@ -301,7 +240,7 @@ void test_complex_multiply_fp64()
bgc_complex_set_values_fp64(1.18, -0.25, &vector);
bgc_complex_multiply_fp64(&vector, 4.0, &result);
bgc_complex_multiply_by_number_fp64(&vector, 4.0, &result);
if (!bgc_are_close_fp64(result.real, 4.72) || !bgc_are_close_fp64(result.imaginary, -1.0)) {
print_testing_error("second test failed");
@ -327,7 +266,7 @@ void test_complex_divide_fp32()
bgc_complex_set_values_fp32(10.0f, -20.0f, &vector);
bgc_complex_divide_fp32(&vector, 10.0f, &result);
bgc_complex_divide_by_number_fp32(&vector, 10.0f, &result);
if (!bgc_are_close_fp32(result.real, 1.0f) || !bgc_are_close_fp32(result.imaginary, -2.0f)) {
print_testing_error("first test failed");
@ -336,7 +275,7 @@ void test_complex_divide_fp32()
bgc_complex_set_values_fp32(1.78f, -0.1f, &vector);
bgc_complex_divide_fp32(&vector, 0.2f, &result);
bgc_complex_divide_by_number_fp32(&vector, 0.2f, &result);
if (!bgc_are_close_fp32(result.real, 8.9f) || !bgc_are_close_fp32(result.imaginary, -0.5f)) {
print_testing_error("second test failed");
@ -354,7 +293,7 @@ void test_complex_divide_fp64()
bgc_complex_set_values_fp64(30.0, -10.0, &vector);
bgc_complex_divide_fp64(&vector, 5.0, &result);
bgc_complex_divide_by_number_fp64(&vector, 5.0, &result);
if (!bgc_are_close_fp64(result.real, 6.0) || !bgc_are_close_fp64(result.imaginary, -2.0)) {
print_testing_error("first test failed");
@ -363,7 +302,7 @@ void test_complex_divide_fp64()
bgc_complex_set_values_fp64(1.18, -0.25, &vector);
bgc_complex_divide_fp64(&vector, 0.5, &result);
bgc_complex_divide_by_number_fp64(&vector, 0.5, &result);
if (!bgc_are_close_fp64(result.real, 2.36) || !bgc_are_close_fp64(result.imaginary, -0.5)) {
print_testing_error("second test failed");

4
basic-geometry-test/tests/complex/complex_arithmetics.h
View file

@ -17,12 +17,8 @@ void test_complex_add();
void test_complex_subtract_fp32();
void test_complex_subtract_scaled_fp32();
void test_complex_subtract_fp64();
void test_complex_subtract_scaled_fp64();
void test_complex_subtract();
// ================== Multiply ================== //

4
basic-geometry-test/tests/quaternion/quaternion_set_to_identity.c
View file

@ -8,7 +8,7 @@ void test_quaternion_set_to_identity_fp32()
print_testing_name("bgc_quaternion_set_to_identity_fp32");
bgc_quaternion_set_to_identity_fp32(&vector);
bgc_quaternion_make_unit_fp32(&vector);
if (vector.s0 != 1.0f || vector.x1 != 0.0f || vector.x2 != 0.0f || vector.x3 != 0.0f) {
print_testing_failed();
@ -24,7 +24,7 @@ void test_quaternion_set_to_identity_fp64()
print_testing_name("bgc_quaternion_set_to_identity_fp64");
bgc_quaternion_set_to_identity_fp64(&vector);
bgc_quaternion_make_unit_fp64(&vector);
if (vector.s0 != 1.0 || vector.x1 != 0.0 || vector.x2 != 0.0 || vector.x3 != 0.0) {
print_testing_failed();

61
basic-geometry-test/tests/vector2/vector2_arithmetics.c
View file

@ -159,35 +159,6 @@ void test_vector2_subtract_fp32()
print_testing_success();
}
void test_vector2_subtract_scaled_fp32()
{
BgcVector2FP32 vector1, vector2, result;
print_testing_name("bgc_vector2_subtract_scaled_fp32");
bgc_vector2_set_values_fp32(10.0f, -20.0f, &vector1);
bgc_vector2_set_values_fp32(4.0f, 5.0f, &vector2);
bgc_vector2_subtract_scaled_fp32(&vector1, &vector2, 2.0f, &result);
if (!bgc_are_close_fp32(result.x1, 2.0f) || !bgc_are_close_fp32(result.x2, -30.0f)) {
print_testing_error("first test failed");
return;
}
bgc_vector2_set_values_fp32(0.36f, 100.4f, &vector1);
bgc_vector2_set_values_fp32(1.09f, 0.1f, &vector2);
bgc_vector2_subtract_scaled_fp32(&vector1, &vector2, 4.0f, &result);
if (!bgc_are_close_fp32(result.x1, -4.0f) || !bgc_are_close_fp32(result.x2, 100.0f)) {
print_testing_error("second test failed");
return;
}
print_testing_success();
}
void test_vector2_subtract_fp64()
{
BgcVector2FP64 vector1, vector2, result;
@ -217,42 +188,10 @@ void test_vector2_subtract_fp64()
print_testing_success();
}
void test_vector2_subtract_scaled_fp64()
{
BgcVector2FP64 vector1, vector2, result;
print_testing_name("bgc_vector2_subtract_scaled_fp64");
bgc_vector2_set_values_fp64(10.0, 20.0, &vector1);
bgc_vector2_set_values_fp64(4.0, 5.0, &vector2);
bgc_vector2_subtract_scaled_fp64(&vector1, &vector2, 2.5, &result);
if (!bgc_are_close_fp64(result.x1, 0.0) || !bgc_are_close_fp64(result.x2, 7.5)) {
print_testing_error("first test failed");
return;
}
bgc_vector2_set_values_fp64(-0.27, 100.3, &vector1);
bgc_vector2_set_values_fp64(-1.29, -0.1, &vector2);
bgc_vector2_subtract_scaled_fp64(&vector1, &vector2, 3.0, &result);
if (!bgc_are_close_fp64(result.x1, 3.6) || !bgc_are_close_fp64(result.x2, 100.6)) {
print_testing_error("second test failed");
return;
}
print_testing_success();
}
void test_vector2_subtract()
{
test_vector2_subtract_fp32();
test_vector2_subtract_fp64();
test_vector2_subtract_scaled_fp32();
test_vector2_subtract_scaled_fp64();
}
// ================== Multiply ================== //

4
basic-geometry-test/tests/vector2/vector2_arithmetics.h
View file

@ -17,12 +17,8 @@ void test_vector2_add();
void test_vector2_subtract_fp32();
void test_vector2_subtract_scaled_fp32();
void test_vector2_subtract_fp64();
void test_vector2_subtract_scaled_fp64();
void test_vector2_subtract();
// ================== Multiply ================== //

61
basic-geometry-test/tests/vector3/vector3_arithmetics.c
View file

@ -159,35 +159,6 @@ void test_vector3_subtract_fp32()
print_testing_success();
}
void test_vector3_subtract_scaled_fp32()
{
BgcVector3FP32 vector1, vector2, result;
print_testing_name("bgc_vector3_subtract_scaled_fp32");
bgc_vector3_set_values_fp32(10.0f, -20.0f, 1.25f, &vector1);
bgc_vector3_set_values_fp32(4.0f, 5.0f, -0.4f, &vector2);
bgc_vector3_subtract_scaled_fp32(&vector1, &vector2, 2.0f, &result);
if (!bgc_are_close_fp32(result.x1, 2.0f) || !bgc_are_close_fp32(result.x2, -30.0f) || !bgc_are_close_fp32(result.x3, 2.05f)) {
print_testing_error("first test failed");
return;
}
bgc_vector3_set_values_fp32(0.36f, 100.4f, 10, &vector1);
bgc_vector3_set_values_fp32(1.09f, 0.1f, 2.5f, &vector2);
bgc_vector3_subtract_scaled_fp32(&vector1, &vector2, 4.0f, &result);
if (!bgc_are_close_fp32(result.x1, -4.0f) || !bgc_are_close_fp32(result.x2, 100.0f) || !bgc_are_close_fp32(result.x3, 0.0f)) {
print_testing_error("second test failed");
return;
}
print_testing_success();
}
void test_vector3_subtract_fp64()
{
BgcVector3FP64 vector1, vector2, result;
@ -217,42 +188,10 @@ void test_vector3_subtract_fp64()
print_testing_success();
}
void test_vector3_subtract_scaled_fp64()
{
BgcVector3FP64 vector1, vector2, result;
print_testing_name("bgc_vector3_subtract_scaled_fp64");
bgc_vector3_set_values_fp64(10.0, 20.0, 0.1, &vector1);
bgc_vector3_set_values_fp64(4.0, 5.0, -4.0, &vector2);
bgc_vector3_subtract_scaled_fp64(&vector1, &vector2, 2.5, &result);
if (!bgc_are_close_fp64(result.x1, 0.0) || !bgc_are_close_fp64(result.x2, 7.5) || !bgc_are_close_fp64(result.x3, 10.1)) {
print_testing_error("first test failed");
return;
}
bgc_vector3_set_values_fp64(-0.27, 100.3, -0.01, &vector1);
bgc_vector3_set_values_fp64(-1.29, -0.1, 0.33, &vector2);
bgc_vector3_subtract_scaled_fp64(&vector1, &vector2, 3.0, &result);
if (!bgc_are_close_fp64(result.x1, 3.6) || !bgc_are_close_fp64(result.x2, 100.6) || !bgc_are_close_fp64(result.x3, -1.0)) {
print_testing_error("second test failed");
return;
}
print_testing_success();
}
void test_vector3_subtract()
{
test_vector3_subtract_fp32();
test_vector3_subtract_fp64();
test_vector3_subtract_scaled_fp32();
test_vector3_subtract_scaled_fp64();
}
// ================== Multiply ================== //

16
basic-geometry-test/tests/versor/versor_copy.c
View file

@ -28,10 +28,10 @@ void test_versor_copy_fp32()
bgc_versor_copy_fp32(&_TEST_FP32_VERSOR_LIST[i], &versor);
if (versor.s0 != _TEST_FP32_VERSOR_LIST[i].s0 ||
versor.x1 != _TEST_FP32_VERSOR_LIST[i].x1 ||
versor.x2 != _TEST_FP32_VERSOR_LIST[i].x2 ||
versor.x3 != _TEST_FP32_VERSOR_LIST[i].x3) {
if (versor._s0 != _TEST_FP32_VERSOR_LIST[i]._s0 ||
versor._x1 != _TEST_FP32_VERSOR_LIST[i]._x1 ||
versor._x2 != _TEST_FP32_VERSOR_LIST[i]._x2 ||
versor._x3 != _TEST_FP32_VERSOR_LIST[i]._x3) {
print_testing_failed();
return;
}
@ -64,10 +64,10 @@ void test_versor_copy_fp64()
bgc_versor_copy_fp64(&_TEST_FP64_VERSOR_LIST[i], &versor);
if (versor.s0 != _TEST_FP64_VERSOR_LIST[i].s0 ||
versor.x1 != _TEST_FP64_VERSOR_LIST[i].x1 ||
versor.x2 != _TEST_FP64_VERSOR_LIST[i].x2 ||
versor.x3 != _TEST_FP64_VERSOR_LIST[i].x3) {
if (versor._s0 != _TEST_FP64_VERSOR_LIST[i]._s0 ||
versor._x1 != _TEST_FP64_VERSOR_LIST[i]._x1 ||
versor._x2 != _TEST_FP64_VERSOR_LIST[i]._x2 ||
versor._x3 != _TEST_FP64_VERSOR_LIST[i]._x3) {
print_testing_failed();
return;
}

4
basic-geometry-test/tests/versor/versor_reset.c
View file

@ -10,7 +10,7 @@ void test_versor_reset_fp32()
bgc_versor_reset_fp32(&versor);
if (versor.s0 != 1.0f || versor.x1 != 0.0f || versor.x2 != 0.0f || versor.x3 != 0.0f) {
if (versor._s0 != 1.0f || versor._x1 != 0.0f || versor._x2 != 0.0f || versor._x3 != 0.0f) {
print_testing_failed();
return;
}
@ -26,7 +26,7 @@ void test_versor_reset_fp64()
bgc_versor_reset_fp64(&versor);
if (versor.s0 != 1.0 || versor.x1 != 0.0 || versor.x2 != 0.0 || versor.x3 != 0.0) {
if (versor._s0 != 1.0 || versor._x1 != 0.0 || versor._x2 != 0.0 || versor._x3 != 0.0) {
print_testing_failed();
return;
}

20
basic-geometry-test/tests/versor/versor_set_values.c
View file

@ -30,7 +30,7 @@ void test_versor_set_values_fp32()
&versor
);
versor_module = sqrtf(versor.s0 * versor.s0 + versor.x1 * versor.x1 + versor.x2 * versor.x2 + versor.x3 * versor.x3);
versor_module = sqrtf(versor._s0 * versor._s0 + versor._x1 * versor._x1 + versor._x2 * versor._x2 + versor._x3 * versor._x3);
if (!bgc_is_unit_fp32(versor_module)) {
print_testing_error("Versor module is not equal to one.");
@ -41,19 +41,19 @@ void test_versor_set_values_fp32()
continue;
}
ratio = _TEST_FP32_VERSOR_DATA_LIST[i].s0 / versor.s0;
ratio = _TEST_FP32_VERSOR_DATA_LIST[i].s0 / versor._s0;
if (!bgc_is_zero_fp32(_TEST_FP32_VERSOR_DATA_LIST[i].x1) && !bgc_are_close_fp32(ratio, _TEST_FP32_VERSOR_DATA_LIST[i].x1 / versor.x1)) {
if (!bgc_is_zero_fp32(_TEST_FP32_VERSOR_DATA_LIST[i].x1) && !bgc_are_close_fp32(ratio, _TEST_FP32_VERSOR_DATA_LIST[i].x1 / versor._x1)) {
print_testing_error("Versor was not normalized proportionally (x1).");
return;
}
if (!bgc_is_zero_fp32(_TEST_FP32_VERSOR_DATA_LIST[i].x2) && !bgc_are_close_fp32(ratio, _TEST_FP32_VERSOR_DATA_LIST[i].x2 / versor.x2)) {
if (!bgc_is_zero_fp32(_TEST_FP32_VERSOR_DATA_LIST[i].x2) && !bgc_are_close_fp32(ratio, _TEST_FP32_VERSOR_DATA_LIST[i].x2 / versor._x2)) {
print_testing_error("Versor was not normalized proportionally (x2).");
return;
}
if (!bgc_is_zero_fp32(_TEST_FP32_VERSOR_DATA_LIST[i].x3) && !bgc_are_close_fp32(ratio, _TEST_FP32_VERSOR_DATA_LIST[i].x3 / versor.x3)) {
if (!bgc_is_zero_fp32(_TEST_FP32_VERSOR_DATA_LIST[i].x3) && !bgc_are_close_fp32(ratio, _TEST_FP32_VERSOR_DATA_LIST[i].x3 / versor._x3)) {
print_testing_error("Versor was not normalized proportionally (x3).");
return;
}
@ -88,7 +88,7 @@ void test_versor_set_values_fp64()
&versor
);
versor_module = sqrt(versor.s0 * versor.s0 + versor.x1 * versor.x1 + versor.x2 * versor.x2 + versor.x3 * versor.x3);
versor_module = sqrt(versor._s0 * versor._s0 + versor._x1 * versor._x1 + versor._x2 * versor._x2 + versor._x3 * versor._x3);
if (!bgc_is_unit_fp64(versor_module)) {
print_testing_error("Versor module is not equal to one.");
@ -99,19 +99,19 @@ void test_versor_set_values_fp64()
continue;
}
ratio = _TEST_FP64_VERSOR_DATA_LIST[i].s0 / versor.s0;
ratio = _TEST_FP64_VERSOR_DATA_LIST[i].s0 / versor._s0;
if (!bgc_is_zero_fp64(_TEST_FP64_VERSOR_DATA_LIST[i].x1) && !bgc_are_close_fp64(ratio, _TEST_FP64_VERSOR_DATA_LIST[i].x1 / versor.x1)) {
if (!bgc_is_zero_fp64(_TEST_FP64_VERSOR_DATA_LIST[i].x1) && !bgc_are_close_fp64(ratio, _TEST_FP64_VERSOR_DATA_LIST[i].x1 / versor._x1)) {
print_testing_error("Versor was not normalized proportionally (x1).");
return;
}
if (!bgc_is_zero_fp64(_TEST_FP64_VERSOR_DATA_LIST[i].x2) && !bgc_are_close_fp64(ratio, _TEST_FP64_VERSOR_DATA_LIST[i].x2 / versor.x2)) {
if (!bgc_is_zero_fp64(_TEST_FP64_VERSOR_DATA_LIST[i].x2) && !bgc_are_close_fp64(ratio, _TEST_FP64_VERSOR_DATA_LIST[i].x2 / versor._x2)) {
print_testing_error("Versor was not normalized proportionally (x2).");
return;
}
if (!bgc_is_zero_fp64(_TEST_FP64_VERSOR_DATA_LIST[i].x3) && !bgc_are_close_fp64(ratio, _TEST_FP64_VERSOR_DATA_LIST[i].x3 / versor.x3)) {
if (!bgc_is_zero_fp64(_TEST_FP64_VERSOR_DATA_LIST[i].x3) && !bgc_are_close_fp64(ratio, _TEST_FP64_VERSOR_DATA_LIST[i].x3 / versor._x3)) {
print_testing_error("Versor was not normalized proportionally (x3).");
return;
}

8
basic-geometry-test/tests/versor/versor_swap.c
View file

@ -48,8 +48,8 @@ void test_versor_swap_fp32()
bgc_versor_swap_fp32(&versor1b, &versor2b);
if (versor1a.s0 != versor2b.s0 || versor1a.x1 != versor2b.x1 || versor1a.x2 != versor2b.x2 || versor1a.x3 != versor2b.x3 ||
versor2a.s0 != versor1b.s0 || versor2a.x1 != versor1b.x1 || versor2a.x2 != versor1b.x2 || versor2a.x3 != versor1b.x3) {
if (versor1a._s0 != versor2b._s0 || versor1a._x1 != versor2b._x1 || versor1a._x2 != versor2b._x2 || versor1a._x3 != versor2b._x3 ||
versor2a._s0 != versor1b._s0 || versor2a._x1 != versor1b._x1 || versor2a._x2 != versor1b._x2 || versor2a._x3 != versor1b._x3) {
print_testing_failed();
return;
}
@ -88,8 +88,8 @@ void test_versor_swap_fp64()
bgc_versor_swap_fp64(&versor1b, &versor2b);
if (versor1a.s0 != versor2b.s0 || versor1a.x1 != versor2b.x1 || versor1a.x2 != versor2b.x2 || versor1a.x3 != versor2b.x3 ||
versor2a.s0 != versor1b.s0 || versor2a.x1 != versor1b.x1 || versor2a.x2 != versor1b.x2 || versor2a.x3 != versor1b.x3) {
if (versor1a._s0 != versor2b._s0 || versor1a._x1 != versor2b._x1 || versor1a._x2 != versor2b._x2 || versor1a._x3 != versor2b._x3 ||
versor2a._s0 != versor1b._s0 || versor2a._x1 != versor1b._x1 || versor2a._x2 != versor1b._x2 || versor2a._x3 != versor1b._x3) {
print_testing_failed();
return;
}

1
basic-geometry/basic-geometry.vcxproj
View file

@ -30,6 +30,7 @@
<ClInclude Include="matrixes.h" />
<ClInclude Include="quaternion.h" />
<ClInclude Include="rotation3.h" />
<ClInclude Include="types.h" />
<ClInclude Include="utilities.h" />
<ClInclude Include="slerp.h" />
<ClInclude Include="versor.h" />

3
basic-geometry/basic-geometry.vcxproj.filters
View file

@ -69,6 +69,9 @@
<ClInclude Include="slerp.h">
<Filter>Файлы заголовков</Filter>
</ClInclude>
<ClInclude Include="types.h">
<Filter>Файлы заголовков</Filter>
</ClInclude>
</ItemGroup>
<ItemGroup>
<ClCompile Include="angle.c">

53
basic-geometry/complex.c
View file

@ -27,23 +27,35 @@ extern inline void bgc_complex_swap_fp64(BgcComplexFP64* number1, BgcComplexFP64
extern inline void bgc_complex_convert_fp64_to_fp32(const BgcComplexFP64* source, BgcComplexFP32* destination);
extern inline void bgc_complex_convert_fp32_to_fp64(const BgcComplexFP32* source, BgcComplexFP64* destination);
extern inline void bgc_complex_reverse_fp32(const BgcComplexFP32* number, BgcComplexFP32* reverse);
extern inline void bgc_complex_reverse_fp64(const BgcComplexFP64* number, BgcComplexFP64* reverse);
extern inline void bgc_complex_make_opposite_fp32(BgcComplexFP32* number);
extern inline void bgc_complex_make_opposite_fp64(BgcComplexFP64* number);
extern inline int bgc_complex_normalize_fp32(const BgcComplexFP32* number, BgcComplexFP32* normalized);
extern inline int bgc_complex_normalize_fp64(const BgcComplexFP64* number, BgcComplexFP64* normalized);
extern inline void bgc_complex_get_opposite_fp32(const BgcComplexFP32* number, BgcComplexFP32* opposite);
extern inline void bgc_complex_get_opposite_fp64(const BgcComplexFP64* number, BgcComplexFP64* opposite);
extern inline void bgc_complex_conjugate_fp32(const BgcComplexFP32* number, BgcComplexFP32* conjugate);
extern inline void bgc_complex_conjugate_fp64(const BgcComplexFP64* number, BgcComplexFP64* conjugate);
extern inline int bgc_complex_normalize_fp32(BgcComplexFP32* number);
extern inline int bgc_complex_normalize_fp64(BgcComplexFP64* number);
extern inline int bgc_complex_invert_fp32(const BgcComplexFP32* number, BgcComplexFP32* inverted);
extern inline int bgc_complex_invert_fp64(const BgcComplexFP64* number, BgcComplexFP64* inverted);
extern inline int bgc_complex_get_normalized_fp32(const BgcComplexFP32* number, BgcComplexFP32* normalized);
extern inline int bgc_complex_get_normalized_fp64(const BgcComplexFP64* number, BgcComplexFP64* normalized);
extern inline void bgc_complex_get_product_fp32(const BgcComplexFP32* number1, const BgcComplexFP32* number2, BgcComplexFP32* result);
extern inline void bgc_complex_get_product_fp64(const BgcComplexFP64* number1, const BgcComplexFP64* number2, BgcComplexFP64* result);
extern inline void bgc_complex_conjugate_fp32(BgcComplexFP32* number);
extern inline void bgc_complex_conjugate_fp64(BgcComplexFP64* number);
extern inline int bgc_complex_get_ratio_fp32(const BgcComplexFP32* divident, const BgcComplexFP32* divisor, BgcComplexFP32* quotient);
extern inline int bgc_complex_get_ratio_fp64(const BgcComplexFP64* divident, const BgcComplexFP64* divisor, BgcComplexFP64* quotient);
extern inline void bgc_complex_get_conjugate_fp32(const BgcComplexFP32* number, BgcComplexFP32* conjugate);
extern inline void bgc_complex_get_conjugate_fp64(const BgcComplexFP64* number, BgcComplexFP64* conjugate);
extern inline int bgc_complex_invert_fp32(BgcComplexFP32* number);
extern inline int bgc_complex_invert_fp64(BgcComplexFP64* number);
extern inline int bgc_complex_get_inverse_fp32(const BgcComplexFP32* number, BgcComplexFP32* inverse);
extern inline int bgc_complex_get_inverse_fp64(const BgcComplexFP64* number, BgcComplexFP64* inverse);
extern inline void bgc_complex_multiply_fp32(const BgcComplexFP32* number1, const BgcComplexFP32* number2, BgcComplexFP32* result);
extern inline void bgc_complex_multiply_fp64(const BgcComplexFP64* number1, const BgcComplexFP64* number2, BgcComplexFP64* result);
extern inline int bgc_complex_devide_fp32(const BgcComplexFP32* divident, const BgcComplexFP32* divisor, BgcComplexFP32* quotient);
extern inline int bgc_complex_devide_fp64(const BgcComplexFP64* divident, const BgcComplexFP64* divisor, BgcComplexFP64* quotient);
extern inline void bgc_complex_add_fp32(const BgcComplexFP32* number1, const BgcComplexFP32* number2, BgcComplexFP32* sum);
extern inline void bgc_complex_add_fp64(const BgcComplexFP64* number1, const BgcComplexFP64* number2, BgcComplexFP64* sum);
@ -54,13 +66,10 @@ extern inline void bgc_complex_add_scaled_fp64(const BgcComplexFP64* basic_numbe
extern inline void bgc_complex_subtract_fp32(const BgcComplexFP32* minuend, const BgcComplexFP32* subtrahend, BgcComplexFP32* difference);
extern inline void bgc_complex_subtract_fp64(const BgcComplexFP64* minuend, const BgcComplexFP64* subtrahend, BgcComplexFP64* difference);
extern inline void bgc_complex_subtract_scaled_fp32(const BgcComplexFP32* basic_number, const BgcComplexFP32* scalable_number, const float scale, BgcComplexFP32* difference);
extern inline void bgc_complex_subtract_scaled_fp64(const BgcComplexFP64* basic_number, const BgcComplexFP64* scalable_number, const double scale, BgcComplexFP64* difference);
extern inline void bgc_complex_multiply_fp32(const BgcComplexFP32* multiplicand, const float multiplier, BgcComplexFP32* product);
extern inline void bgc_complex_multiply_by_number_fp32(const BgcComplexFP32* multiplicand, const float multiplier, BgcComplexFP32* product);
extern inline void bgc_complex_multiply_fp64(const BgcComplexFP64* multiplicand, const double multiplier, BgcComplexFP64* product);
extern inline void bgc_complex_divide_fp32(const BgcComplexFP32* dividend, const float divisor, BgcComplexFP32* quotient);
extern inline void bgc_complex_divide_by_number_fp32(const BgcComplexFP32* dividend, const float divisor, BgcComplexFP32* quotient);
extern inline void bgc_complex_divide_fp64(const BgcComplexFP64* dividend, const double divisor, BgcComplexFP64* quotient);
extern inline void bgc_complex_get_mean_of_two_fp32(const BgcComplexFP32* number1, const BgcComplexFP32* number2, BgcComplexFP32* mean);
@ -69,14 +78,8 @@ extern inline void bgc_complex_get_mean_of_two_fp64(const BgcComplexFP64* number
extern inline void bgc_complex_get_mean_of_three_fp32(const BgcComplexFP32* number1, const BgcComplexFP32* number2, const BgcComplexFP32* number3, BgcComplexFP32* mean);
extern inline void bgc_complex_get_mean_of_three_fp64(const BgcComplexFP64* number1, const BgcComplexFP64* number2, const BgcComplexFP64* number3, BgcComplexFP64* mean);
extern inline void bgc_complex_interpolate_linearly_fp32(const BgcComplexFP32* number1, const BgcComplexFP32* number2, const float phase, BgcComplexFP32* interpolation);
extern inline void bgc_complex_interpolate_linearly_fp64(const BgcComplexFP64* number1, const BgcComplexFP64* number2, const double phase, BgcComplexFP64* interpolation);
extern inline void bgc_complex_minimize_fp32(const BgcComplexFP32* number, BgcComplexFP32* minimal);
extern inline void bgc_complex_minimize_fp64(const BgcComplexFP64* number, BgcComplexFP64* minimal);
extern inline void bgc_complex_maximize_fp32(const BgcComplexFP32* number, BgcComplexFP32* maximal);
extern inline void bgc_complex_maximize_fp64(const BgcComplexFP64* number, BgcComplexFP64* maximal);
extern inline void bgc_complex_interpolate_fp32(const BgcComplexFP32* number1, const BgcComplexFP32* number2, const float phase, BgcComplexFP32* interpolation);
extern inline void bgc_complex_interpolate_fp64(const BgcComplexFP64* number1, const BgcComplexFP64* number2, const double phase, BgcComplexFP64* interpolation);
extern inline int bgc_complex_are_close_fp32(const BgcComplexFP32* number1, const BgcComplexFP32* number2);
extern inline int bgc_complex_are_close_fp64(const BgcComplexFP64* number1, const BgcComplexFP64* number2);

298
basic-geometry/complex.h
View file

@ -142,23 +142,75 @@ inline void bgc_complex_convert_fp32_to_fp64(const BgcComplexFP32* source, BgcCo
destination->imaginary = source->imaginary;
}
// ================== Reverse =================== //
// ================== Negative ================== //
inline void bgc_complex_reverse_fp32(const BgcComplexFP32* number, BgcComplexFP32* reverse)
inline void bgc_complex_make_opposite_fp32(BgcComplexFP32* number)
{
reverse->real = -number->real;
reverse->imaginary = -number->imaginary;
number->real = -number->real;
number->imaginary = -number->imaginary;
}
inline void bgc_complex_reverse_fp64(const BgcComplexFP64* number, BgcComplexFP64* reverse)
inline void bgc_complex_make_opposite_fp64(BgcComplexFP64* number)
{
reverse->real = -number->real;
reverse->imaginary = -number->imaginary;
number->real = -number->real;
number->imaginary = -number->imaginary;
}
inline void bgc_complex_get_opposite_fp32(const BgcComplexFP32* number, BgcComplexFP32* opposite)
{
opposite->real = -number->real;
opposite->imaginary = -number->imaginary;
}
inline void bgc_complex_get_opposite_fp64(const BgcComplexFP64* number, BgcComplexFP64* opposite)
{
opposite->real = -number->real;
opposite->imaginary = -number->imaginary;
}
// ================= Normalize ================== //
inline int bgc_complex_normalize_fp32(const BgcComplexFP32* number, BgcComplexFP32* normalized)
inline int bgc_complex_normalize_fp32(BgcComplexFP32* number)
{
const float square_modulus = bgc_complex_get_square_modulus_fp32(number);
if (bgc_is_sqare_unit_fp32(square_modulus)) {
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
return 0;
}
const float multiplicand = sqrtf(1.0f / square_modulus);
number->real *= multiplicand;
number->imaginary *= multiplicand;
return 1;
}
inline int bgc_complex_normalize_fp64(BgcComplexFP64* number)
{
const double square_modulus = bgc_complex_get_square_modulus_fp64(number);
if (bgc_is_sqare_unit_fp64(square_modulus)) {
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
return 0;
}
const double multiplicand = sqrt(1.0 / square_modulus);
number->real *= multiplicand;
number->imaginary *= multiplicand;
return 1;
}
inline int bgc_complex_get_normalized_fp32(const BgcComplexFP32* number, BgcComplexFP32* normalized)
{
const float square_modulus = bgc_complex_get_square_modulus_fp32(number);
@ -169,6 +221,8 @@ inline int bgc_complex_normalize_fp32(const BgcComplexFP32* number, BgcComplexFP
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
normalized->real = 0.0f;
normalized->imaginary = 0.0f;
return 0;
}
@ -180,7 +234,7 @@ inline int bgc_complex_normalize_fp32(const BgcComplexFP32* number, BgcComplexFP
return 1;
}
inline int bgc_complex_normalize_fp64(const BgcComplexFP64* number, BgcComplexFP64* normalized)
inline int bgc_complex_get_normalized_fp64(const BgcComplexFP64* number, BgcComplexFP64* normalized)
{
const double square_modulus = bgc_complex_get_square_modulus_fp64(number);
@ -191,6 +245,8 @@ inline int bgc_complex_normalize_fp64(const BgcComplexFP64* number, BgcComplexFP
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
normalized->real = 0.0;
normalized->imaginary = 0.0;
return 0;
}
@ -204,13 +260,23 @@ inline int bgc_complex_normalize_fp64(const BgcComplexFP64* number, BgcComplexFP
// ================= Conjugate ================== //
inline void bgc_complex_conjugate_fp32(const BgcComplexFP32* number, BgcComplexFP32* conjugate)
inline void bgc_complex_conjugate_fp32(BgcComplexFP32* number)
{
number->imaginary = -number->imaginary;
}
inline void bgc_complex_conjugate_fp64(BgcComplexFP64* number)
{
number->imaginary = -number->imaginary;
}
inline void bgc_complex_get_conjugate_fp32(const BgcComplexFP32* number, BgcComplexFP32* conjugate)
{
conjugate->real = number->real;
conjugate->imaginary = -number->imaginary;
}
inline void bgc_complex_conjugate_fp64(const BgcComplexFP64* number, BgcComplexFP64* conjugate)
inline void bgc_complex_get_conjugate_fp64(const BgcComplexFP64* number, BgcComplexFP64* conjugate)
{
conjugate->real = number->real;
conjugate->imaginary = -number->imaginary;
@ -218,7 +284,7 @@ inline void bgc_complex_conjugate_fp64(const BgcComplexFP64* number, BgcComplexF
// =================== Invert =================== //
inline int bgc_complex_invert_fp32(const BgcComplexFP32* number, BgcComplexFP32* inverted)
inline int bgc_complex_get_inverse_fp32(const BgcComplexFP32* number, BgcComplexFP32* inverse)
{
const float square_modulus = bgc_complex_get_square_modulus_fp32(number);
@ -228,13 +294,13 @@ inline int bgc_complex_invert_fp32(const BgcComplexFP32* number, BgcComplexFP32*
const float multiplicand = 1.0f / square_modulus;
inverted->real = number->real * multiplicand;
inverted->imaginary = -number->imaginary * multiplicand;
inverse->real = number->real * multiplicand;
inverse->imaginary = -number->imaginary * multiplicand;
return 1;
}
inline int bgc_complex_invert_fp64(const BgcComplexFP64* number, BgcComplexFP64* inverted)
inline int bgc_complex_get_inverse_fp64(const BgcComplexFP64* number, BgcComplexFP64* inverse)
{
const double square_modulus = bgc_complex_get_square_modulus_fp64(number);
@ -244,70 +310,20 @@ inline int bgc_complex_invert_fp64(const BgcComplexFP64* number, BgcComplexFP64*
const double multiplicand = 1.0 / square_modulus;
inverted->real = number->real * multiplicand;
inverted->imaginary = -number->imaginary * multiplicand;
inverse->real = number->real * multiplicand;
inverse->imaginary = -number->imaginary * multiplicand;
return 1;
}
// ================ Get Product ================= //
inline void bgc_complex_get_product_fp32(const BgcComplexFP32* number1, const BgcComplexFP32* number2, BgcComplexFP32* result)
inline int bgc_complex_invert_fp32(BgcComplexFP32* number)
{
const float real = number1->real * number2->real - number1->imaginary * number2->imaginary;
const float imaginary = number1->real * number2->imaginary + number1->imaginary * number2->real;
result->real = real;
result->imaginary = imaginary;
return bgc_complex_get_inverse_fp32(number, number);
}
inline void bgc_complex_get_product_fp64(const BgcComplexFP64* number1, const BgcComplexFP64* number2, BgcComplexFP64* result)
inline int bgc_complex_invert_fp64(BgcComplexFP64* number)
{
const double real = number1->real * number2->real - number1->imaginary * number2->imaginary;
const double imaginary = number1->real * number2->imaginary + number1->imaginary * number2->real;
result->real = real;
result->imaginary = imaginary;
}
// ================= Get Ratio ================== //
inline int bgc_complex_get_ratio_fp32(const BgcComplexFP32* divident, const BgcComplexFP32* divisor, BgcComplexFP32* quotient)
{
const float square_modulus = bgc_complex_get_square_modulus_fp32(divisor);
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
return 0;
}
const float real = divident->real * divisor->real + divident->imaginary * divisor->imaginary;
const float imaginary = divident->imaginary * divisor->real - divident->real * divisor->imaginary;
const float multiplier = 1.0f / square_modulus;
quotient->real = real * multiplier;
quotient->imaginary = imaginary * multiplier;
return 1;
}
inline int bgc_complex_get_ratio_fp64(const BgcComplexFP64* divident, const BgcComplexFP64* divisor, BgcComplexFP64* quotient)
{
const double square_modulus = bgc_complex_get_square_modulus_fp64(divisor);
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64) {
return 0;
}
const double real = divident->real * divisor->real + divident->imaginary * divisor->imaginary;
const double imaginary = divident->imaginary * divisor->real - divident->real * divisor->imaginary;
const double multiplier = 1.0 / square_modulus;
quotient->real = real * multiplier;
quotient->imaginary = imaginary * multiplier;
return 1;
return bgc_complex_get_inverse_fp64(number, number);
}
// =============== Get Exponation =============== //
@ -358,29 +374,35 @@ inline void bgc_complex_subtract_fp64(const BgcComplexFP64* minuend, const BgcCo
difference->imaginary = minuend->imaginary - subtrahend->imaginary;
}
// ============== Subtract scaled =============== //
inline void bgc_complex_subtract_scaled_fp32(const BgcComplexFP32* basic_number, const BgcComplexFP32* scalable_number, const float scale, BgcComplexFP32* difference)
{
difference->real = basic_number->real - scalable_number->real * scale;
difference->imaginary = basic_number->imaginary - scalable_number->imaginary * scale;
}
inline void bgc_complex_subtract_scaled_fp64(const BgcComplexFP64* basic_number, const BgcComplexFP64* scalable_number, const double scale, BgcComplexFP64* difference)
{
difference->real = basic_number->real - scalable_number->real * scale;
difference->imaginary = basic_number->imaginary - scalable_number->imaginary * scale;
}
// ================== Multiply ================== //
inline void bgc_complex_multiply_fp32(const BgcComplexFP32* multiplicand, const float multiplier, BgcComplexFP32* product)
inline void bgc_complex_multiply_fp32(const BgcComplexFP32* number1, const BgcComplexFP32* number2, BgcComplexFP32* product)
{
const float real = number1->real * number2->real - number1->imaginary * number2->imaginary;
const float imaginary = number1->real * number2->imaginary + number1->imaginary * number2->real;
product->real = real;
product->imaginary = imaginary;
}
inline void bgc_complex_multiply_fp64(const BgcComplexFP64* number1, const BgcComplexFP64* number2, BgcComplexFP64* product)
{
const double real = number1->real * number2->real - number1->imaginary * number2->imaginary;
const double imaginary = number1->real * number2->imaginary + number1->imaginary * number2->real;
product->real = real;
product->imaginary = imaginary;
}
// ============= Multiply By Number ============= //
inline void bgc_complex_multiply_by_number_fp32(const BgcComplexFP32* multiplicand, const float multiplier, BgcComplexFP32* product)
{
product->real = multiplicand->real * multiplier;
product->imaginary = multiplicand->imaginary * multiplier;
}
inline void bgc_complex_multiply_fp64(const BgcComplexFP64* multiplicand, const double multiplier, BgcComplexFP64* product)
inline void bgc_complex_multiply_by_number_fp64(const BgcComplexFP64* multiplicand, const double multiplier, BgcComplexFP64* product)
{
product->real = multiplicand->real * multiplier;
product->imaginary = multiplicand->imaginary * multiplier;
@ -388,14 +410,54 @@ inline void bgc_complex_multiply_fp64(const BgcComplexFP64* multiplicand, const
// =================== Divide =================== //
inline void bgc_complex_divide_fp32(const BgcComplexFP32* dividend, const float divisor, BgcComplexFP32* quotient)
inline int bgc_complex_devide_fp32(const BgcComplexFP32* divident, const BgcComplexFP32* divisor, BgcComplexFP32* quotient)
{
bgc_complex_multiply_fp32(dividend, 1.0f / divisor, quotient);
const float square_modulus = bgc_complex_get_square_modulus_fp32(divisor);
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
return 0;
}
const float real = divident->real * divisor->real + divident->imaginary * divisor->imaginary;
const float imaginary = divident->imaginary * divisor->real - divident->real * divisor->imaginary;
const float multiplier = 1.0f / square_modulus;
quotient->real = real * multiplier;
quotient->imaginary = imaginary * multiplier;
return 1;
}
inline void bgc_complex_divide_fp64(const BgcComplexFP64* dividend, const double divisor, BgcComplexFP64* quotient)
inline int bgc_complex_devide_fp64(const BgcComplexFP64* divident, const BgcComplexFP64* divisor, BgcComplexFP64* quotient)
{
bgc_complex_multiply_fp64(dividend, 1.0 / divisor, quotient);
const double square_modulus = bgc_complex_get_square_modulus_fp64(divisor);
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64) {
return 0;
}
const double real = divident->real * divisor->real + divident->imaginary * divisor->imaginary;
const double imaginary = divident->imaginary * divisor->real - divident->real * divisor->imaginary;
const double multiplier = 1.0 / square_modulus;
quotient->real = real * multiplier;
quotient->imaginary = imaginary * multiplier;
return 1;
}
// ============== Divide By Number ============== //
inline void bgc_complex_divide_by_number_fp32(const BgcComplexFP32* dividend, const float divisor, BgcComplexFP32* quotient)
{
bgc_complex_multiply_by_number_fp32(dividend, 1.0f / divisor, quotient);
}
inline void bgc_complex_divide_by_number_fp64(const BgcComplexFP64* dividend, const double divisor, BgcComplexFP64* quotient)
{
bgc_complex_multiply_by_number_fp64(dividend, 1.0 / divisor, quotient);
}
// ================== Average2 ================== //
@ -428,7 +490,7 @@ inline void bgc_complex_get_mean_of_three_fp64(const BgcComplexFP64* number1, co
// =================== Linear =================== //
inline void bgc_complex_interpolate_linearly_fp32(const BgcComplexFP32* number1, const BgcComplexFP32* number2, const float phase, BgcComplexFP32* interpolation)
inline void bgc_complex_interpolate_fp32(const BgcComplexFP32* number1, const BgcComplexFP32* number2, const float phase, BgcComplexFP32* interpolation)
{
const float counterphase = 1.0f - phase;
@ -436,7 +498,7 @@ inline void bgc_complex_interpolate_linearly_fp32(const BgcComplexFP32* number1,
interpolation->imaginary = number1->imaginary * counterphase + number2->imaginary * phase;
}
inline void bgc_complex_interpolate_linearly_fp64(const BgcComplexFP64* number1, const BgcComplexFP64* number2, const double phase, BgcComplexFP64* interpolation)
inline void bgc_complex_interpolate_fp64(const BgcComplexFP64* number1, const BgcComplexFP64* number2, const double phase, BgcComplexFP64* interpolation)
{
const double counterphase = 1.0 - phase;
@ -444,54 +506,6 @@ inline void bgc_complex_interpolate_linearly_fp64(const BgcComplexFP64* number1,
interpolation->imaginary = number1->imaginary * counterphase + number2->imaginary * phase;
}
// ================== Minimal =================== //
inline void bgc_complex_minimize_fp32(const BgcComplexFP32* number, BgcComplexFP32* minimal)
{
if (number->real < minimal->real) {
minimal->real = number->real;
}
if (number->imaginary < minimal->imaginary) {
minimal->imaginary = number->imaginary;
}
}
inline void bgc_complex_minimize_fp64(const BgcComplexFP64* number, BgcComplexFP64* minimal)
{
if (number->real < minimal->real) {
minimal->real = number->real;
}
if (number->imaginary < minimal->imaginary) {
minimal->imaginary = number->imaginary;
}
}
// ================== Maximal =================== //
inline void bgc_complex_maximize_fp32(const BgcComplexFP32* number, BgcComplexFP32* maximal)
{
if (number->real > maximal->real) {
maximal->real = number->real;
}
if (number->imaginary > maximal->imaginary) {
maximal->imaginary = number->imaginary;
}
}
inline void bgc_complex_maximize_fp64(const BgcComplexFP64* number, BgcComplexFP64* maximal)
{
if (number->real > maximal->real) {
maximal->real = number->real;
}
if (number->imaginary > maximal->imaginary) {
maximal->imaginary = number->imaginary;
}
}
// ================== Are Close ================= //
inline int bgc_complex_are_close_fp32(const BgcComplexFP32* number1, const BgcComplexFP32* number2)
@ -525,7 +539,7 @@ inline int bgc_complex_are_close_fp64(const BgcComplexFP64* number1, const BgcCo
return square_distance <= BGC_SQUARE_EPSYLON_FP64;
}
return square_distance <= BGC_SQUARE_EPSYLON_FP32 * square_modulus1 && square_distance <= BGC_SQUARE_EPSYLON_FP32 * square_modulus2;
return square_distance <= BGC_SQUARE_EPSYLON_FP64 * square_modulus1 && square_distance <= BGC_SQUARE_EPSYLON_FP64 * square_modulus2;
}
#endif

33
basic-geometry/cotes-number.c
View file

@ -25,8 +25,17 @@ extern inline void bgc_cotes_number_swap_fp64(BgcCotesNumberFP64* number1, BgcCo
extern inline void bgc_cotes_number_convert_fp64_to_fp32(const BgcCotesNumberFP64* source, BgcCotesNumberFP32* destination);
extern inline void bgc_cotes_number_convert_fp32_to_fp64(const BgcCotesNumberFP32* source, BgcCotesNumberFP64* destination);
extern inline void bgc_cotes_number_invert_fp32(const BgcCotesNumberFP32* number, BgcCotesNumberFP32* inverted);
extern inline void bgc_cotes_number_invert_fp64(const BgcCotesNumberFP64* number, BgcCotesNumberFP64* inverted);
extern inline void bgc_cotes_number_make_opposite_fp32(BgcCotesNumberFP32* number);
extern inline void bgc_cotes_number_make_opposite_fp64(BgcCotesNumberFP64* number);
extern inline void bgc_cotes_number_get_opposite_fp32(const BgcCotesNumberFP32* number, BgcCotesNumberFP32* opposite);
extern inline void bgc_cotes_number_get_opposite_fp64(const BgcCotesNumberFP64* number, BgcCotesNumberFP64* opposite);
extern inline void bgc_cotes_number_invert_fp32(BgcCotesNumberFP32* number);
extern inline void bgc_cotes_number_invert_fp64(BgcCotesNumberFP64* number);
extern inline void bgc_cotes_number_get_inverse_fp32(const BgcCotesNumberFP32* number, BgcCotesNumberFP32* inverse);
extern inline void bgc_cotes_number_get_inverse_fp64(const BgcCotesNumberFP64* number, BgcCotesNumberFP64* inverse);
extern inline void bgc_cotes_number_get_exponation_fp32(const BgcCotesNumberFP32* base, const float exponent, BgcCotesNumberFP32* power);
extern inline void bgc_cotes_number_get_exponation_fp64(const BgcCotesNumberFP64* base, const double exponent, BgcCotesNumberFP64* power);
@ -52,34 +61,34 @@ extern inline void bgc_cotes_number_turn_vector_back_fp64(const BgcCotesNumberFP
extern inline int bgc_cotes_number_are_close_fp32(const BgcCotesNumberFP32* number1, const BgcCotesNumberFP32* number2);
extern inline int bgc_cotes_number_are_close_fp64(const BgcCotesNumberFP64* number1, const BgcCotesNumberFP64* number2);
void _bgc_cotes_number_normalize_fp32(const float square_modulus, _BgcTwinCotesNumberFP32* twin)
void _bgc_cotes_number_normalize_fp32(const float square_modulus, BgcCotesNumberFP32* number)
{
// (square_modulus != square_modulus) is true when square_modulus is NaN
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
twin->cos = 1.0f;
twin->sin = 0.0f;
number->_cos = 1.0f;
number->_sin = 0.0f;
return;
}
const float multiplier = sqrtf(1.0f / square_modulus);
twin->cos *= multiplier;
twin->sin *= multiplier;
number->_cos *= multiplier;
number->_sin *= multiplier;
}
void _bgc_cotes_number_normalize_fp64(const double square_modulus, _BgcTwinCotesNumberFP64* twin)
void _bgc_cotes_number_normalize_fp64(const double square_modulus, BgcCotesNumberFP64* number)
{
// (square_modulus != square_modulus) is true when square_modulus is NaN
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
twin->cos = 1.0;
twin->sin = 0.0;
number->_cos = 1.0;
number->_sin = 0.0;
return;
}
const double multiplier = sqrt(1.0 / square_modulus);
twin->cos *= multiplier;
twin->sin *= multiplier;
number->_cos *= multiplier;
number->_sin *= multiplier;
}

280
basic-geometry/cotes-number.h
View file

@ -12,24 +12,14 @@
typedef struct
{
const float cos, sin;
float _cos, _sin;
} BgcCotesNumberFP32;
typedef struct
{
const double cos, sin;
double _cos, _sin;
} BgcCotesNumberFP64;
// ================= Dark Twins ================= //
typedef struct {
float cos, sin;
} _BgcTwinCotesNumberFP32;
typedef struct {
double cos, sin;
} _BgcTwinCotesNumberFP64;
// ================= Constants ================== //
extern const BgcCotesNumberFP32 BGC_IDLE_COTES_NUMBER_FP32;
@ -39,37 +29,31 @@ extern const BgcCotesNumberFP64 BGC_IDLE_COTES_NUMBER_FP64;
inline void bgc_cotes_number_reset_fp32(BgcCotesNumberFP32* number)
{
_BgcTwinCotesNumberFP32* twin = (_BgcTwinCotesNumberFP32*)number;
twin->cos = 1.0f;
twin->sin = 0.0f;
number->_cos = 1.0f;
number->_sin = 0.0f;
}
inline void bgc_cotes_number_reset_fp64(BgcCotesNumberFP64* number)
{
_BgcTwinCotesNumberFP64* twin = (_BgcTwinCotesNumberFP64*)number;
twin->cos = 1.0;
twin->sin = 0.0;
number->_cos = 1.0;
number->_sin = 0.0;
}
// ==================== Set ===================== //
void _bgc_cotes_number_normalize_fp32(const float square_modulus, _BgcTwinCotesNumberFP32* twin);
void _bgc_cotes_number_normalize_fp32(const float square_modulus, BgcCotesNumberFP32* twin);
void _bgc_cotes_number_normalize_fp64(const double square_modulus, _BgcTwinCotesNumberFP64* twin);
void _bgc_cotes_number_normalize_fp64(const double square_modulus, BgcCotesNumberFP64* twin);
inline void bgc_cotes_number_set_values_fp32(const float x1, const float x2, BgcCotesNumberFP32* number)
{
const float square_modulus = x1 * x1 + x2 * x2;
_BgcTwinCotesNumberFP32* twin = (_BgcTwinCotesNumberFP32*)number;
twin->cos = x1;
twin->sin = x2;
number->_cos = x1;
number->_sin = x2;
if (!bgc_is_sqare_unit_fp32(square_modulus)) {
_bgc_cotes_number_normalize_fp32(square_modulus, twin);
_bgc_cotes_number_normalize_fp32(square_modulus, number);
}
}
@ -77,13 +61,11 @@ inline void bgc_cotes_number_set_values_fp64(const double x1, const double x2, B
{
const double square_modulus = x1 * x1 + x2 * x2;
_BgcTwinCotesNumberFP64* twin = (_BgcTwinCotesNumberFP64*)number;
twin->cos = x1;
twin->sin = x2;
number->_cos = x1;
number->_sin = x2;
if (!bgc_is_sqare_unit_fp64(square_modulus)) {
_bgc_cotes_number_normalize_fp64(square_modulus, twin);
_bgc_cotes_number_normalize_fp64(square_modulus, number);
}
}
@ -93,168 +75,148 @@ inline void bgc_cotes_number_set_turn_fp32(const float angle, const BgcAngleUnit
{
const float radians = bgc_angle_to_radians_fp32(angle, unit);
_BgcTwinCotesNumberFP32* twin = (_BgcTwinCotesNumberFP32*)number;
twin->cos = cosf(radians);
twin->sin = sinf(radians);
number->_cos = cosf(radians);
number->_sin = sinf(radians);
}
inline void bgc_cotes_number_set_turn_fp64(const double angle, const BgcAngleUnitEnum unit, BgcCotesNumberFP64* number)
{
const double radians = bgc_angle_to_radians_fp64(angle, unit);
_BgcTwinCotesNumberFP64* twin = (_BgcTwinCotesNumberFP64*)number;
twin->cos = cos(radians);
twin->sin = sin(radians);
number->_cos = cos(radians);
number->_sin = sin(radians);
}
// =================== Angle =================== //
inline float bgc_cotes_number_get_angle_fp32(const BgcCotesNumberFP32* number, const BgcAngleUnitEnum unit)
{
if (number->cos >= 1.0f - BGC_EPSYLON_FP32) {
return 0.0f;
}
if (number->cos <= -1.0f + BGC_EPSYLON_FP32) {
return bgc_angle_get_half_circle_fp32(unit);
}
if (number->sin >= 1.0f - BGC_EPSYLON_FP32) {
return bgc_angle_get_quater_circle_fp32(unit);
}
if (number->sin <= -1.0f + BGC_EPSYLON_FP32) {
return 0.75f * bgc_angle_get_full_circle_fp32(unit);
}
return bgc_radians_to_units_fp32(atan2f(number->sin, number->cos), unit);
return bgc_radians_to_units_fp32(atan2f(number->_sin, number->_cos), unit);
}
inline double bgc_cotes_number_get_angle_fp64(const BgcCotesNumberFP64* number, const BgcAngleUnitEnum unit)
{
if (number->cos >= 1.0 - BGC_EPSYLON_FP64) {
return 0.0;
}
if (number->cos <= -1.0 + BGC_EPSYLON_FP64) {
return bgc_angle_get_half_circle_fp64(unit);
}
if (number->sin >= 1.0 - BGC_EPSYLON_FP64) {
return bgc_angle_get_quater_circle_fp64(unit);
}
if (number->sin <= -1.0 + BGC_EPSYLON_FP64) {
return 0.75 * bgc_angle_get_full_circle_fp64(unit);
}
return bgc_radians_to_units_fp64(atan2(number->sin, number->cos), unit);
return bgc_radians_to_units_fp64(atan2(number->_sin, number->_cos), unit);
}
// ==================== Copy ==================== //
inline void bgc_cotes_number_copy_fp32(const BgcCotesNumberFP32* source, BgcCotesNumberFP32* destination)
{
_BgcTwinCotesNumberFP32* twin = (_BgcTwinCotesNumberFP32*)destination;
twin->cos = source->cos;
twin->sin = source->sin;
destination->_cos = source->_cos;
destination->_sin = source->_sin;
}
inline void bgc_cotes_number_copy_fp64(const BgcCotesNumberFP64* source, BgcCotesNumberFP64* destination)
{
_BgcTwinCotesNumberFP64* twin = (_BgcTwinCotesNumberFP64*)destination;
twin->cos = source->cos;
twin->sin = source->sin;
destination->_cos = source->_cos;
destination->_sin = source->_sin;
}
// ==================== Swap ==================== //
inline void bgc_cotes_number_swap_fp32(BgcCotesNumberFP32* number1, BgcCotesNumberFP32* number2)
{
const float cos = number1->cos;
const float sin = number1->sin;
const float cos = number1->_cos;
const float sin = number1->_sin;
_BgcTwinCotesNumberFP32* twin1 = (_BgcTwinCotesNumberFP32*)number1;
number1->_cos = number2->_cos;
number1->_sin = number2->_sin;
twin1->cos = number2->cos;
twin1->sin = number2->sin;
_BgcTwinCotesNumberFP32* twin2 = (_BgcTwinCotesNumberFP32*)number2;
twin2->cos = cos;
twin2->sin = sin;
number2->_cos = cos;
number2->_sin = sin;
}
inline void bgc_cotes_number_swap_fp64(BgcCotesNumberFP64* number1, BgcCotesNumberFP64* number2)
{
const double cos = number1->cos;
const double sin = number1->sin;
const double cos = number1->_cos;
const double sin = number1->_sin;
_BgcTwinCotesNumberFP64* twin1 = (_BgcTwinCotesNumberFP64*)number1;
number1->_cos = number2->_cos;
number1->_sin = number2->_sin;
twin1->cos = number2->cos;
twin1->sin = number2->sin;
_BgcTwinCotesNumberFP64* twin2 = (_BgcTwinCotesNumberFP64*)number2;
twin2->cos = cos;
twin2->sin = sin;
number2->_cos = cos;
number2->_sin = sin;
}
// ================== Convert =================== //
inline void bgc_cotes_number_convert_fp64_to_fp32(const BgcCotesNumberFP64* source, BgcCotesNumberFP32* destination)
{
bgc_cotes_number_set_values_fp32((float)source->cos, (float)source->sin, destination);
bgc_cotes_number_set_values_fp32((float)source->_cos, (float)source->_sin, destination);
}
inline void bgc_cotes_number_convert_fp32_to_fp64(const BgcCotesNumberFP32* source, BgcCotesNumberFP64* destination)
{
bgc_cotes_number_set_values_fp64((double)source->cos, (double)source->sin, destination);
bgc_cotes_number_set_values_fp64((double)source->_cos, (double)source->_sin, destination);
}
// ================== Negative ================== //
inline void bgc_cotes_number_make_opposite_fp32(BgcCotesNumberFP32* number)
{
number->_cos = -number->_cos;
number->_sin = -number->_sin;
}
inline void bgc_cotes_number_make_opposite_fp64(BgcCotesNumberFP64* number)
{
number->_cos = -number->_cos;
number->_sin = -number->_sin;
}
inline void bgc_cotes_number_get_opposite_fp32(const BgcCotesNumberFP32* number, BgcCotesNumberFP32* opposite)
{
opposite->_cos = -number->_cos;
opposite->_sin = -number->_sin;
}
inline void bgc_cotes_number_get_opposite_fp64(const BgcCotesNumberFP64* number, BgcCotesNumberFP64* opposite)
{
opposite->_cos = -number->_cos;
opposite->_sin = -number->_sin;
}
// =================== Invert =================== //
inline void bgc_cotes_number_invert_fp32(const BgcCotesNumberFP32* number, BgcCotesNumberFP32* inverted)
inline void bgc_cotes_number_invert_fp32(BgcCotesNumberFP32* number)
{
_BgcTwinCotesNumberFP32* twin = (_BgcTwinCotesNumberFP32*)inverted;
twin->cos = number->cos;
twin->sin = -number->sin;
number->_sin = -number->_sin;
}
inline void bgc_cotes_number_invert_fp64(const BgcCotesNumberFP64* number, BgcCotesNumberFP64* inverted)
inline void bgc_cotes_number_invert_fp64(BgcCotesNumberFP64* number)
{
_BgcTwinCotesNumberFP64* twin = (_BgcTwinCotesNumberFP64*)inverted;
number->_sin = -number->_sin;
}
twin->cos = number->cos;
twin->sin = -number->sin;
inline void bgc_cotes_number_get_inverse_fp32(const BgcCotesNumberFP32* number, BgcCotesNumberFP32* inverse)
{
inverse->_cos = number->_cos;
inverse->_sin = -number->_sin;
}
inline void bgc_cotes_number_get_inverse_fp64(const BgcCotesNumberFP64* number, BgcCotesNumberFP64* inverse)
{
inverse->_cos = number->_cos;
inverse->_sin = -number->_sin;
}
// ================= Exponation ================= //
inline void bgc_cotes_number_get_exponation_fp32(const BgcCotesNumberFP32* base, const float exponent, BgcCotesNumberFP32* power)
{
const float power_angle = exponent * atan2f(base->sin, base->cos);
const float power_angle = exponent * atan2f(base->_sin, base->_cos);
_BgcTwinCotesNumberFP32* twin = (_BgcTwinCotesNumberFP32*)power;
twin->cos = cosf(power_angle);
twin->sin = sinf(power_angle);
power->_cos = cosf(power_angle);
power->_sin = sinf(power_angle);
}
inline void bgc_cotes_number_get_exponation_fp64(const BgcCotesNumberFP64* base, const double exponent, BgcCotesNumberFP64* power)
{
const double power_angle = exponent * atan2(base->sin, base->cos);
const double power_angle = exponent * atan2(base->_sin, base->_cos);
_BgcTwinCotesNumberFP64* twin = (_BgcTwinCotesNumberFP64*)power;
twin->cos = cos(power_angle);
twin->sin = sin(power_angle);
power->_cos = cos(power_angle);
power->_sin = sin(power_angle);
}
// ================ Combination ================= //
@ -262,8 +224,8 @@ inline void bgc_cotes_number_get_exponation_fp64(const BgcCotesNumberFP64* base,
inline void bgc_cotes_number_combine_fp32(const BgcCotesNumberFP32* number1, const BgcCotesNumberFP32* number2, BgcCotesNumberFP32* result)
{
bgc_cotes_number_set_values_fp32(
number1->cos * number2->cos - number1->sin * number2->sin,
number1->cos * number2->sin + number1->sin * number2->cos,
number1->_cos * number2->_cos - number1->_sin * number2->_sin,
number1->_cos * number2->_sin + number1->_sin * number2->_cos,
result
);
}
@ -271,8 +233,8 @@ inline void bgc_cotes_number_combine_fp32(const BgcCotesNumberFP32* number1, con
inline void bgc_cotes_number_combine_fp64(const BgcCotesNumberFP64* number1, const BgcCotesNumberFP64* number2, BgcCotesNumberFP64* result)
{
bgc_cotes_number_set_values_fp64(
number1->cos * number2->cos - number1->sin * number2->sin,
number1->cos * number2->sin + number1->sin * number2->cos,
number1->_cos * number2->_cos - number1->_sin * number2->_sin,
number1->_cos * number2->_sin + number1->_sin * number2->_cos,
result
);
}
@ -282,8 +244,8 @@ inline void bgc_cotes_number_combine_fp64(const BgcCotesNumberFP64* number1, con
inline void bgc_cotes_number_exclude_fp32(const BgcCotesNumberFP32* base, const BgcCotesNumberFP32* excludant, BgcCotesNumberFP32* difference)
{
bgc_cotes_number_set_values_fp32(
base->cos * excludant->cos + base->sin * excludant->sin,
base->sin * excludant->cos - base->cos * excludant->sin,
base->_cos * excludant->_cos + base->_sin * excludant->_sin,
base->_sin * excludant->_cos - base->_cos * excludant->_sin,
difference
);
}
@ -291,8 +253,8 @@ inline void bgc_cotes_number_exclude_fp32(const BgcCotesNumberFP32* base, const
inline void bgc_cotes_number_exclude_fp64(const BgcCotesNumberFP64* base, const BgcCotesNumberFP64* excludant, BgcCotesNumberFP64* difference)
{
bgc_cotes_number_set_values_fp64(
base->cos * excludant->cos + base->sin * excludant->sin,
base->sin * excludant->cos - base->cos * excludant->sin,
base->_cos * excludant->_cos + base->_sin * excludant->_sin,
base->_sin * excludant->_cos - base->_cos * excludant->_sin,
difference
);
}
@ -301,44 +263,44 @@ inline void bgc_cotes_number_exclude_fp64(const BgcCotesNumberFP64* base, const
inline void bgc_cotes_number_get_rotation_matrix_fp32(const BgcCotesNumberFP32* number, BgcMatrix2x2FP32* matrix)
{
matrix->r1c1 = number->cos;
matrix->r1c2 = -number->sin;
matrix->r2c1 = number->sin;
matrix->r2c2 = number->cos;
matrix->r1c1 = number->_cos;
matrix->r1c2 = -number->_sin;
matrix->r2c1 = number->_sin;
matrix->r2c2 = number->_cos;
}
inline void bgc_cotes_number_get_rotation_matrix_fp64(const BgcCotesNumberFP64* number, BgcMatrix2x2FP64* matrix)
{
matrix->r1c1 = number->cos;
matrix->r1c2 = -number->sin;
matrix->r2c1 = number->sin;
matrix->r2c2 = number->cos;
matrix->r1c1 = number->_cos;
matrix->r1c2 = -number->_sin;
matrix->r2c1 = number->_sin;
matrix->r2c2 = number->_cos;
}
// ============== Reverse Matrix ================ //
inline void bgc_cotes_number_get_reverse_matrix_fp32(const BgcCotesNumberFP32* number, BgcMatrix2x2FP32* matrix)
{
matrix->r1c1 = number->cos;
matrix->r1c2 = number->sin;
matrix->r2c1 = -number->sin;
matrix->r2c2 = number->cos;
matrix->r1c1 = number->_cos;
matrix->r1c2 = number->_sin;
matrix->r2c1 = -number->_sin;
matrix->r2c2 = number->_cos;
}
inline void bgc_cotes_number_get_reverse_matrix_fp64(const BgcCotesNumberFP64* number, BgcMatrix2x2FP64* matrix)
{
matrix->r1c1 = number->cos;
matrix->r1c2 = number->sin;
matrix->r2c1 = -number->sin;
matrix->r2c2 = number->cos;
matrix->r1c1 = number->_cos;
matrix->r1c2 = number->_sin;
matrix->r2c1 = -number->_sin;
matrix->r2c2 = number->_cos;
}
// ================ Turn Vector ================= //
inline void bgc_cotes_number_turn_vector_fp32(const BgcCotesNumberFP32* number, const BgcVector2FP32* vector, BgcVector2FP32* result)
{
const float x1 = number->cos * vector->x1 - number->sin * vector->x2;
const float x2 = number->sin * vector->x1 + number->cos * vector->x2;
const float x1 = number->_cos * vector->x1 - number->_sin * vector->x2;
const float x2 = number->_sin * vector->x1 + number->_cos * vector->x2;
result->x1 = x1;
result->x2 = x2;
@ -346,8 +308,8 @@ inline void bgc_cotes_number_turn_vector_fp32(const BgcCotesNumberFP32* number,
inline void bgc_cotes_number_turn_vector_fp64(const BgcCotesNumberFP64* number, const BgcVector2FP64* vector, BgcVector2FP64* result)
{
const double x1 = number->cos * vector->x1 - number->sin * vector->x2;
const double x2 = number->sin * vector->x1 + number->cos * vector->x2;
const double x1 = number->_cos * vector->x1 - number->_sin * vector->x2;
const double x2 = number->_sin * vector->x1 + number->_cos * vector->x2;
result->x1 = x1;
result->x2 = x2;
@ -357,8 +319,8 @@ inline void bgc_cotes_number_turn_vector_fp64(const BgcCotesNumberFP64* number,
inline void bgc_cotes_number_turn_vector_back_fp32(const BgcCotesNumberFP32* number, const BgcVector2FP32* vector, BgcVector2FP32* result)
{
const float x1 = number->sin * vector->x2 + number->cos * vector->x1;
const float x2 = number->cos * vector->x2 - number->sin * vector->x1;
const float x1 = number->_sin * vector->x2 + number->_cos * vector->x1;
const float x2 = number->_cos * vector->x2 - number->_sin * vector->x1;
result->x1 = x1;
result->x2 = x2;
@ -366,8 +328,8 @@ inline void bgc_cotes_number_turn_vector_back_fp32(const BgcCotesNumberFP32* num
inline void bgc_cotes_number_turn_vector_back_fp64(const BgcCotesNumberFP64* number, const BgcVector2FP64* vector, BgcVector2FP64* result)
{
const double x1 = number->sin * vector->x2 + number->cos * vector->x1;
const double x2 = number->cos * vector->x2 - number->sin * vector->x1;
const double x1 = number->_sin * vector->x2 + number->_cos * vector->x1;
const double x2 = number->_cos * vector->x2 - number->_sin * vector->x1;
result->x1 = x1;
result->x2 = x2;
@ -377,16 +339,16 @@ inline void bgc_cotes_number_turn_vector_back_fp64(const BgcCotesNumberFP64* num
inline int bgc_cotes_number_are_close_fp32(const BgcCotesNumberFP32* number1, const BgcCotesNumberFP32* number2)
{
const float d_cos = number1->cos - number2->cos;
const float d_sin = number1->sin - number2->sin;
const float d_cos = number1->_cos - number2->_cos;
const float d_sin = number1->_sin - number2->_sin;
return d_cos * d_cos + d_sin * d_sin <= BGC_SQUARE_EPSYLON_FP32;
}
inline int bgc_cotes_number_are_close_fp64(const BgcCotesNumberFP64* number1, const BgcCotesNumberFP64* number2)
{
const double d_cos = number1->cos - number2->cos;
const double d_sin = number1->sin - number2->sin;
const double d_cos = number1->_cos - number2->_cos;
const double d_sin = number1->_sin - number2->_sin;
return d_cos * d_cos + d_sin * d_sin <= BGC_SQUARE_EPSYLON_FP64;
}

16
basic-geometry/matrix3x3.h
View file

@ -274,22 +274,6 @@ inline int bgc_matrix3x3_is_singular_fp64(const BgcMatrix3x3FP64* matrix)
// ================ Is Rotation ================= //
inline int bgc_matrix3x3_is_rotation_fp32(const BgcMatrix3x3FP32* matrix)
{
if (!bgc_is_unit_fp32(bgc_matrix3x3_get_determinant_fp32(matrix))) {
return 0;
}
BgcMatrix3x3FP32 transposed, product;
bgc_matrix3x3_transpose_fp32(matrix, &transposed);
bgc_matrix_product_3x3_at_3x3_fp32(matrix, &transposed, &product);
return bgc_is_unit_fp32(product.r1c1) && bgc_is_zero_fp32(product.r1c2) && bgc_is_zero_fp32(product.r1c3)
&& bgc_is_zero_fp32(product.r2c1) && bgc_is_unit_fp32(product.r2c2) && bgc_is_zero_fp32(product.r2c3)
&& bgc_is_zero_fp32(product.r3c1) && bgc_is_zero_fp32(product.r3c2) && bgc_is_unit_fp32(product.r3c3);
}
inline int bgc_matrix3x3_is_rotation_fp32a(const BgcMatrix3x3FP32* matrix)
{
if (!bgc_is_unit_fp32(bgc_matrix3x3_get_determinant_fp32(matrix))) {

72
basic-geometry/quaternion.c
View file

@ -4,8 +4,8 @@
extern inline void bgc_quaternion_reset_fp32(BgcQuaternionFP32* quaternion);
extern inline void bgc_quaternion_reset_fp64(BgcQuaternionFP64* quaternion);
extern inline void bgc_quaternion_set_to_identity_fp32(BgcQuaternionFP32* quaternion);
extern inline void bgc_quaternion_set_to_identity_fp64(BgcQuaternionFP64* quaternion);
extern inline void bgc_quaternion_make_unit_fp32(BgcQuaternionFP32* quaternion);
extern inline void bgc_quaternion_make_unit_fp64(BgcQuaternionFP64* quaternion);
extern inline void bgc_quaternion_set_values_fp32(const float s0, const float x1, const float x2, const float x3, BgcQuaternionFP32* quaternion);
extern inline void bgc_quaternion_set_values_fp64(const double s0, const double x1, const double x2, const double x3, BgcQuaternionFP64* quaternion);
@ -31,21 +31,6 @@ extern inline void bgc_quaternion_swap_fp64(BgcQuaternionFP64* quarternion1, Bgc
extern inline void bgc_quaternion_convert_fp64_to_fp32(const BgcQuaternionFP64* source, BgcQuaternionFP32* destination);
extern inline void bgc_quaternion_convert_fp32_to_fp64(const BgcQuaternionFP32* source, BgcQuaternionFP64* destination);
extern inline void bgc_quaternion_conjugate_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* conjugate);
extern inline void bgc_quaternion_conjugate_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* conjugate);
extern inline int bgc_quaternion_invert_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* inverted);
extern inline int bgc_quaternion_invert_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* inverted);
extern inline int bgc_quaternion_normalize_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* normalized);
extern inline int bgc_quaternion_normalize_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* normalized);
extern inline void bgc_quaternion_get_product_fp32(const BgcQuaternionFP32* left, const BgcQuaternionFP32* right, BgcQuaternionFP32* product);
extern inline void bgc_quaternion_get_product_fp64(const BgcQuaternionFP64* left, const BgcQuaternionFP64* right, BgcQuaternionFP64* product);
extern inline int bgc_quaternion_get_ratio_fp32(const BgcQuaternionFP32* divident, const BgcQuaternionFP32* divisor, BgcQuaternionFP32* quotient);
extern inline int bgc_quaternion_get_ratio_fp64(const BgcQuaternionFP64* divident, const BgcQuaternionFP64* divisor, BgcQuaternionFP64* quotient);
extern inline void bgc_quaternion_add_fp32(const BgcQuaternionFP32* quaternion1, const BgcQuaternionFP32* quaternion2, BgcQuaternionFP32* sum);
extern inline void bgc_quaternion_add_fp64(const BgcQuaternionFP64* quaternion1, const BgcQuaternionFP64* quaternion2, BgcQuaternionFP64* sum);
@ -55,17 +40,50 @@ extern inline void bgc_quaternion_add_scaled_fp64(const BgcQuaternionFP64* basic
extern inline void bgc_quaternion_subtract_fp32(const BgcQuaternionFP32* minuend, const BgcQuaternionFP32* subtrahend, BgcQuaternionFP32* difference);
extern inline void bgc_quaternion_subtract_fp64(const BgcQuaternionFP64* minuend, const BgcQuaternionFP64* subtrahend, BgcQuaternionFP64* difference);
extern inline void bgc_quaternion_subtract_scaled_fp32(const BgcQuaternionFP32* basic_quaternion, const BgcQuaternionFP32* scalable_quaternion, const float scale, BgcQuaternionFP32* difference);
extern inline void bgc_quaternion_subtract_scaled_fp64(const BgcQuaternionFP64* basic_quaternion, const BgcQuaternionFP64* scalable_quaternion, const double scale, BgcQuaternionFP64* difference);
extern inline void bgc_quaternion_multiply_fp32(const BgcQuaternionFP32* left, const BgcQuaternionFP32* right, BgcQuaternionFP32* product);
extern inline void bgc_quaternion_multiply_fp64(const BgcQuaternionFP64* left, const BgcQuaternionFP64* right, BgcQuaternionFP64* product);
extern inline void bgc_quaternion_multiply_fp32(const BgcQuaternionFP32* multiplicand, const float multipier, BgcQuaternionFP32* product);
extern inline void bgc_quaternion_multiply_fp64(const BgcQuaternionFP64* multiplicand, const double multipier, BgcQuaternionFP64* product);
extern inline void bgc_quaternion_multiply_by_number_fp32(const BgcQuaternionFP32* multiplicand, const float multipier, BgcQuaternionFP32* product);
extern inline void bgc_quaternion_multiply_by_number_fp64(const BgcQuaternionFP64* multiplicand, const double multipier, BgcQuaternionFP64* product);
extern inline void bgc_quaternion_divide_fp32(const BgcQuaternionFP32* dividend, const float divisor, BgcQuaternionFP32* quotient);
extern inline void bgc_quaternion_divide_fp64(const BgcQuaternionFP64* dividend, const double divisor, BgcQuaternionFP64* quotient);
extern inline int bgc_quaternion_divide_fp32(const BgcQuaternionFP32* divident, const BgcQuaternionFP32* divisor, BgcQuaternionFP32* quotient);
extern inline int bgc_quaternion_divide_fp64(const BgcQuaternionFP64* divident, const BgcQuaternionFP64* divisor, BgcQuaternionFP64* quotient);
extern inline void bgc_quaternion_interpolate_linearly_fp32(const BgcQuaternionFP32* vector1, const BgcQuaternionFP32* vector2, const float phase, BgcQuaternionFP32* interpolation);
extern inline void bgc_quaternion_interpolate_linearly_fp64(const BgcQuaternionFP64* vector1, const BgcQuaternionFP64* vector2, const double phase, BgcQuaternionFP64* interpolation);
extern inline void bgc_quaternion_divide_by_number_fp32(const BgcQuaternionFP32* dividend, const float divisor, BgcQuaternionFP32* quotient);
extern inline void bgc_quaternion_divide_by_number_fp64(const BgcQuaternionFP64* dividend, const double divisor, BgcQuaternionFP64* quotient);
extern inline void bgc_quaternion_get_mean_of_two_fp32(const BgcQuaternionFP32* vector1, const BgcQuaternionFP32* vector2, BgcQuaternionFP32* mean);
extern inline void bgc_quaternion_get_mean_of_two_fp64(const BgcQuaternionFP64* vector1, const BgcQuaternionFP64* vector2, BgcQuaternionFP64* mean);
extern inline void bgc_quaternion_get_mean_of_three_fp32(const BgcQuaternionFP32* vector1, const BgcQuaternionFP32* vector2, const BgcQuaternionFP32* vector3, BgcQuaternionFP32* mean);
extern inline void bgc_quaternion_get_mean_of_three_fp64(const BgcQuaternionFP64* vector1, const BgcQuaternionFP64* vector2, const BgcQuaternionFP64* vector3, BgcQuaternionFP64* mean);
extern inline void bgc_quaternion_interpolate_fp32(const BgcQuaternionFP32* vector1, const BgcQuaternionFP32* vector2, const float phase, BgcQuaternionFP32* interpolation);
extern inline void bgc_quaternion_interpolate_fp64(const BgcQuaternionFP64* vector1, const BgcQuaternionFP64* vector2, const double phase, BgcQuaternionFP64* interpolation);
extern inline void bgc_quaternion_conjugate_fp32(BgcQuaternionFP32* quaternion);
extern inline void bgc_quaternion_conjugate_fp64(BgcQuaternionFP64* quaternion);
extern inline void bgc_quaternion_get_conjugate_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* conjugate);
extern inline void bgc_quaternion_get_conjugate_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* conjugate);
extern inline void bgc_quaternion_make_opposite_fp32(BgcQuaternionFP32* quaternion);
extern inline void bgc_quaternion_make_opposite_fp64(BgcQuaternionFP64* quaternion);
extern inline void bgc_quaternion_get_opposite_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* opposite);
extern inline void bgc_quaternion_get_opposite_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* opposite);
extern inline int bgc_quaternion_invert_fp32(BgcQuaternionFP32* quaternion);
extern inline int bgc_quaternion_invert_fp64(BgcQuaternionFP64* quaternion);
extern inline int bgc_quaternion_get_inverse_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* inverse);
extern inline int bgc_quaternion_get_inverse_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* inverse);
extern inline int bgc_quaternion_normalize_fp32(BgcQuaternionFP32* quaternion);
extern inline int bgc_quaternion_normalize_fp64(BgcQuaternionFP64* quaternion);
extern inline int bgc_quaternion_get_normalized_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* normalized);
extern inline int bgc_quaternion_get_normalized_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* normalized);
extern inline int bgc_quaternion_get_rotation_matrix_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* rotation);
extern inline int bgc_quaternion_get_rotation_matrix_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* rotation);
@ -73,8 +91,8 @@ extern inline int bgc_quaternion_get_rotation_matrix_fp64(const BgcQuaternionFP6
extern inline int bgc_quaternion_get_reverse_matrix_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* reverse);
extern inline int bgc_quaternion_get_reverse_matrix_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* reverse);
extern inline int bgc_quaternion_get_both_matrixes_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* rotation, BgcMatrix3x3FP32* reverse);
extern inline int bgc_quaternion_get_both_matrixes_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* rotation, BgcMatrix3x3FP64* reverse);
extern inline int bgc_quaternion_get_both_matrices_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* rotation, BgcMatrix3x3FP32* reverse);
extern inline int bgc_quaternion_get_both_matrices_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* rotation, BgcMatrix3x3FP64* reverse);
extern inline int bgc_quaternion_are_close_fp32(const BgcQuaternionFP32* quaternion1, const BgcQuaternionFP32* quaternion2);
extern inline int bgc_quaternion_are_close_fp32(const BgcQuaternionFP32* quaternion1, const BgcQuaternionFP32* quaternion2);

532
basic-geometry/quaternion.h
View file

@ -33,9 +33,9 @@ inline void bgc_quaternion_reset_fp64(BgcQuaternionFP64 * quaternion)
quaternion->x3 = 0.0;
}
// ================== Set Unit ================== //
// ================= Make Unit ================== //
inline void bgc_quaternion_set_to_identity_fp32(BgcQuaternionFP32 * quaternion)
inline void bgc_quaternion_make_unit_fp32(BgcQuaternionFP32 * quaternion)
{
quaternion->s0 = 1.0f;
quaternion->x1 = 0.0f;
@ -43,7 +43,7 @@ inline void bgc_quaternion_set_to_identity_fp32(BgcQuaternionFP32 * quaternion)
quaternion->x3 = 0.0f;
}
inline void bgc_quaternion_set_to_identity_fp64(BgcQuaternionFP64 * quaternion)
inline void bgc_quaternion_make_unit_fp64(BgcQuaternionFP64 * quaternion)
{
quaternion->s0 = 1.0;
quaternion->x1 = 0.0;
@ -191,186 +191,6 @@ inline void bgc_quaternion_convert_fp32_to_fp64(const BgcQuaternionFP32* source,
destination->x3 = source->x3;
}
// ================= Conjugate ================== //
inline void bgc_quaternion_conjugate_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* conjugate)
{
conjugate->s0 = quaternion->s0;
conjugate->x1 = -quaternion->x1;
conjugate->x2 = -quaternion->x2;
conjugate->x3 = -quaternion->x3;
}
inline void bgc_quaternion_conjugate_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* conjugate)
{
conjugate->s0 = quaternion->s0;
conjugate->x1 = -quaternion->x1;
conjugate->x2 = -quaternion->x2;
conjugate->x3 = -quaternion->x3;
}
// =================== Invert =================== //
inline int bgc_quaternion_invert_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* inverted)
{
const float square_modulus = bgc_quaternion_get_square_modulus_fp32(quaternion);
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
return 0;
}
const float multiplicand = 1.0f / square_modulus;
inverted->s0 = quaternion->s0 * multiplicand;
inverted->x1 = -quaternion->x1 * multiplicand;
inverted->x2 = -quaternion->x2 * multiplicand;
inverted->x3 = -quaternion->x3 * multiplicand;
return 1;
}
inline int bgc_quaternion_invert_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* inverted)
{
const double square_modulus = bgc_quaternion_get_square_modulus_fp64(quaternion);
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
return 0;
}
const double multiplicand = 1.0 / square_modulus;
inverted->s0 = quaternion->s0 * multiplicand;
inverted->x1 = -quaternion->x1 * multiplicand;
inverted->x2 = -quaternion->x2 * multiplicand;
inverted->x3 = -quaternion->x3 * multiplicand;
return 1;
}
// ================= Normalize ================== //
inline int bgc_quaternion_normalize_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* normalized)
{
const float square_modulus = bgc_quaternion_get_square_modulus_fp32(quaternion);
if (bgc_is_sqare_unit_fp32(square_modulus)) {
bgc_quaternion_copy_fp32(quaternion, normalized);
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
return 0;
}
const float multiplier = sqrtf(1.0f / square_modulus);
normalized->s0 = quaternion->s0 * multiplier;
normalized->x1 = quaternion->x1 * multiplier;
normalized->x2 = quaternion->x2 * multiplier;
normalized->x3 = quaternion->x3 * multiplier;
return 1;
}
inline int bgc_quaternion_normalize_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* normalized)
{
const double square_modulus = bgc_quaternion_get_square_modulus_fp64(quaternion);
if (bgc_is_sqare_unit_fp64(square_modulus)) {
bgc_quaternion_copy_fp64(quaternion, normalized);
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
return 0;
}
const double multiplier = sqrt(1.0 / square_modulus);
normalized->s0 *= multiplier;
normalized->x1 *= multiplier;
normalized->x2 *= multiplier;
normalized->x3 *= multiplier;
return 1;
}
// ================ Get Product ================= //
inline void bgc_quaternion_get_product_fp32(const BgcQuaternionFP32* left, const BgcQuaternionFP32* right, BgcQuaternionFP32* product)
{
const float s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
const float x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
const float x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
const float x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);
product->s0 = s0;
product->x1 = x1;
product->x2 = x2;
product->x3 = x3;
}
inline void bgc_quaternion_get_product_fp64(const BgcQuaternionFP64* left, const BgcQuaternionFP64* right, BgcQuaternionFP64* product)
{
const double s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
const double x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
const double x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
const double x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);
product->s0 = s0;
product->x1 = x1;
product->x2 = x2;
product->x3 = x3;
}
// ================= Get Ratio ================== //
inline int bgc_quaternion_get_ratio_fp32(const BgcQuaternionFP32* divident, const BgcQuaternionFP32* divisor, BgcQuaternionFP32* quotient)
{
const float square_modulus = bgc_quaternion_get_square_modulus_fp32(divisor);
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
return 0;
}
const float s0 = (divident->s0 * divisor->s0 + divident->x1 * divisor->x1) + (divident->x2 * divisor->x2 + divident->x3 * divisor->x3);
const float x1 = (divident->x1 * divisor->s0 + divident->x3 * divisor->x2) - (divident->s0 * divisor->x1 + divident->x2 * divisor->x3);
const float x2 = (divident->x2 * divisor->s0 + divident->x1 * divisor->x3) - (divident->s0 * divisor->x2 + divident->x3 * divisor->x1);
const float x3 = (divident->x3 * divisor->s0 + divident->x2 * divisor->x1) - (divident->s0 * divisor->x3 + divident->x1 * divisor->x2);
const float multiplicand = 1.0f / square_modulus;
quotient->s0 = s0 * multiplicand;
quotient->x1 = x1 * multiplicand;
quotient->x2 = x2 * multiplicand;
quotient->x3 = x3 * multiplicand;
return 1;
}
inline int bgc_quaternion_get_ratio_fp64(const BgcQuaternionFP64* divident, const BgcQuaternionFP64* divisor, BgcQuaternionFP64* quotient)
{
const double square_modulus = bgc_quaternion_get_square_modulus_fp64(divisor);
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
return 0;
}
const double s0 = (divident->s0 * divisor->s0 + divident->x1 * divisor->x1) + (divident->x2 * divisor->x2 + divident->x3 * divisor->x3);
const double x1 = (divident->x1 * divisor->s0 + divident->x3 * divisor->x2) - (divident->s0 * divisor->x1 + divident->x2 * divisor->x3);
const double x2 = (divident->x2 * divisor->s0 + divident->x1 * divisor->x3) - (divident->s0 * divisor->x2 + divident->x3 * divisor->x1);
const double x3 = (divident->x3 * divisor->s0 + divident->x2 * divisor->x1) - (divident->s0 * divisor->x3 + divident->x1 * divisor->x2);
const double multiplicand = 1.0 / square_modulus;
quotient->s0 = s0 * multiplicand;
quotient->x1 = x1 * multiplicand;
quotient->x2 = x2 * multiplicand;
quotient->x3 = x3 * multiplicand;
return 1;
}
// ==================== Add ===================== //
inline void bgc_quaternion_add_fp32(const BgcQuaternionFP32 * quaternion1, const BgcQuaternionFP32 * quaternion2, BgcQuaternionFP32 * sum)
@ -425,27 +245,35 @@ inline void bgc_quaternion_subtract_fp64(const BgcQuaternionFP64 * minuend, cons
difference->x3 = minuend->x3 - subtrahend->x3;
}
// ============== Subtract scaled =============== //
inline void bgc_quaternion_subtract_scaled_fp32(const BgcQuaternionFP32 * basic_quaternion, const BgcQuaternionFP32 * scalable_quaternion, const float scale, BgcQuaternionFP32 * difference)
{
difference->s0 = basic_quaternion->s0 - scalable_quaternion->s0 * scale;
difference->x1 = basic_quaternion->x1 - scalable_quaternion->x1 * scale;
difference->x2 = basic_quaternion->x2 - scalable_quaternion->x2 * scale;
difference->x3 = basic_quaternion->x3 - scalable_quaternion->x3 * scale;
}
inline void bgc_quaternion_subtract_scaled_fp64(const BgcQuaternionFP64 * basic_quaternion, const BgcQuaternionFP64 * scalable_quaternion, const double scale, BgcQuaternionFP64 * difference)
{
difference->s0 = basic_quaternion->s0 - scalable_quaternion->s0 * scale;
difference->x1 = basic_quaternion->x1 - scalable_quaternion->x1 * scale;
difference->x2 = basic_quaternion->x2 - scalable_quaternion->x2 * scale;
difference->x3 = basic_quaternion->x3 - scalable_quaternion->x3 * scale;
}
// ================== Multiply ================== //
inline void bgc_quaternion_multiply_fp32(const BgcQuaternionFP32* multiplicand, const float multipier, BgcQuaternionFP32* product)
inline void bgc_quaternion_multiply_fp32(const BgcQuaternionFP32* left, const BgcQuaternionFP32* right, BgcQuaternionFP32* product)
{
const float s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
const float x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
const float x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
const float x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);
product->s0 = s0;
product->x1 = x1;
product->x2 = x2;
product->x3 = x3;
}
inline void bgc_quaternion_multiply_fp64(const BgcQuaternionFP64* left, const BgcQuaternionFP64* right, BgcQuaternionFP64* product)
{
const double s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
const double x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
const double x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
const double x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);
product->s0 = s0;
product->x1 = x1;
product->x2 = x2;
product->x3 = x3;
}
inline void bgc_quaternion_multiply_by_number_fp32(const BgcQuaternionFP32* multiplicand, const float multipier, BgcQuaternionFP32* product)
{
product->s0 = multiplicand->s0 * multipier;
product->x1 = multiplicand->x1 * multipier;
@ -453,7 +281,7 @@ inline void bgc_quaternion_multiply_fp32(const BgcQuaternionFP32* multiplicand,
product->x3 = multiplicand->x3 * multipier;
}
inline void bgc_quaternion_multiply_fp64(const BgcQuaternionFP64* multiplicand, const double multipier, BgcQuaternionFP64* product)
inline void bgc_quaternion_multiply_by_number_fp64(const BgcQuaternionFP64* multiplicand, const double multipier, BgcQuaternionFP64* product)
{
product->s0 = multiplicand->s0 * multipier;
product->x1 = multiplicand->x1 * multipier;
@ -463,19 +291,101 @@ inline void bgc_quaternion_multiply_fp64(const BgcQuaternionFP64* multiplicand,
// =================== Divide =================== //
inline void bgc_quaternion_divide_fp32(const BgcQuaternionFP32* dividend, const float divisor, BgcQuaternionFP32* quotient)
inline int bgc_quaternion_divide_fp32(const BgcQuaternionFP32* divident, const BgcQuaternionFP32* divisor, BgcQuaternionFP32* quotient)
{
bgc_quaternion_multiply_fp32(dividend, 1.0f / divisor, quotient);
const float square_modulus = bgc_quaternion_get_square_modulus_fp32(divisor);
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
return 0;
}
const float s0 = (divident->s0 * divisor->s0 + divident->x1 * divisor->x1) + (divident->x2 * divisor->x2 + divident->x3 * divisor->x3);
const float x1 = (divident->x1 * divisor->s0 + divident->x3 * divisor->x2) - (divident->s0 * divisor->x1 + divident->x2 * divisor->x3);
const float x2 = (divident->x2 * divisor->s0 + divident->x1 * divisor->x3) - (divident->s0 * divisor->x2 + divident->x3 * divisor->x1);
const float x3 = (divident->x3 * divisor->s0 + divident->x2 * divisor->x1) - (divident->s0 * divisor->x3 + divident->x1 * divisor->x2);
const float multiplicand = 1.0f / square_modulus;
quotient->s0 = s0 * multiplicand;
quotient->x1 = x1 * multiplicand;
quotient->x2 = x2 * multiplicand;
quotient->x3 = x3 * multiplicand;
return 1;
}
inline void bgc_quaternion_divide_fp64(const BgcQuaternionFP64* dividend, const double divisor, BgcQuaternionFP64* quotient)
inline int bgc_quaternion_divide_fp64(const BgcQuaternionFP64* divident, const BgcQuaternionFP64* divisor, BgcQuaternionFP64* quotient)
{
bgc_quaternion_multiply_fp64(dividend, 1.0 / divisor, quotient);
const double square_modulus = bgc_quaternion_get_square_modulus_fp64(divisor);
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
return 0;
}
const double s0 = (divident->s0 * divisor->s0 + divident->x1 * divisor->x1) + (divident->x2 * divisor->x2 + divident->x3 * divisor->x3);
const double x1 = (divident->x1 * divisor->s0 + divident->x3 * divisor->x2) - (divident->s0 * divisor->x1 + divident->x2 * divisor->x3);
const double x2 = (divident->x2 * divisor->s0 + divident->x1 * divisor->x3) - (divident->s0 * divisor->x2 + divident->x3 * divisor->x1);
const double x3 = (divident->x3 * divisor->s0 + divident->x2 * divisor->x1) - (divident->s0 * divisor->x3 + divident->x1 * divisor->x2);
const double multiplicand = 1.0 / square_modulus;
quotient->s0 = s0 * multiplicand;
quotient->x1 = x1 * multiplicand;
quotient->x2 = x2 * multiplicand;
quotient->x3 = x3 * multiplicand;
return 1;
}
inline void bgc_quaternion_divide_by_number_fp32(const BgcQuaternionFP32* dividend, const float divisor, BgcQuaternionFP32* quotient)
{
bgc_quaternion_multiply_by_number_fp32(dividend, 1.0f / divisor, quotient);
}
inline void bgc_quaternion_divide_by_number_fp64(const BgcQuaternionFP64* dividend, const double divisor, BgcQuaternionFP64* quotient)
{
bgc_quaternion_multiply_by_number_fp64(dividend, 1.0 / divisor, quotient);
}
// ================ Mean of Two ================= //
inline void bgc_quaternion_get_mean_of_two_fp32(const BgcQuaternionFP32* vector1, const BgcQuaternionFP32* vector2, BgcQuaternionFP32* mean)
{
mean->s0 = (vector1->s0 + vector2->s0) * 0.5f;
mean->x1 = (vector1->x1 + vector2->x1) * 0.5f;
mean->x2 = (vector1->x2 + vector2->x2) * 0.5f;
mean->x3 = (vector1->x3 + vector2->x3) * 0.5f;
}
inline void bgc_quaternion_get_mean_of_two_fp64(const BgcQuaternionFP64* vector1, const BgcQuaternionFP64* vector2, BgcQuaternionFP64* mean)
{
mean->s0 = (vector1->s0 + vector2->s0) * 0.5f;
mean->x1 = (vector1->x1 + vector2->x1) * 0.5f;
mean->x2 = (vector1->x2 + vector2->x2) * 0.5f;
mean->x3 = (vector1->x3 + vector2->x3) * 0.5f;
}
// =============== Mean of Three ================ //
inline void bgc_quaternion_get_mean_of_three_fp32(const BgcQuaternionFP32* vector1, const BgcQuaternionFP32* vector2, const BgcQuaternionFP32* vector3, BgcQuaternionFP32* mean)
{
mean->s0 = (vector1->s0 + vector2->s0 + vector3->s0) * BGC_ONE_THIRD_FP32;
mean->x1 = (vector1->x1 + vector2->x1 + vector3->x1) * BGC_ONE_THIRD_FP32;
mean->x2 = (vector1->x2 + vector2->x2 + vector3->x2) * BGC_ONE_THIRD_FP32;
mean->x3 = (vector1->x3 + vector2->x3 + vector3->x3) * BGC_ONE_THIRD_FP32;
}
inline void bgc_quaternion_get_mean_of_three_fp64(const BgcQuaternionFP64* vector1, const BgcQuaternionFP64* vector2, const BgcQuaternionFP64* vector3, BgcQuaternionFP64* mean)
{
mean->s0 = (vector1->s0 + vector2->s0 + vector3->s0) * BGC_ONE_THIRD_FP64;
mean->x1 = (vector1->x1 + vector2->x1 + vector3->x1) * BGC_ONE_THIRD_FP64;
mean->x2 = (vector1->x2 + vector2->x2 + vector3->x2) * BGC_ONE_THIRD_FP64;
mean->x3 = (vector1->x3 + vector2->x3 + vector3->x3) * BGC_ONE_THIRD_FP64;
}
// ============ Linear Interpolation ============ //
inline void bgc_quaternion_interpolate_linearly_fp32(const BgcQuaternionFP32* quaternion1, const BgcQuaternionFP32* quaternion2, const float phase, BgcQuaternionFP32* interpolation)
inline void bgc_quaternion_interpolate_fp32(const BgcQuaternionFP32* quaternion1, const BgcQuaternionFP32* quaternion2, const float phase, BgcQuaternionFP32* interpolation)
{
const float counterphase = 1.0f - phase;
@ -485,7 +395,7 @@ inline void bgc_quaternion_interpolate_linearly_fp32(const BgcQuaternionFP32* qu
interpolation->x3 = quaternion1->x3 * counterphase + quaternion2->x3 * phase;
}
inline void bgc_quaternion_interpolate_linearly_fp64(const BgcQuaternionFP64* quaternion1, const BgcQuaternionFP64* quaternion2, const double phase, BgcQuaternionFP64* interpolation)
inline void bgc_quaternion_interpolate_fp64(const BgcQuaternionFP64* quaternion1, const BgcQuaternionFP64* quaternion2, const double phase, BgcQuaternionFP64* interpolation)
{
const double counterphase = 1.0 - phase;
@ -495,6 +405,202 @@ inline void bgc_quaternion_interpolate_linearly_fp64(const BgcQuaternionFP64* qu
interpolation->x3 = quaternion1->x3 * counterphase + quaternion2->x3 * phase;
}
// ================= Conjugate ================== //
inline void bgc_quaternion_conjugate_fp32(BgcQuaternionFP32* quaternion)
{
quaternion->x1 = -quaternion->x1;
quaternion->x2 = -quaternion->x2;
quaternion->x3 = -quaternion->x3;
}
inline void bgc_quaternion_conjugate_fp64(BgcQuaternionFP64* quaternion)
{
quaternion->x1 = -quaternion->x1;
quaternion->x2 = -quaternion->x2;
quaternion->x3 = -quaternion->x3;
}
inline void bgc_quaternion_get_conjugate_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* conjugate)
{
conjugate->s0 = quaternion->s0;
conjugate->x1 = -quaternion->x1;
conjugate->x2 = -quaternion->x2;
conjugate->x3 = -quaternion->x3;
}
inline void bgc_quaternion_get_conjugate_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* conjugate)
{
conjugate->s0 = quaternion->s0;
conjugate->x1 = -quaternion->x1;
conjugate->x2 = -quaternion->x2;
conjugate->x3 = -quaternion->x3;
}
// ================== Negative ================== //
inline void bgc_quaternion_make_opposite_fp32(BgcQuaternionFP32* quaternion)
{
quaternion->s0 = -quaternion->s0;
quaternion->x1 = -quaternion->x1;
quaternion->x2 = -quaternion->x2;
quaternion->x3 = -quaternion->x3;
}
inline void bgc_quaternion_make_opposite_fp64(BgcQuaternionFP64* quaternion)
{
quaternion->s0 = -quaternion->s0;
quaternion->x1 = -quaternion->x1;
quaternion->x2 = -quaternion->x2;
quaternion->x3 = -quaternion->x3;
}
inline void bgc_quaternion_get_opposite_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* opposite)
{
opposite->s0 = -quaternion->s0;
opposite->x1 = -quaternion->x1;
opposite->x2 = -quaternion->x2;
opposite->x3 = -quaternion->x3;
}
inline void bgc_quaternion_get_opposite_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* opposite)
{
opposite->s0 = -quaternion->s0;
opposite->x1 = -quaternion->x1;
opposite->x2 = -quaternion->x2;
opposite->x3 = -quaternion->x3;
}
// =================== Invert =================== //
inline int bgc_quaternion_get_inverse_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* inverse)
{
const float square_modulus = bgc_quaternion_get_square_modulus_fp32(quaternion);
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
return 0;
}
const float multiplicand = 1.0f / square_modulus;
inverse->s0 = quaternion->s0 * multiplicand;
inverse->x1 = -quaternion->x1 * multiplicand;
inverse->x2 = -quaternion->x2 * multiplicand;
inverse->x3 = -quaternion->x3 * multiplicand;
return 1;
}
inline int bgc_quaternion_get_inverse_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* inverse)
{
const double square_modulus = bgc_quaternion_get_square_modulus_fp64(quaternion);
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
return 0;
}
const double multiplicand = 1.0 / square_modulus;
inverse->s0 = quaternion->s0 * multiplicand;
inverse->x1 = -quaternion->x1 * multiplicand;
inverse->x2 = -quaternion->x2 * multiplicand;
inverse->x3 = -quaternion->x3 * multiplicand;
return 1;
}
inline int bgc_quaternion_invert_fp32(BgcQuaternionFP32* quaternion)
{
return bgc_quaternion_get_inverse_fp32(quaternion, quaternion);
}
inline int bgc_quaternion_invert_fp64(BgcQuaternionFP64* quaternion)
{
return bgc_quaternion_get_inverse_fp64(quaternion, quaternion);
}
// ================= Normalize ================== //
inline int bgc_quaternion_normalize_fp32(BgcQuaternionFP32* quaternion)
{
const float square_modulus = bgc_quaternion_get_square_modulus_fp32(quaternion);
if (bgc_is_sqare_unit_fp32(square_modulus)) {
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
return 0;
}
const float multiplier = sqrtf(1.0f / square_modulus);
quaternion->s0 *= multiplier;
quaternion->x1 *= multiplier;
quaternion->x2 *= multiplier;
quaternion->x3 *= multiplier;
return 1;
}
inline int bgc_quaternion_normalize_fp64(BgcQuaternionFP64* quaternion)
{
const double square_modulus = bgc_quaternion_get_square_modulus_fp64(quaternion);
if (bgc_is_sqare_unit_fp64(square_modulus)) {
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
return 0;
}
const double multiplier = sqrt(1.0 / square_modulus);
quaternion->s0 *= multiplier;
quaternion->x1 *= multiplier;
quaternion->x2 *= multiplier;
quaternion->x3 *= multiplier;
return 1;
}
inline int bgc_quaternion_get_normalized_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* normalized)
{
const float square_modulus = bgc_quaternion_get_square_modulus_fp32(quaternion);
if (bgc_is_sqare_unit_fp32(square_modulus)) {
bgc_quaternion_copy_fp32(quaternion, normalized);
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
bgc_quaternion_reset_fp32(normalized);
return 0;
}
bgc_quaternion_multiply_by_number_fp32(quaternion, sqrtf(1.0f / square_modulus), normalized);
return 1;
}
inline int bgc_quaternion_get_normalized_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* normalized)
{
const double square_modulus = bgc_quaternion_get_square_modulus_fp64(quaternion);
if (bgc_is_sqare_unit_fp64(square_modulus)) {
bgc_quaternion_copy_fp64(quaternion, normalized);
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
bgc_quaternion_reset_fp64(normalized);
return 0;
}
bgc_quaternion_multiply_by_number_fp64(quaternion, sqrt(1.0 / square_modulus), normalized);
return 1;
}
// =============== Get Exponation =============== //
int bgc_quaternion_get_exponation_fp32(const BgcQuaternionFP32* base, const float exponent, BgcQuaternionFP32* power);
@ -514,6 +620,7 @@ inline int bgc_quaternion_get_rotation_matrix_fp32(const BgcQuaternionFP32* quat
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus)
{
bgc_matrix3x3_set_to_identity_fp32(rotation);
return 0;
}
@ -554,6 +661,7 @@ inline int bgc_quaternion_get_rotation_matrix_fp64(const BgcQuaternionFP64* quat
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus)
{
bgc_matrix3x3_set_to_identity_fp64(rotation);
return 0;
}
@ -596,6 +704,7 @@ inline int bgc_quaternion_get_reverse_matrix_fp32(const BgcQuaternionFP32* quate
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus)
{
bgc_matrix3x3_set_to_identity_fp32(reverse);
return 0;
}
@ -636,6 +745,7 @@ inline int bgc_quaternion_get_reverse_matrix_fp64(const BgcQuaternionFP64* quate
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus)
{
bgc_matrix3x3_set_to_identity_fp64(reverse);
return 0;
}
@ -667,7 +777,7 @@ inline int bgc_quaternion_get_reverse_matrix_fp64(const BgcQuaternionFP64* quate
// ============= Get Both Matrixes ============== //
inline int bgc_quaternion_get_both_matrixes_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* rotation, BgcMatrix3x3FP32* reverse)
inline int bgc_quaternion_get_both_matrices_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* rotation, BgcMatrix3x3FP32* reverse)
{
if (bgc_quaternion_get_reverse_matrix_fp32(quaternion, reverse)) {
bgc_matrix3x3_transpose_fp32(reverse, rotation);
@ -677,7 +787,7 @@ inline int bgc_quaternion_get_both_matrixes_fp32(const BgcQuaternionFP32* quater
return 0;
}
inline int bgc_quaternion_get_both_matrixes_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* rotation, BgcMatrix3x3FP64* reverse)
inline int bgc_quaternion_get_both_matrices_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* rotation, BgcMatrix3x3FP64* reverse)
{
if (bgc_quaternion_get_reverse_matrix_fp64(quaternion, reverse)) {
bgc_matrix3x3_transpose_fp64(reverse, rotation);

8
basic-geometry/rotation3.h
View file

@ -72,9 +72,7 @@ inline void bgc_rotation3_set_values_fp64(const double x1, const double x2, cons
inline void bgc_rotation3_set_with_axis_fp32(const BgcVector3FP32* axis, const float angle, const BgcAngleUnitEnum unit, BgcRotation3FP32* rotation)
{
bgc_vector3_copy_fp32(axis, &rotation->axis);
if (bgc_vector3_normalize_fp32(&rotation->axis)) {
if (bgc_vector3_get_normalized_fp32(axis, &rotation->axis)) {
rotation->radians = bgc_angle_to_radians_fp32(angle, unit);
}
else {
@ -84,9 +82,7 @@ inline void bgc_rotation3_set_with_axis_fp32(const BgcVector3FP32* axis, const f
inline void bgc_rotation3_set_with_axis_fp64(const BgcVector3FP64* axis, const double angle, const BgcAngleUnitEnum unit, BgcRotation3FP64* rotation)
{
bgc_vector3_copy_fp64(axis, &rotation->axis);
if (bgc_vector3_normalize_fp64(&rotation->axis)) {
if (bgc_vector3_get_normalized_fp64(axis, &rotation->axis)) {
rotation->radians = bgc_angle_to_radians_fp64(angle, unit);
}
else {

56
basic-geometry/slerp.c
View file

@ -14,7 +14,7 @@ extern inline void bgc_slerp_get_turn_for_phase_fp64(const BgcSlerpFP64* slerp,
void bgc_slerp_make_fp32(const BgcVersorFP32* start, const BgcVersorFP32* augment, BgcSlerpFP32* slerp)
{
const float square_vector = augment->x1 * augment->x1 + augment->x2 * augment->x2 + augment->x3 * augment->x3;
const float square_vector = augment->_x1 * augment->_x1 + augment->_x2 * augment->_x2 + augment->_x3 * augment->_x3;
if (square_vector != square_vector) {
bgc_slerp_reset_fp32(slerp);
@ -22,10 +22,10 @@ void bgc_slerp_make_fp32(const BgcVersorFP32* start, const BgcVersorFP32* augmen
}
if (square_vector <= BGC_SQUARE_EPSYLON_FP32) {
slerp->s0_cos_weight = start->s0;
slerp->x1_cos_weight = start->x1;
slerp->x2_cos_weight = start->x2;
slerp->x3_cos_weight = start->x3;
slerp->s0_cos_weight = start->_s0;
slerp->x1_cos_weight = start->_x1;
slerp->x2_cos_weight = start->_x2;
slerp->x3_cos_weight = start->_x3;
slerp->s0_sin_weight = 0.0f;
slerp->x1_sin_weight = 0.0f;
@ -38,24 +38,24 @@ void bgc_slerp_make_fp32(const BgcVersorFP32* start, const BgcVersorFP32* augmen
const float vector_modulus = sqrtf(square_vector);
slerp->radians = atan2f(vector_modulus, augment->s0);
slerp->radians = atan2f(vector_modulus, augment->_s0);
const float multiplier = 1.0f / vector_modulus;
slerp->s0_cos_weight = start->s0;
slerp->x1_cos_weight = start->x1;
slerp->x2_cos_weight = start->x2;
slerp->x3_cos_weight = start->x3;
slerp->s0_cos_weight = start->_s0;
slerp->x1_cos_weight = start->_x1;
slerp->x2_cos_weight = start->_x2;
slerp->x3_cos_weight = start->_x3;
slerp->s0_sin_weight = -multiplier * (augment->x1 * start->x1 + augment->x2 * start->x2 + augment->x3 * start->x3);
slerp->x1_sin_weight = multiplier * (augment->x1 * start->s0 + augment->x2 * start->x3 - augment->x3 * start->x2);
slerp->x2_sin_weight = multiplier * (augment->x2 * start->s0 - augment->x1 * start->x3 + augment->x3 * start->x1);
slerp->x3_sin_weight = multiplier * (augment->x3 * start->s0 - augment->x2 * start->x1 + augment->x1 * start->x2);
slerp->s0_sin_weight = -multiplier * (augment->_x1 * start->_x1 + augment->_x2 * start->_x2 + augment->_x3 * start->_x3);
slerp->x1_sin_weight = multiplier * (augment->_x1 * start->_s0 + augment->_x2 * start->_x3 - augment->_x3 * start->_x2);
slerp->x2_sin_weight = multiplier * (augment->_x2 * start->_s0 - augment->_x1 * start->_x3 + augment->_x3 * start->_x1);
slerp->x3_sin_weight = multiplier * (augment->_x3 * start->_s0 - augment->_x2 * start->_x1 + augment->_x1 * start->_x2);
}
void bgc_slerp_make_fp64(const BgcVersorFP64* start, const BgcVersorFP64* augment, BgcSlerpFP64* slerp)
{
const double square_vector = augment->x1 * augment->x1 + augment->x2 * augment->x2 + augment->x3 * augment->x3;
const double square_vector = augment->_x1 * augment->_x1 + augment->_x2 * augment->_x2 + augment->_x3 * augment->_x3;
if (square_vector != square_vector) {
bgc_slerp_reset_fp64(slerp);
@ -63,10 +63,10 @@ void bgc_slerp_make_fp64(const BgcVersorFP64* start, const BgcVersorFP64* augmen
}
if (square_vector <= BGC_SQUARE_EPSYLON_FP64) {
slerp->s0_cos_weight = start->s0;
slerp->x1_cos_weight = start->x1;
slerp->x2_cos_weight = start->x2;
slerp->x3_cos_weight = start->x3;
slerp->s0_cos_weight = start->_s0;
slerp->x1_cos_weight = start->_x1;
slerp->x2_cos_weight = start->_x2;
slerp->x3_cos_weight = start->_x3;
slerp->s0_sin_weight = 0.0;
slerp->x1_sin_weight = 0.0;
@ -79,17 +79,17 @@ void bgc_slerp_make_fp64(const BgcVersorFP64* start, const BgcVersorFP64* augmen
const double vector_modulus = sqrt(square_vector);
slerp->radians = atan2(vector_modulus, augment->s0);
slerp->radians = atan2(vector_modulus, augment->_s0);
const double multiplier = 1.0 / vector_modulus;
slerp->s0_cos_weight = start->s0;
slerp->x1_cos_weight = start->x1;
slerp->x2_cos_weight = start->x2;
slerp->x3_cos_weight = start->x3;
slerp->s0_cos_weight = start->_s0;
slerp->x1_cos_weight = start->_x1;
slerp->x2_cos_weight = start->_x2;
slerp->x3_cos_weight = start->_x3;
slerp->s0_sin_weight = -multiplier * (augment->x1 * start->x1 + augment->x2 * start->x2 + augment->x3 * start->x3);
slerp->x1_sin_weight = multiplier * (augment->x1 * start->s0 + augment->x2 * start->x3 - augment->x3 * start->x2);
slerp->x2_sin_weight = multiplier * (augment->x2 * start->s0 - augment->x1 * start->x3 + augment->x3 * start->x1);
slerp->x3_sin_weight = multiplier * (augment->x3 * start->s0 - augment->x2 * start->x1 + augment->x1 * start->x2);
slerp->s0_sin_weight = -multiplier * (augment->_x1 * start->_x1 + augment->_x2 * start->_x2 + augment->_x3 * start->_x3);
slerp->x1_sin_weight = multiplier * (augment->_x1 * start->_s0 + augment->_x2 * start->_x3 - augment->_x3 * start->_x2);
slerp->x2_sin_weight = multiplier * (augment->_x2 * start->_s0 - augment->_x1 * start->_x3 + augment->_x3 * start->_x1);
slerp->x3_sin_weight = multiplier * (augment->_x3 * start->_s0 - augment->_x2 * start->_x1 + augment->_x1 * start->_x2);
}

4
basic-geometry/slerp.h
View file

@ -80,7 +80,7 @@ inline void bgc_slerp_make_shortened_fp32(const BgcVersorFP32* start, const BgcV
BgcVersorFP32 augment;
bgc_versor_exclude_fp32(end, start, &augment);
bgc_versor_shorten_fp32(&augment, &augment);
bgc_versor_shorten_fp32(&augment);
bgc_slerp_make_fp32(start, &augment, slerp);
}
@ -90,7 +90,7 @@ inline void bgc_slerp_make_shortened_fp64(const BgcVersorFP64* start, const BgcV
BgcVersorFP64 augment;
bgc_versor_exclude_fp64(end, start, &augment);
bgc_versor_shorten_fp64(&augment, &augment);
bgc_versor_shorten_fp64(&augment);
bgc_slerp_make_fp64(start, &augment, slerp);
}

16
basic-geometry/types.h Normal file
View file

@ -0,0 +1,16 @@
#ifndef _BGC_TYPES_H_
#define _BGC_TYPES_H_
// ================== Complex =================== //
typedef struct
{
float real, imaginary;
} BgcComplexFP32;
typedef struct
{
double real, imaginary;
} BgcComplexFP64;
#endif

2
basic-geometry/utilities.c
View file

@ -1,6 +1,6 @@
#include "utilities.h"
extern inline int bgc_is_correct_direction(const int direction);
extern inline int bgc_is_correct_axis(const int axis);
extern inline int bgc_is_zero_fp32(const float square_value);
extern inline int bgc_is_zero_fp64(const double square_value);

24
basic-geometry/utilities.h
View file

@ -32,15 +32,25 @@
#define BGC_SUCCESS 0
#define BGC_FAILED -1
#define BGC_DIRECTION_X1 1
#define BGC_DIRECTION_X2 2
#define BGC_DIRECTION_X3 3
#define BGC_ATTITUDE_ANY 0
#define BGC_ATTITUDE_ZERO 1
#define BGC_ATTITUDE_ORTHOGONAL 2
#define BGC_ATTITUDE_CO_DIRECTIONAL 3
#define BGC_ATTITUDE_COUNTER_DIRECTIONAL 4
inline int bgc_is_correct_direction(const int direction)
#define BGC_AXIS_X1 1
#define BGC_AXIS_X2 2
#define BGC_AXIS_X3 3
#define BGC_AXIS_REVERSE_X1 -1
#define BGC_AXIS_REVERSE_X2 -2
#define BGC_AXIS_REVERSE_X3 -3
inline int bgc_is_correct_axis(const int axis)
{
return direction == BGC_DIRECTION_X1 || direction == -BGC_DIRECTION_X1
|| direction == BGC_DIRECTION_X2 || direction == -BGC_DIRECTION_X2
|| direction == BGC_DIRECTION_X3 || direction == -BGC_DIRECTION_X3;
return axis == BGC_AXIS_X1 || axis == BGC_AXIS_REVERSE_X1
|| axis == BGC_AXIS_X2 || axis == BGC_AXIS_REVERSE_X2
|| axis == BGC_AXIS_X3 || axis == BGC_AXIS_REVERSE_X3;
}
inline int bgc_is_zero_fp32(const float value)

55
basic-geometry/vector2.c
View file

@ -6,9 +6,6 @@ extern inline void bgc_vector2_reset_fp64(BgcVector2FP64* vector);
extern inline void bgc_vector2_set_values_fp32(const float x1, const float x2, BgcVector2FP32* destination);
extern inline void bgc_vector2_set_values_fp64(const double x1, const double x2, BgcVector2FP64* destination);
extern inline int bgc_vector2_get_direction_fp32(const int direction, BgcVector2FP32* vector);
extern inline int bgc_vector2_get_direction_fp64(const int direction, BgcVector2FP64* vector);
extern inline float bgc_vector2_get_square_modulus_fp32(const BgcVector2FP32* vector);
extern inline double bgc_vector2_get_square_modulus_fp64(const BgcVector2FP64* vector);
@ -30,12 +27,6 @@ extern inline void bgc_vector2_swap_fp64(BgcVector2FP64* vector1, BgcVector2FP64
extern inline void bgc_vector2_convert_fp64_to_fp32(const BgcVector2FP64* source, BgcVector2FP32* destination);
extern inline void bgc_vector2_convert_fp32_to_fp64(const BgcVector2FP32* source, BgcVector2FP64* destination);
extern inline void bgc_vector2_reverse_fp32(const BgcVector2FP32* vector, BgcVector2FP32* reverse);
extern inline void bgc_vector2_reverse_fp64(const BgcVector2FP64* vector, BgcVector2FP64* reverse);
extern inline int bgc_vector2_normalize_fp32(const BgcVector2FP32* vector, BgcVector2FP32* normalized);
extern inline int bgc_vector2_normalize_fp64(const BgcVector2FP64* vector, BgcVector2FP64* normalized);
extern inline void bgc_vector2_add_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, BgcVector2FP32* sum);
extern inline void bgc_vector2_add_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, BgcVector2FP64* sum);
@ -45,9 +36,6 @@ extern inline void bgc_vector2_add_scaled_fp64(const BgcVector2FP64* basic_vecto
extern inline void bgc_vector2_subtract_fp32(const BgcVector2FP32* minuend, const BgcVector2FP32* subtrahend, BgcVector2FP32* difference);
extern inline void bgc_vector2_subtract_fp64(const BgcVector2FP64* minuend, const BgcVector2FP64* subtrahend, BgcVector2FP64* difference);
extern inline void bgc_vector2_subtract_scaled_fp32(const BgcVector2FP32* basic_vector, const BgcVector2FP32* scalable_vector, const float scale, BgcVector2FP32* difference);
extern inline void bgc_vector2_subtract_scaled_fp64(const BgcVector2FP64* basic_vector, const BgcVector2FP64* scalable_vector, const double scale, BgcVector2FP64* difference);
extern inline void bgc_vector2_multiply_fp32(const BgcVector2FP32* multiplicand, const float multiplier, BgcVector2FP32* product);
extern inline void bgc_vector2_multiply_fp64(const BgcVector2FP64* multiplicand, const double multiplier, BgcVector2FP64* product);
@ -60,14 +48,20 @@ extern inline void bgc_vector2_get_mean_of_two_fp64(const BgcVector2FP64* vector
extern inline void bgc_vector2_get_mean_of_three_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const BgcVector2FP32* vector3, BgcVector2FP32* mean);
extern inline void bgc_vector2_get_mean_of_three_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, const BgcVector2FP64* vector3, BgcVector2FP64* mean);
extern inline void bgc_vector2_interpolate_linearly_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const float phase, BgcVector2FP32* interpolation);
extern inline void bgc_vector2_interpolate_linearly_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, const double phase, BgcVector2FP64* interpolation);
extern inline void bgc_vector2_interpolate_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const float phase, BgcVector2FP32* interpolation);
extern inline void bgc_vector2_interpolate_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, const double phase, BgcVector2FP64* interpolation);
extern inline void bgc_vector2_minimize_fp32(const BgcVector2FP32* vector, BgcVector2FP32* minimal);
extern inline void bgc_vector2_minimize_fp64(const BgcVector2FP64* vector, BgcVector2FP64* minimal);
extern inline void bgc_vector2_make_opposite_fp32(BgcVector2FP32* vector);
extern inline void bgc_vector2_make_opposite_fp64(BgcVector2FP64* vector);
extern inline void bgc_vector2_maximize_fp32(const BgcVector2FP32* vector, BgcVector2FP32* maximal);
extern inline void bgc_vector2_maximize_fp64(const BgcVector2FP64* vector, BgcVector2FP64* maximal);
extern inline void bgc_vector2_get_opposite_fp32(const BgcVector2FP32* vector, BgcVector2FP32* opposite);
extern inline void bgc_vector2_get_opposite_fp64(const BgcVector2FP64* vector, BgcVector2FP64* opposite);
extern inline int bgc_vector2_normalize_fp32(BgcVector2FP32* vector);
extern inline int bgc_vector2_normalize_fp64(BgcVector2FP64* vector);
extern inline int bgc_vector2_get_normalized_fp32(const BgcVector2FP32* vector, BgcVector2FP32* normalized);
extern inline int bgc_vector2_get_normalized_fp64(const BgcVector2FP64* vector, BgcVector2FP64* normalized);
extern inline float bgc_vector2_get_scalar_product_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2);
extern inline double bgc_vector2_get_scalar_product_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2);
@ -87,6 +81,15 @@ extern inline int bgc_vector2_are_close_enough_fp64(const BgcVector2FP64* vector
extern inline int bgc_vector2_are_close_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2);
extern inline int bgc_vector2_are_close_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2);
extern inline int bgc_vector2_are_parallel_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2);
extern inline int bgc_vector2_are_parallel_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2);
extern inline int bgc_vector2_are_orthogonal_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2);
extern inline int bgc_vector2_are_orthogonal_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2);
extern inline int bgc_vector2_get_attitude_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2);
extern inline int bgc_vector2_get_attitude_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2);
// =================== Angle ==================== //
float bgc_vector2_get_angle_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const BgcAngleUnitEnum unit)
@ -105,11 +108,13 @@ float bgc_vector2_get_angle_fp32(const BgcVector2FP32* vector1, const BgcVector2
return 0.0f;
}
const float scalar = bgc_vector2_get_scalar_product_fp32(vector1, vector2);
const float multiplier = sqrtf(1.0f / (square_modulus1 * square_modulus2));
const float cross = bgc_vector2_get_cross_product_fp32(vector1, vector2);
const float x = bgc_vector2_get_scalar_product_fp32(vector1, vector2);
return bgc_radians_to_units_fp32(atan2f(cross >= 0 ? cross : -cross, scalar), unit);
const float y = fabsf(bgc_vector2_get_cross_product_fp32(vector1, vector2));
return bgc_radians_to_units_fp32(atan2f(y * multiplier, x * multiplier), unit);
}
double bgc_vector2_get_angle_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, const BgcAngleUnitEnum unit)
@ -128,9 +133,11 @@ double bgc_vector2_get_angle_fp64(const BgcVector2FP64* vector1, const BgcVector
return 0.0;
}
const double scalar = bgc_vector2_get_scalar_product_fp64(vector1, vector2);
const double multiplier = sqrt(1.0 / (square_modulus1 * square_modulus2));
const double cross = bgc_vector2_get_cross_product_fp64(vector1, vector2);
const double x = bgc_vector2_get_scalar_product_fp64(vector1, vector2);
return bgc_radians_to_units_fp64(atan2(cross >= 0 ? cross : -cross, scalar), unit);
const double y = bgc_vector2_get_cross_product_fp64(vector1, vector2);
return bgc_radians_to_units_fp64(atan2(y * multiplier, x * multiplier), unit);
}

412
basic-geometry/vector2.h
View file

@ -44,62 +44,6 @@ inline void bgc_vector2_set_values_fp64(const double x1, const double x2, BgcVec
destination->x2 = x2;
}
// ================= Directions ================= //
inline int bgc_vector2_get_direction_fp32(const int direction, BgcVector2FP32* vector)
{
switch (direction) {
case BGC_DIRECTION_X1:
vector->x1 = 1.0f;
vector->x2 = 0.0f;
return 1;
case BGC_DIRECTION_X2:
vector->x1 = 0.0f;
vector->x2 = 1.0f;
return 1;
case -BGC_DIRECTION_X1:
vector->x1 = -1.0f;
vector->x2 = 0.0f;
return 1;
case -BGC_DIRECTION_X2:
vector->x1 = 0.0f;
vector->x2 = -1.0f;
return 1;
}
return 0;
}
inline int bgc_vector2_get_direction_fp64(const int direction, BgcVector2FP64* vector)
{
switch (direction) {
case BGC_DIRECTION_X1:
vector->x1 = 1.0;
vector->x2 = 0.0;
return 1;
case BGC_DIRECTION_X2:
vector->x1 = 0.0;
vector->x2 = 1.0;
return 1;
case -BGC_DIRECTION_X1:
vector->x1 = -1.0;
vector->x2 = 0.0;
return 1;
case -BGC_DIRECTION_X2:
vector->x1 = 0.0;
vector->x2 = -1.0;
return 1;
}
return 0;
}
// ================== Modulus =================== //
inline float bgc_vector2_get_square_modulus_fp32(const BgcVector2FP32* vector)
@ -198,66 +142,6 @@ inline void bgc_vector2_convert_fp32_to_fp64(const BgcVector2FP32* source, BgcVe
destination->x2 = source->x2;
}
// ================== Reverse =================== //
inline void bgc_vector2_reverse_fp32(const BgcVector2FP32* vector, BgcVector2FP32* reverse)
{
reverse->x1 = -vector->x1;
reverse->x2 = -vector->x2;
}
inline void bgc_vector2_reverse_fp64(const BgcVector2FP64* vector, BgcVector2FP64* reverse)
{
reverse->x1 = -vector->x1;
reverse->x2 = -vector->x2;
}
// ================= Normalize ================== //
inline int bgc_vector2_normalize_fp32(const BgcVector2FP32* vector, BgcVector2FP32* normalized)
{
const float square_modulus = bgc_vector2_get_square_modulus_fp32(vector);
if (bgc_is_sqare_unit_fp32(square_modulus)) {
normalized->x1 = vector->x1;
normalized->x2 = vector->x2;
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
return 0;
}
const float multiplicand = sqrtf(1.0f / square_modulus);
normalized->x1 = vector->x1 * multiplicand;
normalized->x2 = vector->x2 * multiplicand;
return 1;
}
inline int bgc_vector2_normalize_fp64(const BgcVector2FP64* vector, BgcVector2FP64* normalized)
{
const double square_modulus = bgc_vector2_get_square_modulus_fp64(vector);
if (bgc_is_sqare_unit_fp64(square_modulus)) {
normalized->x1 = vector->x1;
normalized->x2 = vector->x2;
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
return 0;
}
const double multiplicand = sqrt(1.0 / square_modulus);
normalized->x1 = vector->x1 * multiplicand;
normalized->x2 = vector->x2 * multiplicand;
return 1;
}
// ==================== Add ===================== //
inline void bgc_vector2_add_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, BgcVector2FP32* sum)
@ -300,20 +184,6 @@ inline void bgc_vector2_subtract_fp64(const BgcVector2FP64* minuend, const BgcVe
difference->x2 = minuend->x2 - subtrahend->x2;
}
// ============== Subtract scaled =============== //
inline void bgc_vector2_subtract_scaled_fp32(const BgcVector2FP32* basic_vector, const BgcVector2FP32* scalable_vector, const float scale, BgcVector2FP32* difference)
{
difference->x1 = basic_vector->x1 - scalable_vector->x1 * scale;
difference->x2 = basic_vector->x2 - scalable_vector->x2 * scale;
}
inline void bgc_vector2_subtract_scaled_fp64(const BgcVector2FP64* basic_vector, const BgcVector2FP64* scalable_vector, const double scale, BgcVector2FP64* difference)
{
difference->x1 = basic_vector->x1 - scalable_vector->x1 * scale;
difference->x2 = basic_vector->x2 - scalable_vector->x2 * scale;
}
// ================== Multiply ================== //
inline void bgc_vector2_multiply_fp32(const BgcVector2FP32* multiplicand, const float multiplier, BgcVector2FP32* product)
@ -340,7 +210,7 @@ inline void bgc_vector2_divide_fp64(const BgcVector2FP64* dividend, const double
bgc_vector2_multiply_fp64(dividend, 1.0 / divisor, quotient);
}
// ================== Average2 ================== //
// ================ Mean of Two ================= //
inline void bgc_vector2_get_mean_of_two_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, BgcVector2FP32* mean)
{
@ -354,7 +224,7 @@ inline void bgc_vector2_get_mean_of_two_fp64(const BgcVector2FP64* vector1, cons
mean->x2 = (vector1->x2 + vector2->x2) * 0.5;
}
// ================== Average3 ================== //
// =============== Mean of Three ================ //
inline void bgc_vector2_get_mean_of_three_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const BgcVector2FP32* vector3, BgcVector2FP32* mean)
{
@ -370,7 +240,7 @@ inline void bgc_vector2_get_mean_of_three_fp64(const BgcVector2FP64* vector1, co
// =================== Linear =================== //
inline void bgc_vector2_interpolate_linearly_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const float phase, BgcVector2FP32* interpolation)
inline void bgc_vector2_interpolate_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const float phase, BgcVector2FP32* interpolation)
{
const float counterphase = 1.0f - phase;
@ -378,7 +248,7 @@ inline void bgc_vector2_interpolate_linearly_fp32(const BgcVector2FP32* vector1,
interpolation->x2 = vector1->x2 * counterphase + vector2->x2 * phase;
}
inline void bgc_vector2_interpolate_linearly_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, const double phase, BgcVector2FP64* interpolation)
inline void bgc_vector2_interpolate_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, const double phase, BgcVector2FP64* interpolation)
{
const double counterphase = 1.0 - phase;
@ -386,52 +256,108 @@ inline void bgc_vector2_interpolate_linearly_fp64(const BgcVector2FP64* vector1,
interpolation->x2 = vector1->x2 * counterphase + vector2->x2 * phase;
}
// ================== Minimal =================== //
// ================== Negative ================== //
inline void bgc_vector2_minimize_fp32(const BgcVector2FP32* vector, BgcVector2FP32* minimal)
inline void bgc_vector2_make_opposite_fp32(BgcVector2FP32* vector)
{
if (vector->x1 < minimal->x1) {
minimal->x1 = vector->x1;
}
if (vector->x2 < minimal->x2) {
minimal->x2 = vector->x2;
}
vector->x1 = -vector->x1;
vector->x2 = -vector->x2;
}
inline void bgc_vector2_minimize_fp64(const BgcVector2FP64* vector, BgcVector2FP64* minimal)
inline void bgc_vector2_make_opposite_fp64(BgcVector2FP64* vector)
{
if (vector->x1 < minimal->x1) {
minimal->x1 = vector->x1;
}
if (vector->x2 < minimal->x2) {
minimal->x2 = vector->x2;
}
vector->x1 = -vector->x1;
vector->x2 = -vector->x2;
}
// ================== Maximal =================== //
inline void bgc_vector2_maximize_fp32(const BgcVector2FP32* vector, BgcVector2FP32* maximal)
inline void bgc_vector2_get_opposite_fp32(const BgcVector2FP32* vector, BgcVector2FP32* opposite)
{
if (vector->x1 > maximal->x1) {
maximal->x1 = vector->x1;
}
if (vector->x2 > maximal->x2) {
maximal->x2 = vector->x2;
}
opposite->x1 = -vector->x1;
opposite->x2 = -vector->x2;
}
inline void bgc_vector2_maximize_fp64(const BgcVector2FP64* vector, BgcVector2FP64* maximal)
inline void bgc_vector2_get_opposite_fp64(const BgcVector2FP64* vector, BgcVector2FP64* opposite)
{
if (vector->x1 > maximal->x1) {
maximal->x1 = vector->x1;
opposite->x1 = -vector->x1;
opposite->x2 = -vector->x2;
}
// ================= Normalize ================== //
inline int bgc_vector2_normalize_fp32(BgcVector2FP32* vector)
{
const float square_modulus = bgc_vector2_get_square_modulus_fp32(vector);
if (bgc_is_sqare_unit_fp32(square_modulus)) {
return 1;
}
if (vector->x2 > maximal->x2) {
maximal->x2 = vector->x2;
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
return 0;
}
const float multiplier = sqrtf(1.0f / square_modulus);
vector->x1 *= multiplier;
vector->x2 *= multiplier;
return 1;
}
inline int bgc_vector2_normalize_fp64(BgcVector2FP64* vector)
{
const double square_modulus = bgc_vector2_get_square_modulus_fp64(vector);
if (bgc_is_sqare_unit_fp64(square_modulus)) {
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
return 0;
}
const double multiplier = sqrt(1.0 / square_modulus);
vector->x1 *= multiplier;
vector->x2 *= multiplier;
return 1;
}
inline int bgc_vector2_get_normalized_fp32(const BgcVector2FP32* vector, BgcVector2FP32* normalized)
{
const float square_modulus = bgc_vector2_get_square_modulus_fp32(vector);
if (bgc_is_sqare_unit_fp32(square_modulus)) {
bgc_vector2_copy_fp32(vector, normalized);
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
bgc_vector2_reset_fp32(normalized);
return 0;
}
bgc_vector2_multiply_fp32(vector, sqrtf(1.0f / square_modulus), normalized);
return 1;
}
inline int bgc_vector2_get_normalized_fp64(const BgcVector2FP64* vector, BgcVector2FP64* normalized)
{
const double square_modulus = bgc_vector2_get_square_modulus_fp64(vector);
if (bgc_is_sqare_unit_fp64(square_modulus)) {
bgc_vector2_copy_fp64(vector, normalized);
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
bgc_vector2_reset_fp64(normalized);
return 0;
}
bgc_vector2_multiply_fp64(vector, sqrt(1.0 / square_modulus), normalized);
return 1;
}
// ============= Get Scalar Product ============= //
@ -468,16 +394,16 @@ double bgc_vector2_get_angle_fp64(const BgcVector2FP64* vector1, const BgcVector
inline float bgc_vector2_get_square_distance_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2)
{
const float dx1 = (vector1->x1 - vector2->x1);
const float dx2 = (vector1->x2 - vector2->x2);
const float dx1 = vector1->x1 - vector2->x1;
const float dx2 = vector1->x2 - vector2->x2;
return dx1 * dx1 + dx2 * dx2;
}
inline double bgc_vector2_get_square_distance_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2)
{
const double dx1 = (vector1->x1 - vector2->x1);
const double dx2 = (vector1->x2 - vector2->x2);
const double dx1 = vector1->x1 - vector2->x1;
const double dx2 = vector1->x2 - vector2->x2;
return dx1 * dx1 + dx2 * dx2;
}
@ -496,14 +422,14 @@ inline double bgc_vector2_get_distance_fp64(const BgcVector2FP64* vector1, const
// ============== Are Close Enough ============== //
inline int bgc_vector2_are_close_enough_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const float distance)
inline int bgc_vector2_are_close_enough_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2, const float distance_limit)
{
return bgc_vector2_get_square_distance_fp32(vector1, vector2) <= distance * distance;
return bgc_vector2_get_square_distance_fp32(vector1, vector2) <= distance_limit * distance_limit;
}
inline int bgc_vector2_are_close_enough_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, const double distance)
inline int bgc_vector2_are_close_enough_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2, const double distance_limit)
{
return bgc_vector2_get_square_distance_fp64(vector1, vector2) <= distance * distance;
return bgc_vector2_get_square_distance_fp64(vector1, vector2) <= distance_limit * distance_limit;
}
// ================== Are Close ================= //
@ -531,7 +457,143 @@ inline int bgc_vector2_are_close_fp64(const BgcVector2FP64* vector1, const BgcVe
return square_distance <= BGC_SQUARE_EPSYLON_FP64;
}
return square_distance <= BGC_SQUARE_EPSYLON_FP32 * square_modulus1 && square_distance <= BGC_SQUARE_EPSYLON_FP32 * square_modulus2;
return square_distance <= BGC_SQUARE_EPSYLON_FP64 * square_modulus1 && square_distance <= BGC_SQUARE_EPSYLON_FP64 * square_modulus2;
}
// ================== Parallel ================== //
inline int bgc_vector2_are_parallel_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2)
{
const float square_modulus1 = bgc_vector2_get_square_modulus_fp32(vector1);
if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP32) {
return 1;
}
const float square_modulus2 = bgc_vector2_get_square_modulus_fp32(vector2);
if (square_modulus2 <= BGC_SQUARE_EPSYLON_FP32) {
return 1;
}
const float cross_product = bgc_vector2_get_cross_product_fp32(vector1, vector2);
return cross_product * cross_product <= BGC_SQUARE_EPSYLON_FP32 * square_modulus1 * square_modulus2;
}
inline int bgc_vector2_are_parallel_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2)
{
const double square_modulus1 = bgc_vector2_get_square_modulus_fp64(vector1);
if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP64) {
return 1;
}
const double square_modulus2 = bgc_vector2_get_square_modulus_fp64(vector2);
if (square_modulus2 <= BGC_SQUARE_EPSYLON_FP64) {
return 1;
}
const double cross_product = bgc_vector2_get_cross_product_fp64(vector1, vector2);
return cross_product * cross_product <= BGC_SQUARE_EPSYLON_FP64 * square_modulus1 * square_modulus2;
}
// ================= Orthogonal ================= //
inline int bgc_vector2_are_orthogonal_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2)
{
const float square_modulus1 = bgc_vector2_get_square_modulus_fp32(vector1);
if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP32) {
return 1;
}
const float square_modulus2 = bgc_vector2_get_square_modulus_fp32(vector2);
if (square_modulus2 <= BGC_SQUARE_EPSYLON_FP32) {
return 1;
}
const float scalar_product = bgc_vector2_get_scalar_product_fp32(vector1, vector2);
return scalar_product * scalar_product <= BGC_SQUARE_EPSYLON_FP32 * square_modulus1 * square_modulus2;
}
inline int bgc_vector2_are_orthogonal_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2)
{
const double square_modulus1 = bgc_vector2_get_square_modulus_fp64(vector1);
if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP64) {
return 1;
}
const double square_modulus2 = bgc_vector2_get_square_modulus_fp64(vector2);
if (square_modulus2 <= BGC_SQUARE_EPSYLON_FP64) {
return 1;
}
const double scalar_product = bgc_vector2_get_scalar_product_fp64(vector1, vector2);
return scalar_product * scalar_product <= BGC_SQUARE_EPSYLON_FP64 * square_modulus1 * square_modulus2;
}
// ================== Attitude ================== //
inline int bgc_vector2_get_attitude_fp32(const BgcVector2FP32* vector1, const BgcVector2FP32* vector2)
{
const float square_modulus1 = bgc_vector2_get_square_modulus_fp32(vector1);
const float square_modulus2 = bgc_vector2_get_square_modulus_fp32(vector2);
if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP32 || square_modulus2 <= BGC_SQUARE_EPSYLON_FP32) {
return BGC_ATTITUDE_ZERO;
}
const float square_limit = BGC_SQUARE_EPSYLON_FP32 * square_modulus1 * square_modulus2;
const float scalar_product = bgc_vector2_get_scalar_product_fp32(vector1, vector2);
if (scalar_product * scalar_product <= square_limit) {
return BGC_ATTITUDE_ORTHOGONAL;
}
const float cross_product = bgc_vector2_get_cross_product_fp32(vector1, vector2);
if (cross_product * cross_product > square_limit) {
return BGC_ATTITUDE_ANY;
}
return scalar_product > 0.0f ? BGC_ATTITUDE_CO_DIRECTIONAL : BGC_ATTITUDE_COUNTER_DIRECTIONAL;
}
inline int bgc_vector2_get_attitude_fp64(const BgcVector2FP64* vector1, const BgcVector2FP64* vector2)
{
const double square_modulus1 = bgc_vector2_get_square_modulus_fp64(vector1);
const double square_modulus2 = bgc_vector2_get_square_modulus_fp64(vector2);
if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP64 || square_modulus2 <= BGC_SQUARE_EPSYLON_FP64) {
return BGC_ATTITUDE_ZERO;
}
const double square_limit = BGC_SQUARE_EPSYLON_FP64 * square_modulus1 * square_modulus2;
const double scalar_product = bgc_vector2_get_scalar_product_fp64(vector1, vector2);
if (scalar_product * scalar_product <= square_limit) {
return BGC_ATTITUDE_ORTHOGONAL;
}
const double cross_product = bgc_vector2_get_cross_product_fp64(vector1, vector2);
if (cross_product * cross_product > square_limit) {
return BGC_ATTITUDE_ANY;
}
return scalar_product > 0.0 ? BGC_ATTITUDE_CO_DIRECTIONAL : BGC_ATTITUDE_COUNTER_DIRECTIONAL;
}
#endif

50
basic-geometry/vector3.c
View file

@ -6,9 +6,6 @@ extern inline void bgc_vector3_reset_fp64(BgcVector3FP64* vector);
extern inline void bgc_vector3_set_values_fp32(const float x1, const float x2, const float x3, BgcVector3FP32* destination);
extern inline void bgc_vector3_set_values_fp64(const double x1, const double x2, const double x3, BgcVector3FP64* destination);
inline int bgc_vector3_get_direction_fp32(const int direction, BgcVector3FP32* vector);
inline int bgc_vector3_get_direction_fp64(const int direction, BgcVector3FP64* vector);
extern inline float bgc_vector3_get_square_modulus_fp32(const BgcVector3FP32* vector);
extern inline double bgc_vector3_get_square_modulus_fp64(const BgcVector3FP64* vector);
@ -30,15 +27,6 @@ extern inline void bgc_vector3_convert_fp32_to_fp64(const BgcVector3FP32* source
extern inline void bgc_vector3_swap_fp32(BgcVector3FP32* vector1, BgcVector3FP32* vector2);
extern inline void bgc_vector3_swap_fp64(BgcVector3FP64* vector1, BgcVector3FP64* vector2);
extern inline void bgc_vector3_reverse_fp32(const BgcVector3FP32* vector, BgcVector3FP32* reverse);
extern inline void bgc_vector3_reverse_fp64(const BgcVector3FP64* vector, BgcVector3FP64* reverse);
extern inline int bgc_vector3_normalize_fp32(BgcVector3FP32* vector);
extern inline int bgc_vector3_normalize_fp64(BgcVector3FP64* vector);
extern inline int bgc_vector3_get_normalized_fp32(const BgcVector3FP32* vector, BgcVector3FP32* normalized);
extern inline int bgc_vector3_get_normalized_fp64(const BgcVector3FP64* vector, BgcVector3FP64* normalized);
extern inline void bgc_vector3_add_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, BgcVector3FP32* sum);
extern inline void bgc_vector3_add_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, BgcVector3FP64* sum);
@ -48,9 +36,6 @@ extern inline void bgc_vector3_add_scaled_fp64(const BgcVector3FP64* basic_vecto
extern inline void bgc_vector3_subtract_fp32(const BgcVector3FP32* minuend, const BgcVector3FP32* subtrahend, BgcVector3FP32* difference);
extern inline void bgc_vector3_subtract_fp64(const BgcVector3FP64* minuend, const BgcVector3FP64* subtrahend, BgcVector3FP64* difference);
extern inline void bgc_vector3_subtract_scaled_fp32(const BgcVector3FP32* basic_vector, const BgcVector3FP32* scalable_vector, const float scale, BgcVector3FP32* difference);
extern inline void bgc_vector3_subtract_scaled_fp64(const BgcVector3FP64* basic_vector, const BgcVector3FP64* scalable_vector, const double scale, BgcVector3FP64* difference);
extern inline void bgc_vector3_multiply_fp32(const BgcVector3FP32* multiplicand, const float multiplier, BgcVector3FP32* product);
extern inline void bgc_vector3_multiply_fp64(const BgcVector3FP64* multiplicand, const double multiplier, BgcVector3FP64* product);
@ -63,14 +48,20 @@ extern inline void bgc_vector3_get_mean_of_two_fp64(const BgcVector3FP64* vector
extern inline void bgc_vector3_get_mean_of_three_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const BgcVector3FP32* vector3, BgcVector3FP32* result);
extern inline void bgc_vector3_get_mean_of_three_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const BgcVector3FP64* vector3, BgcVector3FP64* result);
extern inline void bgc_vector3_interpolate_linearly_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const float phase, BgcVector3FP32* interpolation);
extern inline void bgc_vector3_interpolate_linearly_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const double phase, BgcVector3FP64* interpolation);
extern inline void bgc_vector3_interpolate_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const float phase, BgcVector3FP32* interpolation);
extern inline void bgc_vector3_interpolate_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const double phase, BgcVector3FP64* interpolation);
extern inline void bgc_vector3_minimize_fp32(const BgcVector3FP32* vector, BgcVector3FP32* minimal);
extern inline void bgc_vector3_minimize_fp64(const BgcVector3FP64* vector, BgcVector3FP64* minimal);
extern inline void bgc_vector3_make_opposite_fp32(BgcVector3FP32* vector);
extern inline void bgc_vector3_make_opposite_fp64(BgcVector3FP64* vector);
extern inline void bgc_vector3_maximize_fp32(const BgcVector3FP32* vector, BgcVector3FP32* maximal);
extern inline void bgc_vector3_maximize_fp64(const BgcVector3FP64* vector, BgcVector3FP64* maximal);
extern inline void bgc_vector3_get_opposite_fp32(const BgcVector3FP32* vector, BgcVector3FP32* opposite);
extern inline void bgc_vector3_get_opposite_fp64(const BgcVector3FP64* vector, BgcVector3FP64* opposite);
extern inline int bgc_vector3_normalize_fp32(BgcVector3FP32* vector);
extern inline int bgc_vector3_normalize_fp64(BgcVector3FP64* vector);
extern inline int bgc_vector3_get_normalized_fp32(const BgcVector3FP32* vector, BgcVector3FP32* normalized);
extern inline int bgc_vector3_get_normalized_fp64(const BgcVector3FP64* vector, BgcVector3FP64* normalized);
extern inline float bgc_vector3_get_scalar_product_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2);
extern inline double bgc_vector3_get_scalar_product_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2);
@ -96,9 +87,18 @@ extern inline int bgc_vector3_are_close_enough_fp64(const BgcVector3FP64* vector
extern inline int bgc_vector3_are_close_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2);
extern inline int bgc_vector3_are_close_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2);
extern inline int bgc_vector3_are_parallel_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2);
extern inline int bgc_vector3_are_parallel_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2);
extern inline int bgc_vector3_are_orthogonal_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2);
extern inline int bgc_vector3_are_orthogonal_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2);
extern inline int bgc_vector3_get_attitude_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2);
extern inline int bgc_vector3_get_attitude_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2);
// =================== Angle ==================== //
float bgc_vector3_get_angle_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const BgcAngleUnitEnum unit)
float bgc_vector3_get_angle_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const BgcAngleUnitEnum angle_unit)
{
const float square_modulus1 = bgc_vector3_get_square_modulus_fp32(vector1);
@ -122,10 +122,10 @@ float bgc_vector3_get_angle_fp32(const BgcVector3FP32* vector1, const BgcVector3
const float cross = bgc_vector3_get_modulus_fp32(&cross_product);
return bgc_radians_to_units_fp32(atan2f(cross, scalar), unit);
return bgc_radians_to_units_fp32(atan2f(cross, scalar), angle_unit);
}
double bgc_vector3_get_angle_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const BgcAngleUnitEnum unit)
double bgc_vector3_get_angle_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const BgcAngleUnitEnum angle_unit)
{
const double square_modulus1 = bgc_vector3_get_square_modulus_fp64(vector1);
@ -149,5 +149,5 @@ double bgc_vector3_get_angle_fp64(const BgcVector3FP64* vector1, const BgcVector
const double cross = bgc_vector3_get_modulus_fp64(&cross_product);
return bgc_radians_to_units_fp64(atan2(cross, scalar), unit);
return bgc_radians_to_units_fp64(atan2(cross, scalar), angle_unit);
}

570
basic-geometry/vector3.h
View file

@ -50,94 +50,6 @@ inline void bgc_vector3_set_values_fp64(const double x1, const double x2, const
destination->x3 = x3;
}
// ================= Directions ================= //
inline int bgc_vector3_get_direction_fp32(const int direction, BgcVector3FP32* vector)
{
switch (direction) {
case BGC_DIRECTION_X1:
vector->x1 = 1.0f;
vector->x2 = 0.0f;
vector->x3 = 0.0f;
return 1;
case BGC_DIRECTION_X2:
vector->x1 = 0.0f;
vector->x2 = 1.0f;
vector->x3 = 0.0f;
return 1;
case BGC_DIRECTION_X3:
vector->x1 = 0.0f;
vector->x2 = 0.0f;
vector->x3 = 1.0f;
return 1;
case -BGC_DIRECTION_X1:
vector->x1 = -1.0f;
vector->x2 = 0.0f;
vector->x3 = 0.0f;
return 1;
case -BGC_DIRECTION_X2:
vector->x1 = 0.0f;
vector->x2 = -1.0f;
vector->x3 = 0.0f;
return 1;
case -BGC_DIRECTION_X3:
vector->x1 = 0.0f;
vector->x2 = 0.0f;
vector->x3 = -1.0f;
return 1;
}
return 0;
}
inline int bgc_vector3_get_direction_fp64(const int direction, BgcVector3FP64* vector)
{
switch (direction) {
case BGC_DIRECTION_X1:
vector->x1 = 1.0;
vector->x2 = 0.0;
vector->x3 = 0.0;
return 1;
case BGC_DIRECTION_X2:
vector->x1 = 0.0;
vector->x2 = 1.0;
vector->x3 = 0.0;
return 1;
case BGC_DIRECTION_X3:
vector->x1 = 0.0;
vector->x2 = 0.0;
vector->x3 = 1.0;
return 1;
case -BGC_DIRECTION_X1:
vector->x1 = -1.0;
vector->x2 = 0.0;
vector->x3 = 0.0;
return 1;
case -BGC_DIRECTION_X2:
vector->x1 = 0.0;
vector->x2 = -1.0;
vector->x3 = 0.0;
return 1;
case -BGC_DIRECTION_X3:
vector->x1 = 0.0;
vector->x2 = 0.0;
vector->x3 = -1.0;
return 1;
}
return 0;
}
// ================== Modulus =================== //
inline float bgc_vector3_get_square_modulus_fp32(const BgcVector3FP32* vector)
@ -246,114 +158,6 @@ inline void bgc_vector3_convert_fp32_to_fp64(const BgcVector3FP32* source, BgcVe
destination->x3 = source->x3;
}
// ================== Reverse =================== //
inline void bgc_vector3_reverse_fp32(const BgcVector3FP32* vector, BgcVector3FP32* reverse)
{
reverse->x1 = -vector->x1;
reverse->x2 = -vector->x2;
reverse->x3 = -vector->x3;
}
inline void bgc_vector3_reverse_fp64(const BgcVector3FP64* vector, BgcVector3FP64* reverse)
{
reverse->x1 = -vector->x1;
reverse->x2 = -vector->x2;
reverse->x3 = -vector->x3;
}
// ================= Normalize ================== //
inline int bgc_vector3_normalize_fp32(BgcVector3FP32* vector)
{
const float square_modulus = bgc_vector3_get_square_modulus_fp32(vector);
if (bgc_is_sqare_unit_fp32(square_modulus)) {
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
return 0;
}
const float multiplicand = sqrtf(1.0f / square_modulus);
vector->x1 *= multiplicand;
vector->x2 *= multiplicand;
vector->x3 *= multiplicand;
return 1;
}
inline int bgc_vector3_normalize_fp64(BgcVector3FP64* vector)
{
const double square_modulus = bgc_vector3_get_square_modulus_fp64(vector);
if (bgc_is_sqare_unit_fp64(square_modulus)) {
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
return 0;
}
const double multiplicand = sqrt(1.0 / square_modulus);
vector->x1 *= multiplicand;
vector->x2 *= multiplicand;
vector->x3 *= multiplicand;
return 1;
}
inline int bgc_vector3_get_normalized_fp32(const BgcVector3FP32* vector, BgcVector3FP32* normalized)
{
const float square_modulus = bgc_vector3_get_square_modulus_fp32(vector);
if (bgc_is_sqare_unit_fp32(square_modulus)) {
normalized->x1 = vector->x1;
normalized->x2 = vector->x2;
normalized->x3 = vector->x3;
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
return 0;
}
const float multiplicand = sqrtf(1.0f / square_modulus);
normalized->x1 = vector->x1 * multiplicand;
normalized->x2 = vector->x2 * multiplicand;
normalized->x3 = vector->x3 * multiplicand;
return 1;
}
inline int bgc_vector3_get_normalized_fp64(const BgcVector3FP64* vector, BgcVector3FP64* normalized)
{
const double square_modulus = bgc_vector3_get_square_modulus_fp64(vector);
if (bgc_is_sqare_unit_fp64(square_modulus)) {
normalized->x1 = vector->x1;
normalized->x2 = vector->x2;
normalized->x3 = vector->x3;
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
return 0;
}
const double multiplicand = sqrt(1.0 / square_modulus);
normalized->x1 = vector->x1 * multiplicand;
normalized->x2 = vector->x2 * multiplicand;
normalized->x3 = vector->x3 * multiplicand;
return 1;
}
// ==================== Add ===================== //
inline void bgc_vector3_add_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, BgcVector3FP32* sum)
@ -372,18 +176,18 @@ inline void bgc_vector3_add_fp64(const BgcVector3FP64* vector1, const BgcVector3
// ================= Add scaled ================= //
inline void bgc_vector3_add_scaled_fp32(const BgcVector3FP32* basic_vector, const BgcVector3FP32* scalable_vector, const float scale, BgcVector3FP32* result)
inline void bgc_vector3_add_scaled_fp32(const BgcVector3FP32* basic_vector, const BgcVector3FP32* scalable_vector, const float scale, BgcVector3FP32* sum)
{
result->x1 = basic_vector->x1 + scalable_vector->x1 * scale;
result->x2 = basic_vector->x2 + scalable_vector->x2 * scale;
result->x3 = basic_vector->x3 + scalable_vector->x3 * scale;
sum->x1 = basic_vector->x1 + scalable_vector->x1 * scale;
sum->x2 = basic_vector->x2 + scalable_vector->x2 * scale;
sum->x3 = basic_vector->x3 + scalable_vector->x3 * scale;
}
inline void bgc_vector3_add_scaled_fp64(const BgcVector3FP64* basic_vector, const BgcVector3FP64* scalable_vector, const double scale, BgcVector3FP64* result)
inline void bgc_vector3_add_scaled_fp64(const BgcVector3FP64* basic_vector, const BgcVector3FP64* scalable_vector, const double scale, BgcVector3FP64* sum)
{
result->x1 = basic_vector->x1 + scalable_vector->x1 * scale;
result->x2 = basic_vector->x2 + scalable_vector->x2 * scale;
result->x3 = basic_vector->x3 + scalable_vector->x3 * scale;
sum->x1 = basic_vector->x1 + scalable_vector->x1 * scale;
sum->x2 = basic_vector->x2 + scalable_vector->x2 * scale;
sum->x3 = basic_vector->x3 + scalable_vector->x3 * scale;
}
// ================== Subtract ================== //
@ -402,22 +206,6 @@ inline void bgc_vector3_subtract_fp64(const BgcVector3FP64* minuend, const BgcVe
difference->x3 = minuend->x3 - subtrahend->x3;
}
// ============== Subtract scaled =============== //
inline void bgc_vector3_subtract_scaled_fp32(const BgcVector3FP32* basic_vector, const BgcVector3FP32* scalable_vector, const float scale, BgcVector3FP32* result)
{
result->x1 = basic_vector->x1 - scalable_vector->x1 * scale;
result->x2 = basic_vector->x2 - scalable_vector->x2 * scale;
result->x3 = basic_vector->x3 - scalable_vector->x3 * scale;
}
inline void bgc_vector3_subtract_scaled_fp64(const BgcVector3FP64* basic_vector, const BgcVector3FP64* scalable_vector, const double scale, BgcVector3FP64* result)
{
result->x1 = basic_vector->x1 - scalable_vector->x1 * scale;
result->x2 = basic_vector->x2 - scalable_vector->x2 * scale;
result->x3 = basic_vector->x3 - scalable_vector->x3 * scale;
}
// ================== Multiply ================== //
inline void bgc_vector3_multiply_fp32(const BgcVector3FP32* multiplicand, const float multiplier, BgcVector3FP32* product)
@ -448,39 +236,39 @@ inline void bgc_vector3_divide_fp64(const BgcVector3FP64* dividend, const double
// ================== Average2 ================== //
inline void bgc_vector3_get_mean_of_two_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, BgcVector3FP32* result)
inline void bgc_vector3_get_mean_of_two_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, BgcVector3FP32* mean)
{
result->x1 = (vector1->x1 + vector2->x1) * 0.5f;
result->x2 = (vector1->x2 + vector2->x2) * 0.5f;
result->x3 = (vector1->x3 + vector2->x3) * 0.5f;
mean->x1 = (vector1->x1 + vector2->x1) * 0.5f;
mean->x2 = (vector1->x2 + vector2->x2) * 0.5f;
mean->x3 = (vector1->x3 + vector2->x3) * 0.5f;
}
inline void bgc_vector3_get_mean_of_two_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, BgcVector3FP64* result)
inline void bgc_vector3_get_mean_of_two_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, BgcVector3FP64* mean)
{
result->x1 = (vector1->x1 + vector2->x1) * 0.5;
result->x2 = (vector1->x2 + vector2->x2) * 0.5;
result->x3 = (vector1->x3 + vector2->x3) * 0.5;
mean->x1 = (vector1->x1 + vector2->x1) * 0.5;
mean->x2 = (vector1->x2 + vector2->x2) * 0.5;
mean->x3 = (vector1->x3 + vector2->x3) * 0.5;
}
// ================== Average3 ================== //
inline void bgc_vector3_get_mean_of_three_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const BgcVector3FP32* vector3, BgcVector3FP32* result)
inline void bgc_vector3_get_mean_of_three_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const BgcVector3FP32* vector3, BgcVector3FP32* mean)
{
result->x1 = (vector1->x1 + vector2->x1 + vector3->x1) * BGC_ONE_THIRD_FP32;
result->x2 = (vector1->x2 + vector2->x2 + vector3->x2) * BGC_ONE_THIRD_FP32;
result->x3 = (vector1->x3 + vector2->x3 + vector3->x3) * BGC_ONE_THIRD_FP32;
mean->x1 = (vector1->x1 + vector2->x1 + vector3->x1) * BGC_ONE_THIRD_FP32;
mean->x2 = (vector1->x2 + vector2->x2 + vector3->x2) * BGC_ONE_THIRD_FP32;
mean->x3 = (vector1->x3 + vector2->x3 + vector3->x3) * BGC_ONE_THIRD_FP32;
}
inline void bgc_vector3_get_mean_of_three_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const BgcVector3FP64* vector3, BgcVector3FP64* result)
inline void bgc_vector3_get_mean_of_three_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const BgcVector3FP64* vector3, BgcVector3FP64* mean)
{
result->x1 = (vector1->x1 + vector2->x1 + vector3->x1) * BGC_ONE_THIRD_FP64;
result->x2 = (vector1->x2 + vector2->x2 + vector3->x2) * BGC_ONE_THIRD_FP64;
result->x3 = (vector1->x3 + vector2->x3 + vector3->x3) * BGC_ONE_THIRD_FP64;
mean->x1 = (vector1->x1 + vector2->x1 + vector3->x1) * BGC_ONE_THIRD_FP64;
mean->x2 = (vector1->x2 + vector2->x2 + vector3->x2) * BGC_ONE_THIRD_FP64;
mean->x3 = (vector1->x3 + vector2->x3 + vector3->x3) * BGC_ONE_THIRD_FP64;
}
// =================== Linear =================== //
inline void bgc_vector3_interpolate_linearly_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const float phase, BgcVector3FP32* interpolation)
inline void bgc_vector3_interpolate_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const float phase, BgcVector3FP32* interpolation)
{
const float counterphase = 1.0f - phase;
@ -489,7 +277,7 @@ inline void bgc_vector3_interpolate_linearly_fp32(const BgcVector3FP32* vector1,
interpolation->x3 = vector1->x3 * counterphase + vector2->x3 * phase;
}
inline void bgc_vector3_interpolate_linearly_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const double phase, BgcVector3FP64* interpolation)
inline void bgc_vector3_interpolate_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const double phase, BgcVector3FP64* interpolation)
{
const double counterphase = 1.0 - phase;
@ -498,68 +286,114 @@ inline void bgc_vector3_interpolate_linearly_fp64(const BgcVector3FP64* vector1,
interpolation->x3 = vector1->x3 * counterphase + vector2->x3 * phase;
}
// ================== Minimal =================== //
// ================== Negative ================== //
inline void bgc_vector3_minimize_fp32(const BgcVector3FP32* vector, BgcVector3FP32* minimal)
inline void bgc_vector3_make_opposite_fp32(BgcVector3FP32* vector)
{
if (vector->x1 < minimal->x1) {
minimal->x1 = vector->x1;
}
if (vector->x2 < minimal->x2) {
minimal->x2 = vector->x2;
}
if (vector->x3 < minimal->x3) {
minimal->x3 = vector->x3;
}
vector->x1 = -vector->x1;
vector->x2 = -vector->x2;
vector->x3 = -vector->x3;
}
inline void bgc_vector3_minimize_fp64(const BgcVector3FP64* vector, BgcVector3FP64* minimal)
inline void bgc_vector3_make_opposite_fp64(BgcVector3FP64* vector)
{
if (vector->x1 < minimal->x1) {
minimal->x1 = vector->x1;
}
if (vector->x2 < minimal->x2) {
minimal->x2 = vector->x2;
}
if (vector->x3 < minimal->x3) {
minimal->x3 = vector->x3;
}
vector->x1 = -vector->x1;
vector->x2 = -vector->x2;
vector->x3 = -vector->x3;
}
// ================== Maximal =================== //
inline void bgc_vector3_maximize_fp32(const BgcVector3FP32* vector, BgcVector3FP32* maximal)
inline void bgc_vector3_get_opposite_fp32(const BgcVector3FP32* vector, BgcVector3FP32* opposite)
{
if (vector->x1 > maximal->x1) {
maximal->x1 = vector->x1;
}
if (vector->x2 > maximal->x2) {
maximal->x2 = vector->x2;
}
if (vector->x3 > maximal->x3) {
maximal->x3 = vector->x3;
}
opposite->x1 = -vector->x1;
opposite->x2 = -vector->x2;
opposite->x3 = -vector->x3;
}
inline void bgc_vector3_maximize_fp64(const BgcVector3FP64* vector, BgcVector3FP64* maximal)
inline void bgc_vector3_get_opposite_fp64(const BgcVector3FP64* vector, BgcVector3FP64* opposite)
{
if (vector->x1 > maximal->x1) {
maximal->x1 = vector->x1;
opposite->x1 = -vector->x1;
opposite->x2 = -vector->x2;
opposite->x3 = -vector->x3;
}
// ================= Normalize ================== //
inline int bgc_vector3_normalize_fp32(BgcVector3FP32* vector)
{
const float square_modulus = bgc_vector3_get_square_modulus_fp32(vector);
if (bgc_is_sqare_unit_fp32(square_modulus)) {
return 1;
}
if (vector->x2 > maximal->x2) {
maximal->x2 = vector->x2;
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
return 0;
}
if (vector->x3 > maximal->x3) {
maximal->x3 = vector->x3;
const float multiplier = sqrtf(1.0f / square_modulus);
vector->x1 *= multiplier;
vector->x2 *= multiplier;
vector->x3 *= multiplier;
return 1;
}
inline int bgc_vector3_normalize_fp64(BgcVector3FP64* vector)
{
const double square_modulus = bgc_vector3_get_square_modulus_fp64(vector);
if (bgc_is_sqare_unit_fp64(square_modulus)) {
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
return 0;
}
const double multiplier = sqrt(1.0 / square_modulus);
vector->x1 *= multiplier;
vector->x2 *= multiplier;
vector->x3 *= multiplier;
return 1;
}
inline int bgc_vector3_get_normalized_fp32(const BgcVector3FP32* vector, BgcVector3FP32* normalized)
{
const float square_modulus = bgc_vector3_get_square_modulus_fp32(vector);
if (bgc_is_sqare_unit_fp32(square_modulus)) {
bgc_vector3_copy_fp32(vector, normalized);
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
bgc_vector3_reset_fp32(normalized);
return 0;
}
bgc_vector3_multiply_fp32(vector, sqrtf(1.0f / square_modulus), normalized);
return 1;
}
inline int bgc_vector3_get_normalized_fp64(const BgcVector3FP64* vector, BgcVector3FP64* normalized)
{
const double square_modulus = bgc_vector3_get_square_modulus_fp64(vector);
if (bgc_is_sqare_unit_fp64(square_modulus)) {
bgc_vector3_copy_fp64(vector, normalized);
return 1;
}
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
bgc_vector3_reset_fp64(normalized);
return 0;
}
bgc_vector3_multiply_fp64(vector, sqrt(1.0 / square_modulus), normalized);
return 1;
}
// =============== Scalar Product =============== //
@ -592,55 +426,55 @@ inline double bgc_vector3_get_triple_product_fp64(const BgcVector3FP64* vector1,
// =============== Cross Product ================ //
inline void bgc_vector3_get_cross_product_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, BgcVector3FP32* result)
inline void bgc_vector3_get_cross_product_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, BgcVector3FP32* product)
{
const float x1 = vector1->x2 * vector2->x3 - vector1->x3 * vector2->x2;
const float x2 = vector1->x3 * vector2->x1 - vector1->x1 * vector2->x3;
const float x3 = vector1->x1 * vector2->x2 - vector1->x2 * vector2->x1;
result->x1 = x1;
result->x2 = x2;
result->x3 = x3;
product->x1 = x1;
product->x2 = x2;
product->x3 = x3;
}
inline void bgc_vector3_get_cross_product_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, BgcVector3FP64* result)
inline void bgc_vector3_get_cross_product_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, BgcVector3FP64* product)
{
const double x1 = vector1->x2 * vector2->x3 - vector1->x3 * vector2->x2;
const double x2 = vector1->x3 * vector2->x1 - vector1->x1 * vector2->x3;
const double x3 = vector1->x1 * vector2->x2 - vector1->x2 * vector2->x1;
result->x1 = x1;
result->x2 = x2;
result->x3 = x3;
product->x1 = x1;
product->x2 = x2;
product->x3 = x3;
}
// ============ Double Cross Product ============ //
inline void bgc_vector3_get_double_cross_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const BgcVector3FP32* vector3, BgcVector3FP32* result)
inline void bgc_vector3_get_double_cross_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const BgcVector3FP32* vector3, BgcVector3FP32* product)
{
const float ac = bgc_vector3_get_scalar_product_fp32(vector1, vector3);
const float ab = bgc_vector3_get_scalar_product_fp32(vector1, vector2);
result->x1 = vector2->x1 * ac - vector3->x1 * ab;
result->x2 = vector2->x2 * ac - vector3->x2 * ab;
result->x3 = vector2->x3 * ac - vector3->x3 * ab;
product->x1 = vector2->x1 * ac - vector3->x1 * ab;
product->x2 = vector2->x2 * ac - vector3->x2 * ab;
product->x3 = vector2->x3 * ac - vector3->x3 * ab;
}
inline void bgc_vector3_get_double_cross_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const BgcVector3FP64* vector3, BgcVector3FP64* result)
inline void bgc_vector3_get_double_cross_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const BgcVector3FP64* vector3, BgcVector3FP64* product)
{
const double ac = bgc_vector3_get_scalar_product_fp64(vector1, vector3);
const double ab = bgc_vector3_get_scalar_product_fp64(vector1, vector2);
result->x1 = vector2->x1 * ac - vector3->x1 * ab;
result->x2 = vector2->x2 * ac - vector3->x2 * ab;
result->x3 = vector2->x3 * ac - vector3->x3 * ab;
product->x1 = vector2->x1 * ac - vector3->x1 * ab;
product->x2 = vector2->x2 * ac - vector3->x2 * ab;
product->x3 = vector2->x3 * ac - vector3->x3 * ab;
}
// =================== Angle ==================== //
float bgc_vector3_get_angle_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const BgcAngleUnitEnum unit);
float bgc_vector3_get_angle_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const BgcAngleUnitEnum angle_unit);
double bgc_vector3_get_angle_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const BgcAngleUnitEnum unit);
double bgc_vector3_get_angle_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const BgcAngleUnitEnum angle_unit);
// =============== Square Distance ============== //
@ -676,14 +510,14 @@ inline double bgc_vector3_get_distance_fp64(const BgcVector3FP64* vector1, const
// ============== Are Close Enough ============== //
inline int bgc_vector3_are_close_enough_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const float distance)
inline int bgc_vector3_are_close_enough_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2, const float distance_limit)
{
return bgc_vector3_get_square_distance_fp32(vector1, vector2) <= distance * distance;
return bgc_vector3_get_square_distance_fp32(vector1, vector2) <= distance_limit * distance_limit;
}
inline int bgc_vector3_are_close_enough_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const double distance)
inline int bgc_vector3_are_close_enough_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2, const double distance_limit)
{
return bgc_vector3_get_square_distance_fp64(vector1, vector2) <= distance * distance;
return bgc_vector3_get_square_distance_fp64(vector1, vector2) <= distance_limit * distance_limit;
}
// ================== Are Close ================= //
@ -711,7 +545,129 @@ inline int bgc_vector3_are_close_fp64(const BgcVector3FP64* vector1, const BgcVe
return square_distance <= BGC_SQUARE_EPSYLON_FP64;
}
return square_distance <= BGC_SQUARE_EPSYLON_FP32 * square_modulus1 && square_distance <= BGC_SQUARE_EPSYLON_FP32 * square_modulus2;
return square_distance <= BGC_SQUARE_EPSYLON_FP64 * square_modulus1 && square_distance <= BGC_SQUARE_EPSYLON_FP64 * square_modulus2;
}
// ================== Parallel ================== //
inline int bgc_vector3_are_parallel_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2)
{
const float square_modulus1 = bgc_vector3_get_square_modulus_fp32(vector1);
const float square_modulus2 = bgc_vector3_get_square_modulus_fp32(vector2);
if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP32 || square_modulus2 <= BGC_SQUARE_EPSYLON_FP32) {
return 1;
}
BgcVector3FP32 product;
bgc_vector3_get_cross_product_fp32(vector1, vector2, &product);
return bgc_vector3_get_square_modulus_fp32(&product) <= BGC_SQUARE_EPSYLON_FP32 * square_modulus1 * square_modulus2;
}
inline int bgc_vector3_are_parallel_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2)
{
const double square_modulus1 = bgc_vector3_get_square_modulus_fp64(vector1);
const double square_modulus2 = bgc_vector3_get_square_modulus_fp64(vector2);
if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP64 || square_modulus2 <= BGC_SQUARE_EPSYLON_FP64) {
return 1;
}
BgcVector3FP64 product;
bgc_vector3_get_cross_product_fp64(vector1, vector2, &product);
return bgc_vector3_get_square_modulus_fp64(&product) <= BGC_SQUARE_EPSYLON_FP64 * square_modulus1 * square_modulus2;
}
// ================= Orthogonal ================= //
inline int bgc_vector3_are_orthogonal_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2)
{
const float square_modulus1 = bgc_vector3_get_square_modulus_fp32(vector1);
const float square_modulus2 = bgc_vector3_get_square_modulus_fp32(vector2);
if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP32 || square_modulus2 <= BGC_SQUARE_EPSYLON_FP32) {
return 1;
}
const float scalar_product = bgc_vector3_get_scalar_product_fp32(vector1, vector2);
return scalar_product * scalar_product <= BGC_SQUARE_EPSYLON_FP32 * square_modulus1 * square_modulus2;
}
inline int bgc_vector3_are_orthogonal_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2)
{
const double square_modulus1 = bgc_vector3_get_square_modulus_fp64(vector1);
const double square_modulus2 = bgc_vector3_get_square_modulus_fp64(vector2);
if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP64 || square_modulus2 <= BGC_SQUARE_EPSYLON_FP64) {
return 1;
}
const double scalar_product = bgc_vector3_get_scalar_product_fp64(vector1, vector2);
return scalar_product * scalar_product <= BGC_SQUARE_EPSYLON_FP64 * square_modulus1 * square_modulus2;
}
// ================== Attitude ================== //
inline int bgc_vector3_get_attitude_fp32(const BgcVector3FP32* vector1, const BgcVector3FP32* vector2)
{
const float square_modulus1 = bgc_vector3_get_square_modulus_fp32(vector1);
const float square_modulus2 = bgc_vector3_get_square_modulus_fp32(vector2);
if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP32 || square_modulus2 <= BGC_SQUARE_EPSYLON_FP32) {
return BGC_ATTITUDE_ZERO;
}
const float square_limit = BGC_SQUARE_EPSYLON_FP32 * square_modulus1 * square_modulus2;
const float scalar_product = bgc_vector3_get_scalar_product_fp32(vector1, vector2);
if (scalar_product * scalar_product <= square_limit) {
return BGC_ATTITUDE_ORTHOGONAL;
}
BgcVector3FP32 product;
bgc_vector3_get_cross_product_fp32(vector1, vector2, &product);
if (bgc_vector3_get_square_modulus_fp32(&product) > square_limit) {
return BGC_ATTITUDE_ANY;
}
return scalar_product > 0.0f ? BGC_ATTITUDE_CO_DIRECTIONAL : BGC_ATTITUDE_COUNTER_DIRECTIONAL;
}
inline int bgc_vector3_get_attitude_fp64(const BgcVector3FP64* vector1, const BgcVector3FP64* vector2)
{
const double square_modulus1 = bgc_vector3_get_square_modulus_fp64(vector1);
const double square_modulus2 = bgc_vector3_get_square_modulus_fp64(vector2);
if (square_modulus1 <= BGC_SQUARE_EPSYLON_FP64 || square_modulus2 <= BGC_SQUARE_EPSYLON_FP64) {
return BGC_ATTITUDE_ZERO;
}
const double square_limit = BGC_SQUARE_EPSYLON_FP64 * square_modulus1 * square_modulus2;
const double scalar_product = bgc_vector3_get_scalar_product_fp64(vector1, vector2);
if (scalar_product * scalar_product <= square_limit) {
return BGC_ATTITUDE_ORTHOGONAL;
}
BgcVector3FP64 product;
bgc_vector3_get_cross_product_fp64(vector1, vector2, &product);
if (bgc_vector3_get_square_modulus_fp64(&product) > square_limit) {
return BGC_ATTITUDE_ANY;
}
return scalar_product > 0.0 ? BGC_ATTITUDE_CO_DIRECTIONAL : BGC_ATTITUDE_COUNTER_DIRECTIONAL;
}
#endif

128
basic-geometry/versor.c
View file

@ -28,11 +28,23 @@ extern inline int bgc_versor_is_identity_fp64(const BgcVersorFP64* versor);
extern inline void bgc_versor_convert_fp64_to_fp32(const BgcVersorFP64* source, BgcVersorFP32* destination);
extern inline void bgc_versor_convert_fp32_to_fp64(const BgcVersorFP32* source, BgcVersorFP64* destination);
extern inline void bgc_versor_shorten_fp32(const BgcVersorFP32* versor, BgcVersorFP32* shortened);
extern inline void bgc_versor_shorten_fp64(const BgcVersorFP64* versor, BgcVersorFP64* shortened);
extern inline void bgc_versor_shorten_fp32(BgcVersorFP32* versor);
extern inline void bgc_versor_shorten_fp64(BgcVersorFP64* versor);
extern inline void bgc_versor_invert_fp32(const BgcVersorFP32* versor, BgcVersorFP32* inverted);
extern inline void bgc_versor_invert_fp64(const BgcVersorFP64* versor, BgcVersorFP64* inverted);
extern inline void bgc_versor_get_shortened_fp32(const BgcVersorFP32* versor, BgcVersorFP32* shortened);
extern inline void bgc_versor_get_shortened_fp64(const BgcVersorFP64* versor, BgcVersorFP64* shortened);
extern inline void bgc_versor_make_opposite_fp32(BgcVersorFP32* versor);
extern inline void bgc_versor_make_opposite_fp64(BgcVersorFP64* versor);
extern inline void bgc_versor_get_opposite_fp32(const BgcVersorFP32* versor, BgcVersorFP32* opposite);
extern inline void bgc_versor_get_opposite_fp64(const BgcVersorFP64* versor, BgcVersorFP64* opposite);
extern inline void bgc_versor_invert_fp32(BgcVersorFP32* versor);
extern inline void bgc_versor_invert_fp64(BgcVersorFP64* versor);
extern inline void bgc_versor_get_inverse_fp32(const BgcVersorFP32* versor, BgcVersorFP32* inverse);
extern inline void bgc_versor_get_inverse_fp64(const BgcVersorFP64* versor, BgcVersorFP64* inverse);
extern inline void bgc_versor_combine_fp32(const BgcVersorFP32* second, const BgcVersorFP32* first, BgcVersorFP32* result);
extern inline void bgc_versor_combine_fp64(const BgcVersorFP64* second, const BgcVersorFP64* first, BgcVersorFP64* result);
@ -49,8 +61,8 @@ extern inline void bgc_versor_get_rotation_matrix_fp64(const BgcVersorFP64* vers
extern inline void bgc_versor_get_reverse_matrix_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* matrix);
extern inline void bgc_versor_get_reverse_matrix_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* matrix);
extern inline void bgc_versor_get_both_matrixes_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* rotation, BgcMatrix3x3FP32* reverse);
extern inline void bgc_versor_get_both_matrixes_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* rotation, BgcMatrix3x3FP64* reverse);
extern inline void bgc_versor_get_both_matrices_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* rotation, BgcMatrix3x3FP32* reverse);
extern inline void bgc_versor_get_both_matrices_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* rotation, BgcMatrix3x3FP64* reverse);
extern inline void bgc_versor_turn_vector_fp32(const BgcVersorFP32* versor, const BgcVector3FP32* vector, BgcVector3FP32* result);
extern inline void bgc_versor_turn_vector_fp64(const BgcVersorFP64* versor, const BgcVector3FP64* vector, BgcVector3FP64* result);
@ -63,44 +75,44 @@ extern inline int bgc_versor_are_close_fp64(const BgcVersorFP64* versor1, const
// ================= Normalize ================== //
void _bgc_versor_normalize_fp32(const float square_modulus, _BgcDarkTwinVersorFP32* twin)
void _bgc_versor_normalize_fp32(const float square_modulus, BgcVersorFP32* versor)
{
// (square_modulus != square_modulus) is true when square_modulus is NaN
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
twin->s0 = 1.0f;
twin->x1 = 0.0f;
twin->x2 = 0.0f;
twin->x3 = 0.0f;
versor->_s0 = 1.0f;
versor->_x1 = 0.0f;
versor->_x2 = 0.0f;
versor->_x3 = 0.0f;
return;
}
const float multiplier = sqrtf(1.0f / square_modulus);
twin->s0 *= multiplier;
twin->x1 *= multiplier;
twin->x2 *= multiplier;
twin->x3 *= multiplier;
versor->_s0 *= multiplier;
versor->_x1 *= multiplier;
versor->_x2 *= multiplier;
versor->_x3 *= multiplier;
}
void _bgc_versor_normalize_fp64(const double square_modulus, _BgcDarkTwinVersorFP64* twin)
void _bgc_versor_normalize_fp64(const double square_modulus, BgcVersorFP64* versor)
{
// (square_modulus != square_modulus) is true when square_modulus is NaN
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
twin->s0 = 1.0;
twin->x1 = 0.0;
twin->x2 = 0.0;
twin->x3 = 0.0;
versor->_s0 = 1.0;
versor->_x1 = 0.0;
versor->_x2 = 0.0;
versor->_x3 = 0.0;
return;
}
const double multiplier = sqrt(1.0 / square_modulus);
twin->s0 *= multiplier;
twin->x1 *= multiplier;
twin->x2 *= multiplier;
twin->x3 *= multiplier;
versor->_s0 *= multiplier;
versor->_x1 *= multiplier;
versor->_x2 *= multiplier;
versor->_x3 *= multiplier;
}
// ================== Set Turn ================== //
@ -249,7 +261,7 @@ inline int _bgc_versor_validate_basis_fp32(const float primary_square_modulus, c
return BGC_FAILED;
}
if (orthogonal_square_modulus / (primary_square_modulus * auxiliary_square_modulus) <= BGC_SQUARE_EPSYLON_FP32) {
if (orthogonal_square_modulus <= BGC_SQUARE_EPSYLON_FP32 * primary_square_modulus * auxiliary_square_modulus) {
//TODO: add error code for: primary_vector and auxiliary_vector are parallel
return BGC_FAILED;
}
@ -269,7 +281,7 @@ inline int _bgc_versor_validate_basis_fp64(const double primary_square_modulus,
return BGC_FAILED;
}
if (orthogonal_square_modulus / (primary_square_modulus * auxiliary_square_modulus) <= BGC_SQUARE_EPSYLON_FP64) {
if (orthogonal_square_modulus <= BGC_SQUARE_EPSYLON_FP64 * primary_square_modulus * auxiliary_square_modulus) {
//TODO: add error code for: primary_vector and auxiliary_vector are parallel
return BGC_FAILED;
}
@ -423,7 +435,7 @@ int bgc_versor_make_basis_difference_fp64(
void bgc_versor_get_exponation_fp32(const BgcVersorFP32* base, const float exponent, BgcVersorFP32* power)
{
const float square_vector = base->x1 * base->x1 + base->x2 * base->x2 + base->x3 * base->x3;
const float square_vector = base->_x1 * base->_x1 + base->_x2 * base->_x2 + base->_x3 * base->_x3;
if (square_vector <= BGC_SQUARE_EPSYLON_FP32 || square_vector != square_vector) {
bgc_versor_reset_fp32(power);
@ -432,16 +444,16 @@ void bgc_versor_get_exponation_fp32(const BgcVersorFP32* base, const float expon
const float vector_modulus = sqrtf(square_vector);
const float angle = atan2f(vector_modulus, base->s0) * exponent;
const float angle = atan2f(vector_modulus, base->_s0) * exponent;
const float multiplier = sinf(angle) / vector_modulus;
bgc_versor_set_values_fp32(cosf(angle), base->x1 * multiplier, base->x2 * multiplier, base->x3 * multiplier, power);
bgc_versor_set_values_fp32(cosf(angle), base->_x1 * multiplier, base->_x2 * multiplier, base->_x3 * multiplier, power);
}
void bgc_versor_get_exponation_fp64(const BgcVersorFP64* base, const double exponent, BgcVersorFP64* power)
{
const double square_vector = base->x1 * base->x1 + base->x2 * base->x2 + base->x3 * base->x3;
const double square_vector = base->_x1 * base->_x1 + base->_x2 * base->_x2 + base->_x3 * base->_x3;
if (square_vector <= BGC_SQUARE_EPSYLON_FP64 || square_vector != square_vector) {
bgc_versor_reset_fp64(power);
@ -450,21 +462,21 @@ void bgc_versor_get_exponation_fp64(const BgcVersorFP64* base, const double expo
const double vector_modulus = sqrt(square_vector);
const double angle = atan2(vector_modulus, base->s0) * exponent;
const double angle = atan2(vector_modulus, base->_s0) * exponent;
const double multiplier = sin(angle) / vector_modulus;
bgc_versor_set_values_fp64(cos(angle), base->x1 * multiplier, base->x2 * multiplier, base->x3 * multiplier, power);
bgc_versor_set_values_fp64(cos(angle), base->_x1 * multiplier, base->_x2 * multiplier, base->_x3 * multiplier, power);
}
// ============ Sphere Interpolation ============ //
void bgc_versor_spherically_interpolate_fp32(const BgcVersorFP32* start, const BgcVersorFP32* end, const float phase, BgcVersorFP32* result)
{
const float delta_s0 = (end->s0 * start->s0 + end->x1 * start->x1) + (end->x2 * start->x2 + end->x3 * start->x3);
const float delta_x1 = (end->x1 * start->s0 + end->x3 * start->x2) - (end->s0 * start->x1 + end->x2 * start->x3);
const float delta_x2 = (end->x2 * start->s0 + end->x1 * start->x3) - (end->s0 * start->x2 + end->x3 * start->x1);
const float delta_x3 = (end->x3 * start->s0 + end->x2 * start->x1) - (end->s0 * start->x3 + end->x1 * start->x2);
const float delta_s0 = (end->_s0 * start->_s0 + end->_x1 * start->_x1) + (end->_x2 * start->_x2 + end->_x3 * start->_x3);
const float delta_x1 = (end->_x1 * start->_s0 + end->_x3 * start->_x2) - (end->_s0 * start->_x1 + end->_x2 * start->_x3);
const float delta_x2 = (end->_x2 * start->_s0 + end->_x1 * start->_x3) - (end->_s0 * start->_x2 + end->_x3 * start->_x1);
const float delta_x3 = (end->_x3 * start->_s0 + end->_x2 * start->_x1) - (end->_s0 * start->_x3 + end->_x1 * start->_x2);
const float square_vector = delta_x1 * delta_x1 + delta_x2 * delta_x2 + delta_x3 * delta_x3;
@ -486,20 +498,20 @@ void bgc_versor_spherically_interpolate_fp32(const BgcVersorFP32* start, const B
// Combining of starting orientation with the turning
bgc_versor_set_values_fp32(
(turn_s0 * start->s0 - turn_x1 * start->x1) - (turn_x2 * start->x2 + turn_x3 * start->x3),
(turn_x1 * start->s0 + turn_s0 * start->x1) - (turn_x3 * start->x2 - turn_x2 * start->x3),
(turn_x2 * start->s0 + turn_s0 * start->x2) - (turn_x1 * start->x3 - turn_x3 * start->x1),
(turn_x3 * start->s0 + turn_s0 * start->x3) - (turn_x2 * start->x1 - turn_x1 * start->x2),
(turn_s0 * start->_s0 - turn_x1 * start->_x1) - (turn_x2 * start->_x2 + turn_x3 * start->_x3),
(turn_x1 * start->_s0 + turn_s0 * start->_x1) - (turn_x3 * start->_x2 - turn_x2 * start->_x3),
(turn_x2 * start->_s0 + turn_s0 * start->_x2) - (turn_x1 * start->_x3 - turn_x3 * start->_x1),
(turn_x3 * start->_s0 + turn_s0 * start->_x3) - (turn_x2 * start->_x1 - turn_x1 * start->_x2),
result
);
}
void bgc_versor_spherically_interpolate_fp64(const BgcVersorFP64* start, const BgcVersorFP64* end, const double phase, BgcVersorFP64* result)
{
const double delta_s0 = (end->s0 * start->s0 + end->x1 * start->x1) + (end->x2 * start->x2 + end->x3 * start->x3);
const double delta_x1 = (end->x1 * start->s0 + end->x3 * start->x2) - (end->s0 * start->x1 + end->x2 * start->x3);
const double delta_x2 = (end->x2 * start->s0 + end->x1 * start->x3) - (end->s0 * start->x2 + end->x3 * start->x1);
const double delta_x3 = (end->x3 * start->s0 + end->x2 * start->x1) - (end->s0 * start->x3 + end->x1 * start->x2);
const double delta_s0 = (end->_s0 * start->_s0 + end->_x1 * start->_x1) + (end->_x2 * start->_x2 + end->_x3 * start->_x3);
const double delta_x1 = (end->_x1 * start->_s0 + end->_x3 * start->_x2) - (end->_s0 * start->_x1 + end->_x2 * start->_x3);
const double delta_x2 = (end->_x2 * start->_s0 + end->_x1 * start->_x3) - (end->_s0 * start->_x2 + end->_x3 * start->_x1);
const double delta_x3 = (end->_x3 * start->_s0 + end->_x2 * start->_x1) - (end->_s0 * start->_x3 + end->_x1 * start->_x2);
const double square_vector = delta_x1 * delta_x1 + delta_x2 * delta_x2 + delta_x3 * delta_x3;
@ -521,10 +533,10 @@ void bgc_versor_spherically_interpolate_fp64(const BgcVersorFP64* start, const B
// Combining of starting orientation with the turning
bgc_versor_set_values_fp64(
(turn_s0 * start->s0 - turn_x1 * start->x1) - (turn_x2 * start->x2 + turn_x3 * start->x3),
(turn_x1 * start->s0 + turn_s0 * start->x1) - (turn_x3 * start->x2 - turn_x2 * start->x3),
(turn_x2 * start->s0 + turn_s0 * start->x2) - (turn_x1 * start->x3 - turn_x3 * start->x1),
(turn_x3 * start->s0 + turn_s0 * start->x3) - (turn_x2 * start->x1 - turn_x1 * start->x2),
(turn_s0 * start->_s0 - turn_x1 * start->_x1) - (turn_x2 * start->_x2 + turn_x3 * start->_x3),
(turn_x1 * start->_s0 + turn_s0 * start->_x1) - (turn_x3 * start->_x2 - turn_x2 * start->_x3),
(turn_x2 * start->_s0 + turn_s0 * start->_x2) - (turn_x1 * start->_x3 - turn_x3 * start->_x1),
(turn_x3 * start->_s0 + turn_s0 * start->_x3) - (turn_x2 * start->_x1 - turn_x1 * start->_x2),
result
);
}
@ -533,7 +545,7 @@ void bgc_versor_spherically_interpolate_fp64(const BgcVersorFP64* start, const B
void bgc_versor_get_rotation_fp32(const BgcVersorFP32* versor, BgcRotation3FP32* result)
{
const float square_modulus = versor->x1 * versor->x1 + versor->x2 * versor->x2 + versor->x3 * versor->x3;
const float square_modulus = versor->_x1 * versor->_x1 + versor->_x2 * versor->_x2 + versor->_x3 * versor->_x3;
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
bgc_rotation3_reset_fp32(result);
@ -544,16 +556,16 @@ void bgc_versor_get_rotation_fp32(const BgcVersorFP32* versor, BgcRotation3FP32*
const float multiplier = 1.0f / vector_modulus;
result->radians = 2.0f * atan2f(vector_modulus, versor->s0);
result->radians = 2.0f * atan2f(vector_modulus, versor->_s0);
result->axis.x1 = versor->x1 * multiplier;
result->axis.x2 = versor->x2 * multiplier;
result->axis.x3 = versor->x3 * multiplier;
result->axis.x1 = versor->_x1 * multiplier;
result->axis.x2 = versor->_x2 * multiplier;
result->axis.x3 = versor->_x3 * multiplier;
}
void bgc_versor_get_rotation_fp64(const BgcVersorFP64* versor, BgcRotation3FP64* result)
{
const double square_modulus = versor->x1 * versor->x1 + versor->x2 * versor->x2 + versor->x3 * versor->x3;
const double square_modulus = versor->_x1 * versor->_x1 + versor->_x2 * versor->_x2 + versor->_x3 * versor->_x3;
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64) {
bgc_rotation3_reset_fp64(result);
@ -564,9 +576,9 @@ void bgc_versor_get_rotation_fp64(const BgcVersorFP64* versor, BgcRotation3FP64*
const double multiplier = 1.0 / vector_modulus;
result->radians = 2.0 * atan2(vector_modulus, versor->s0);
result->radians = 2.0 * atan2(vector_modulus, versor->_s0);
result->axis.x1 = versor->x1 * multiplier;
result->axis.x2 = versor->x2 * multiplier;
result->axis.x3 = versor->x3 * multiplier;
result->axis.x1 = versor->_x1 * multiplier;
result->axis.x2 = versor->_x2 * multiplier;
result->axis.x3 = versor->_x3 * multiplier;
}

558
basic-geometry/versor.h
View file

@ -26,23 +26,13 @@
// =================== Types ==================== //
typedef struct {
const float s0, x1, x2, x3;
float _s0, _x1, _x2, _x3;
} BgcVersorFP32;
typedef struct {
const double s0, x1, x2, x3;
double _s0, _x1, _x2, _x3;
} BgcVersorFP64;
// ================= Dark Twins ================= //
typedef struct {
float s0, x1, x2, x3;
} _BgcDarkTwinVersorFP32;
typedef struct {
double s0, x1, x2, x3;
} _BgcDarkTwinVersorFP64;
// ================= Constants ================== //
extern const BgcVersorFP32 BGC_IDLE_VERSOR_FP32;
@ -52,59 +42,51 @@ extern const BgcVersorFP64 BGC_IDLE_VERSOR_FP64;
inline void bgc_versor_reset_fp32(BgcVersorFP32* versor)
{
_BgcDarkTwinVersorFP32* twin = (_BgcDarkTwinVersorFP32*)versor;
twin->s0 = 1.0f;
twin->x1 = 0.0f;
twin->x2 = 0.0f;
twin->x3 = 0.0f;
versor->_s0 = 1.0f;
versor->_x1 = 0.0f;
versor->_x2 = 0.0f;
versor->_x3 = 0.0f;
}
inline void bgc_versor_reset_fp64(BgcVersorFP64* versor)
{
_BgcDarkTwinVersorFP64* twin = (_BgcDarkTwinVersorFP64*)versor;
twin->s0 = 1.0;
twin->x1 = 0.0;
twin->x2 = 0.0;
twin->x3 = 0.0;
versor->_s0 = 1.0;
versor->_x1 = 0.0;
versor->_x2 = 0.0;
versor->_x3 = 0.0;
}
// ==================== Set ===================== //
void _bgc_versor_normalize_fp32(const float square_modulus, _BgcDarkTwinVersorFP32* twin);
void _bgc_versor_normalize_fp32(const float square_modulus, BgcVersorFP32* twin);
void _bgc_versor_normalize_fp64(const double square_modulus, _BgcDarkTwinVersorFP64* twin);
void _bgc_versor_normalize_fp64(const double square_modulus, BgcVersorFP64* twin);
inline void bgc_versor_set_values_fp32(const float s0, const float x1, const float x2, const float x3, BgcVersorFP32* versor)
{
_BgcDarkTwinVersorFP32* twin = (_BgcDarkTwinVersorFP32*)versor;
twin->s0 = s0;
twin->x1 = x1;
twin->x2 = x2;
twin->x3 = x3;
versor->_s0 = s0;
versor->_x1 = x1;
versor->_x2 = x2;
versor->_x3 = x3;
const float square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
if (!bgc_is_sqare_unit_fp32(square_modulus)) {
_bgc_versor_normalize_fp32(square_modulus, twin);
_bgc_versor_normalize_fp32(square_modulus, versor);
}
}
inline void bgc_versor_set_values_fp64(const double s0, const double x1, const double x2, const double x3, BgcVersorFP64* versor)
{
_BgcDarkTwinVersorFP64* twin = (_BgcDarkTwinVersorFP64*)versor;
twin->s0 = s0;
twin->x1 = x1;
twin->x2 = x2;
twin->x3 = x3;
versor->_s0 = s0;
versor->_x1 = x1;
versor->_x2 = x2;
versor->_x3 = x3;
const double square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
if (!bgc_is_sqare_unit_fp64(square_modulus)) {
_bgc_versor_normalize_fp64(square_modulus, twin);
_bgc_versor_normalize_fp64(square_modulus, versor);
}
}
@ -154,80 +136,68 @@ int bgc_versor_make_basis_difference_fp64(
inline void bgc_versor_copy_fp32(const BgcVersorFP32* source, BgcVersorFP32* destination)
{
_BgcDarkTwinVersorFP32* twin = (_BgcDarkTwinVersorFP32*)destination;
twin->s0 = source->s0;
twin->x1 = source->x1;
twin->x2 = source->x2;
twin->x3 = source->x3;
destination->_s0 = source->_s0;
destination->_x1 = source->_x1;
destination->_x2 = source->_x2;
destination->_x3 = source->_x3;
}
inline void bgc_versor_copy_fp64(const BgcVersorFP64* source, BgcVersorFP64* destination)
{
_BgcDarkTwinVersorFP64* twin = (_BgcDarkTwinVersorFP64*)destination;
twin->s0 = source->s0;
twin->x1 = source->x1;
twin->x2 = source->x2;
twin->x3 = source->x3;
destination->_s0 = source->_s0;
destination->_x1 = source->_x1;
destination->_x2 = source->_x2;
destination->_x3 = source->_x3;
}
// ==================== Swap ==================== //
inline void bgc_versor_swap_fp32(BgcVersorFP32* versor1, BgcVersorFP32* versor2)
{
const float s0 = versor1->s0;
const float x1 = versor1->x1;
const float x2 = versor1->x2;
const float x3 = versor1->x3;
const float s0 = versor1->_s0;
const float x1 = versor1->_x1;
const float x2 = versor1->_x2;
const float x3 = versor1->_x3;
_BgcDarkTwinVersorFP32* twin1 = (_BgcDarkTwinVersorFP32*)versor1;
versor1->_s0 = versor2->_s0;
versor1->_x1 = versor2->_x1;
versor1->_x2 = versor2->_x2;
versor1->_x3 = versor2->_x3;
twin1->s0 = versor2->s0;
twin1->x1 = versor2->x1;
twin1->x2 = versor2->x2;
twin1->x3 = versor2->x3;
_BgcDarkTwinVersorFP32* twin2 = (_BgcDarkTwinVersorFP32*)versor2;
twin2->s0 = s0;
twin2->x1 = x1;
twin2->x2 = x2;
twin2->x3 = x3;
versor2->_s0 = s0;
versor2->_x1 = x1;
versor2->_x2 = x2;
versor2->_x3 = x3;
}
inline void bgc_versor_swap_fp64(BgcVersorFP64* versor1, BgcVersorFP64* versor2)
{
const double s0 = versor1->s0;
const double x1 = versor1->x1;
const double x2 = versor1->x2;
const double x3 = versor1->x3;
const double s0 = versor1->_s0;
const double x1 = versor1->_x1;
const double x2 = versor1->_x2;
const double x3 = versor1->_x3;
_BgcDarkTwinVersorFP64* twin1 = (_BgcDarkTwinVersorFP64*)versor1;
versor1->_s0 = versor2->_s0;
versor1->_x1 = versor2->_x1;
versor1->_x2 = versor2->_x2;
versor1->_x3 = versor2->_x3;
twin1->s0 = versor2->s0;
twin1->x1 = versor2->x1;
twin1->x2 = versor2->x2;
twin1->x3 = versor2->x3;
_BgcDarkTwinVersorFP64* twin2 = (_BgcDarkTwinVersorFP64*)versor2;
twin2->s0 = s0;
twin2->x1 = x1;
twin2->x2 = x2;
twin2->x3 = x3;
versor2->_s0 = s0;
versor2->_x1 = x1;
versor2->_x2 = x2;
versor2->_x3 = x3;
}
// ================= Comparison ================= //
inline int bgc_versor_is_identity_fp32(const BgcVersorFP32* versor)
{
return versor->x1 * versor->x1 + versor->x2 * versor->x2 + versor->x3 * versor->x3 <= BGC_SQUARE_EPSYLON_FP32;
return versor->_x1 * versor->_x1 + versor->_x2 * versor->_x2 + versor->_x3 * versor->_x3 <= BGC_SQUARE_EPSYLON_FP32;
}
inline int bgc_versor_is_identity_fp64(const BgcVersorFP64* versor)
{
return versor->x1 * versor->x1 + versor->x2 * versor->x2 + versor->x3 * versor->x3 <= BGC_SQUARE_EPSYLON_FP64;
return versor->_x1 * versor->_x1 + versor->_x2 * versor->_x2 + versor->_x3 * versor->_x3 <= BGC_SQUARE_EPSYLON_FP64;
}
// ================== Convert =================== //
@ -235,10 +205,10 @@ inline int bgc_versor_is_identity_fp64(const BgcVersorFP64* versor)
inline void bgc_versor_convert_fp64_to_fp32(const BgcVersorFP64* source, BgcVersorFP32* destination)
{
bgc_versor_set_values_fp32(
(float)source->s0,
(float)source->x1,
(float)source->x2,
(float)source->x3,
(float)source->_s0,
(float)source->_x1,
(float)source->_x2,
(float)source->_x3,
destination
);
}
@ -246,70 +216,132 @@ inline void bgc_versor_convert_fp64_to_fp32(const BgcVersorFP64* source, BgcVers
inline void bgc_versor_convert_fp32_to_fp64(const BgcVersorFP32* source, BgcVersorFP64* destination)
{
bgc_versor_set_values_fp64(
source->s0,
source->x1,
source->x2,
source->x3,
source->_s0,
source->_x1,
source->_x2,
source->_x3,
destination
);
}
// ================== Shorten =================== //
inline void bgc_versor_shorten_fp32(const BgcVersorFP32* versor, BgcVersorFP32* shortened)
inline void bgc_versor_shorten_fp32(BgcVersorFP32* versor)
{
_BgcDarkTwinVersorFP32* twin = (_BgcDarkTwinVersorFP32*)shortened;
if (versor->s0 >= 0.0f) {
twin->s0 = versor->s0;
twin->x1 = versor->x1;
twin->x2 = versor->x2;
twin->x3 = versor->x3;
return;
if (versor->_s0 < 0.0f) {
versor->_s0 = -versor->_s0;
versor->_x1 = -versor->_x1;
versor->_x2 = -versor->_x2;
versor->_x3 = -versor->_x3;
}
twin->s0 = -versor->s0;
twin->x1 = -versor->x1;
twin->x2 = -versor->x2;
twin->x3 = -versor->x3;
}
inline void bgc_versor_shorten_fp64(const BgcVersorFP64* versor, BgcVersorFP64* shortened)
inline void bgc_versor_shorten_fp64(BgcVersorFP64* versor)
{
_BgcDarkTwinVersorFP64* twin = (_BgcDarkTwinVersorFP64*)shortened;
if (versor->_s0 < 0.0) {
versor->_s0 = -versor->_s0;
versor->_x1 = -versor->_x1;
versor->_x2 = -versor->_x2;
versor->_x3 = -versor->_x3;
}
}
if (versor->s0 >= 0.0) {
twin->s0 = versor->s0;
twin->x1 = versor->x1;
twin->x2 = versor->x2;
twin->x3 = versor->x3;
inline void bgc_versor_get_shortened_fp32(const BgcVersorFP32* versor, BgcVersorFP32* shortened)
{
if (versor->_s0 >= 0.0f) {
shortened->_s0 = versor->_s0;
shortened->_x1 = versor->_x1;
shortened->_x2 = versor->_x2;
shortened->_x3 = versor->_x3;
return;
}
twin->s0 = -versor->s0;
twin->x1 = -versor->x1;
twin->x2 = -versor->x2;
twin->x3 = -versor->x3;
shortened->_s0 = -versor->_s0;
shortened->_x1 = -versor->_x1;
shortened->_x2 = -versor->_x2;
shortened->_x3 = -versor->_x3;
}
inline void bgc_versor_get_shortened_fp64(const BgcVersorFP64* versor, BgcVersorFP64* shortened)
{
if (versor->_s0 >= 0.0) {
shortened->_s0 = versor->_s0;
shortened->_x1 = versor->_x1;
shortened->_x2 = versor->_x2;
shortened->_x3 = versor->_x3;
return;
}
shortened->_s0 = -versor->_s0;
shortened->_x1 = -versor->_x1;
shortened->_x2 = -versor->_x2;
shortened->_x3 = -versor->_x3;
}
// ================== Negative ================== //
inline void bgc_versor_make_opposite_fp32(BgcVersorFP32* versor)
{
versor->_s0 = -versor->_s0;
versor->_x1 = -versor->_x1;
versor->_x2 = -versor->_x2;
versor->_x3 = -versor->_x3;
}
inline void bgc_versor_make_opposite_fp64(BgcVersorFP64* versor)
{
versor->_s0 = -versor->_s0;
versor->_x1 = -versor->_x1;
versor->_x2 = -versor->_x2;
versor->_x3 = -versor->_x3;
}
inline void bgc_versor_get_opposite_fp32(const BgcVersorFP32* versor, BgcVersorFP32* opposite)
{
opposite->_s0 = -versor->_s0;
opposite->_x1 = -versor->_x1;
opposite->_x2 = -versor->_x2;
opposite->_x3 = -versor->_x3;
}
inline void bgc_versor_get_opposite_fp64(const BgcVersorFP64* versor, BgcVersorFP64* opposite)
{
opposite->_s0 = -versor->_s0;
opposite->_x1 = -versor->_x1;
opposite->_x2 = -versor->_x2;
opposite->_x3 = -versor->_x3;
}
// =================== Invert =================== //
inline void bgc_versor_invert_fp32(const BgcVersorFP32* versor, BgcVersorFP32* inverted)
inline void bgc_versor_invert_fp32(BgcVersorFP32* versor)
{
_BgcDarkTwinVersorFP32* twin = (_BgcDarkTwinVersorFP32*)inverted;
twin->s0 = versor->s0;
twin->x1 = -versor->x1;
twin->x2 = -versor->x2;
twin->x3 = -versor->x3;
versor->_x1 = -versor->_x1;
versor->_x2 = -versor->_x2;
versor->_x3 = -versor->_x3;
}
inline void bgc_versor_invert_fp64(const BgcVersorFP64* versor, BgcVersorFP64* inverted)
inline void bgc_versor_invert_fp64(BgcVersorFP64* versor)
{
_BgcDarkTwinVersorFP64* twin = (_BgcDarkTwinVersorFP64*)inverted;
twin->s0 = versor->s0;
twin->x1 = -versor->x1;
twin->x2 = -versor->x2;
twin->x3 = -versor->x3;
versor->_x1 = -versor->_x1;
versor->_x2 = -versor->_x2;
versor->_x3 = -versor->_x3;
}
inline void bgc_versor_get_inverse_fp32(const BgcVersorFP32* versor, BgcVersorFP32* inverse)
{
inverse->_s0 = versor->_s0;
inverse->_x1 = -versor->_x1;
inverse->_x2 = -versor->_x2;
inverse->_x3 = -versor->_x3;
}
inline void bgc_versor_get_inverse_fp64(const BgcVersorFP64* versor, BgcVersorFP64* inverse)
{
inverse->_s0 = versor->_s0;
inverse->_x1 = -versor->_x1;
inverse->_x2 = -versor->_x2;
inverse->_x3 = -versor->_x3;
}
// =============== Get Exponation =============== //
@ -323,10 +355,10 @@ void bgc_versor_get_exponation_fp64(const BgcVersorFP64* base, const double expo
inline void bgc_versor_combine_fp32(const BgcVersorFP32* second, const BgcVersorFP32* first, BgcVersorFP32* result)
{
bgc_versor_set_values_fp32(
(second->s0 * first->s0 - second->x1 * first->x1) - (second->x2 * first->x2 + second->x3 * first->x3),
(second->x1 * first->s0 + second->s0 * first->x1) - (second->x3 * first->x2 - second->x2 * first->x3),
(second->x2 * first->s0 + second->s0 * first->x2) - (second->x1 * first->x3 - second->x3 * first->x1),
(second->x3 * first->s0 + second->s0 * first->x3) - (second->x2 * first->x1 - second->x1 * first->x2),
(second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3),
(second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3),
(second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1),
(second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2),
result
);
}
@ -334,10 +366,10 @@ inline void bgc_versor_combine_fp32(const BgcVersorFP32* second, const BgcVersor
inline void bgc_versor_combine_fp64(const BgcVersorFP64* second, const BgcVersorFP64* first, BgcVersorFP64* result)
{
bgc_versor_set_values_fp64(
(second->s0 * first->s0 - second->x1 * first->x1) - (second->x2 * first->x2 + second->x3 * first->x3),
(second->x1 * first->s0 + second->s0 * first->x1) - (second->x3 * first->x2 - second->x2 * first->x3),
(second->x2 * first->s0 + second->s0 * first->x2) - (second->x1 * first->x3 - second->x3 * first->x1),
(second->x3 * first->s0 + second->s0 * first->x3) - (second->x2 * first->x1 - second->x1 * first->x2),
(second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3),
(second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3),
(second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1),
(second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2),
result
);
}
@ -346,32 +378,32 @@ inline void bgc_versor_combine_fp64(const BgcVersorFP64* second, const BgcVersor
inline void bgc_versor_combine3_fp32(const BgcVersorFP32* third, const BgcVersorFP32* second, const BgcVersorFP32* first, BgcVersorFP32* result)
{
const float s0 = (second->s0 * first->s0 - second->x1 * first->x1) - (second->x2 * first->x2 + second->x3 * first->x3);
const float x1 = (second->x1 * first->s0 + second->s0 * first->x1) - (second->x3 * first->x2 - second->x2 * first->x3);
const float x2 = (second->x2 * first->s0 + second->s0 * first->x2) - (second->x1 * first->x3 - second->x3 * first->x1);
const float x3 = (second->x3 * first->s0 + second->s0 * first->x3) - (second->x2 * first->x1 - second->x1 * first->x2);
const float s0 = (second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3);
const float x1 = (second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3);
const float x2 = (second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1);
const float x3 = (second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2);
bgc_versor_set_values_fp32(
(third->s0 * s0 - third->x1 * x1) - (third->x2 * x2 + third->x3 * x3),
(third->x1 * s0 + third->s0 * x1) - (third->x3 * x2 - third->x2 * x3),
(third->x2 * s0 + third->s0 * x2) - (third->x1 * x3 - third->x3 * x1),
(third->x3 * s0 + third->s0 * x3) - (third->x2 * x1 - third->x1 * x2),
(third->_s0 * s0 - third->_x1 * x1) - (third->_x2 * x2 + third->_x3 * x3),
(third->_x1 * s0 + third->_s0 * x1) - (third->_x3 * x2 - third->_x2 * x3),
(third->_x2 * s0 + third->_s0 * x2) - (third->_x1 * x3 - third->_x3 * x1),
(third->_x3 * s0 + third->_s0 * x3) - (third->_x2 * x1 - third->_x1 * x2),
result
);
}
inline void bgc_versor_combine3_fp64(const BgcVersorFP64* third, const BgcVersorFP64* second, const BgcVersorFP64* first, BgcVersorFP64* result)
{
const double s0 = (second->s0 * first->s0 - second->x1 * first->x1) - (second->x2 * first->x2 + second->x3 * first->x3);
const double x1 = (second->x1 * first->s0 + second->s0 * first->x1) - (second->x3 * first->x2 - second->x2 * first->x3);
const double x2 = (second->x2 * first->s0 + second->s0 * first->x2) - (second->x1 * first->x3 - second->x3 * first->x1);
const double x3 = (second->x3 * first->s0 + second->s0 * first->x3) - (second->x2 * first->x1 - second->x1 * first->x2);
const double s0 = (second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3);
const double x1 = (second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3);
const double x2 = (second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1);
const double x3 = (second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2);
bgc_versor_set_values_fp64(
(third->s0 * s0 - third->x1 * x1) - (third->x2 * x2 + third->x3 * x3),
(third->x1 * s0 + third->s0 * x1) - (third->x3 * x2 - third->x2 * x3),
(third->x2 * s0 + third->s0 * x2) - (third->x1 * x3 - third->x3 * x1),
(third->x3 * s0 + third->s0 * x3) - (third->x2 * x1 - third->x1 * x2),
(third->_s0 * s0 - third->_x1 * x1) - (third->_x2 * x2 + third->_x3 * x3),
(third->_x1 * s0 + third->_s0 * x1) - (third->_x3 * x2 - third->_x2 * x3),
(third->_x2 * s0 + third->_s0 * x2) - (third->_x1 * x3 - third->_x3 * x1),
(third->_x3 * s0 + third->_s0 * x3) - (third->_x2 * x1 - third->_x1 * x2),
result
);
}
@ -381,10 +413,10 @@ inline void bgc_versor_combine3_fp64(const BgcVersorFP64* third, const BgcVersor
inline void bgc_versor_exclude_fp32(const BgcVersorFP32* base, const BgcVersorFP32* excludant, BgcVersorFP32* difference)
{
bgc_versor_set_values_fp32(
(base->s0 * excludant->s0 + base->x1 * excludant->x1) + (base->x2 * excludant->x2 + base->x3 * excludant->x3),
(base->x1 * excludant->s0 + base->x3 * excludant->x2) - (base->s0 * excludant->x1 + base->x2 * excludant->x3),
(base->x2 * excludant->s0 + base->x1 * excludant->x3) - (base->s0 * excludant->x2 + base->x3 * excludant->x1),
(base->x3 * excludant->s0 + base->x2 * excludant->x1) - (base->s0 * excludant->x3 + base->x1 * excludant->x2),
(base->_s0 * excludant->_s0 + base->_x1 * excludant->_x1) + (base->_x2 * excludant->_x2 + base->_x3 * excludant->_x3),
(base->_x1 * excludant->_s0 + base->_x3 * excludant->_x2) - (base->_s0 * excludant->_x1 + base->_x2 * excludant->_x3),
(base->_x2 * excludant->_s0 + base->_x1 * excludant->_x3) - (base->_s0 * excludant->_x2 + base->_x3 * excludant->_x1),
(base->_x3 * excludant->_s0 + base->_x2 * excludant->_x1) - (base->_s0 * excludant->_x3 + base->_x1 * excludant->_x2),
difference
);
}
@ -392,10 +424,10 @@ inline void bgc_versor_exclude_fp32(const BgcVersorFP32* base, const BgcVersorFP
inline void bgc_versor_exclude_fp64(const BgcVersorFP64* base, const BgcVersorFP64* excludant, BgcVersorFP64* difference)
{
bgc_versor_set_values_fp64(
(base->s0 * excludant->s0 + base->x1 * excludant->x1) + (base->x2 * excludant->x2 + base->x3 * excludant->x3),
(base->x1 * excludant->s0 + base->x3 * excludant->x2) - (base->s0 * excludant->x1 + base->x2 * excludant->x3),
(base->x2 * excludant->s0 + base->x1 * excludant->x3) - (base->s0 * excludant->x2 + base->x3 * excludant->x1),
(base->x3 * excludant->s0 + base->x2 * excludant->x1) - (base->s0 * excludant->x3 + base->x1 * excludant->x2),
(base->_s0 * excludant->_s0 + base->_x1 * excludant->_x1) + (base->_x2 * excludant->_x2 + base->_x3 * excludant->_x3),
(base->_x1 * excludant->_s0 + base->_x3 * excludant->_x2) - (base->_s0 * excludant->_x1 + base->_x2 * excludant->_x3),
(base->_x2 * excludant->_s0 + base->_x1 * excludant->_x3) - (base->_s0 * excludant->_x2 + base->_x3 * excludant->_x1),
(base->_x3 * excludant->_s0 + base->_x2 * excludant->_x1) - (base->_s0 * excludant->_x3 + base->_x1 * excludant->_x2),
difference
);
}
@ -416,127 +448,123 @@ void bgc_versor_get_rotation_fp64(const BgcVersorFP64* versor, BgcRotation3FP64*
inline void bgc_versor_get_rotation_matrix_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* matrix)
{
const float s0s0 = versor->s0 * versor->s0;
const float x1x1 = versor->x1 * versor->x1;
const float x2x2 = versor->x2 * versor->x2;
const float x3x3 = versor->x3 * versor->x3;
const float s0s0 = versor->_s0 * versor->_s0;
const float x1x1 = versor->_x1 * versor->_x1;
const float x2x2 = versor->_x2 * versor->_x2;
const float x3x3 = versor->_x3 * versor->_x3;
const float s0x1 = 2.0f * versor->s0 * versor->x1;
const float s0x2 = 2.0f * versor->s0 * versor->x2;
const float s0x3 = 2.0f * versor->s0 * versor->x3;
const float x1x2 = 2.0f * versor->x1 * versor->x2;
const float x1x3 = 2.0f * versor->x1 * versor->x3;
const float x2x3 = 2.0f * versor->x2 * versor->x3;
const float s0x1 = versor->_s0 * versor->_x1;
const float s0x2 = versor->_s0 * versor->_x2;
const float s0x3 = versor->_s0 * versor->_x3;
const float x1x2 = versor->_x1 * versor->_x2;
const float x1x3 = versor->_x1 * versor->_x3;
const float x2x3 = versor->_x2 * versor->_x3;
matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
matrix->r1c2 = x1x2 - s0x3;
matrix->r2c3 = x2x3 - s0x1;
matrix->r3c1 = x1x3 - s0x2;
matrix->r1c2 = 2.0f * (x1x2 - s0x3);
matrix->r2c3 = 2.0f * (x2x3 - s0x1);
matrix->r3c1 = 2.0f * (x1x3 - s0x2);
matrix->r2c1 = x1x2 + s0x3;
matrix->r3c2 = x2x3 + s0x1;
matrix->r1c3 = x1x3 + s0x2;
matrix->r2c1 = 2.0f * (x1x2 + s0x3);
matrix->r3c2 = 2.0f * (x2x3 + s0x1);
matrix->r1c3 = 2.0f * (x1x3 + s0x2);
}
inline void bgc_versor_get_rotation_matrix_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* matrix)
{
const double s0s0 = versor->s0 * versor->s0;
const double x1x1 = versor->x1 * versor->x1;
const double x2x2 = versor->x2 * versor->x2;
const double x3x3 = versor->x3 * versor->x3;
const double s0s0 = versor->_s0 * versor->_s0;
const double x1x1 = versor->_x1 * versor->_x1;
const double x2x2 = versor->_x2 * versor->_x2;
const double x3x3 = versor->_x3 * versor->_x3;
const double s0x1 = 2.0 * versor->s0 * versor->x1;
const double s0x2 = 2.0 * versor->s0 * versor->x2;
const double s0x3 = 2.0 * versor->s0 * versor->x3;
const double x1x2 = 2.0 * versor->x1 * versor->x2;
const double x1x3 = 2.0 * versor->x1 * versor->x3;
const double x2x3 = 2.0 * versor->x2 * versor->x3;
const double s0x1 = versor->_s0 * versor->_x1;
const double s0x2 = versor->_s0 * versor->_x2;
const double s0x3 = versor->_s0 * versor->_x3;
const double x1x2 = versor->_x1 * versor->_x2;
const double x1x3 = versor->_x1 * versor->_x3;
const double x2x3 = versor->_x2 * versor->_x3;
matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
matrix->r1c2 = x1x2 - s0x3;
matrix->r2c3 = x2x3 - s0x1;
matrix->r3c1 = x1x3 - s0x2;
matrix->r1c2 = 2.0 * (x1x2 - s0x3);
matrix->r2c3 = 2.0 * (x2x3 - s0x1);
matrix->r3c1 = 2.0 * (x1x3 - s0x2);
matrix->r2c1 = x1x2 + s0x3;
matrix->r3c2 = x2x3 + s0x1;
matrix->r1c3 = x1x3 + s0x2;
matrix->r2c1 = 2.0 * (x1x2 + s0x3);
matrix->r3c2 = 2.0 * (x2x3 + s0x1);
matrix->r1c3 = 2.0 * (x1x3 + s0x2);
}
// ============= Get Reverse Matrix ============= //
inline void bgc_versor_get_reverse_matrix_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* matrix)
{
const float s0s0 = versor->s0 * versor->s0;
const float x1x1 = versor->x1 * versor->x1;
const float x2x2 = versor->x2 * versor->x2;
const float x3x3 = versor->x3 * versor->x3;
const float s0s0 = versor->_s0 * versor->_s0;
const float x1x1 = versor->_x1 * versor->_x1;
const float x2x2 = versor->_x2 * versor->_x2;
const float x3x3 = versor->_x3 * versor->_x3;
const float s0x1 = 2.0f * versor->s0 * versor->x1;
const float s0x2 = 2.0f * versor->s0 * versor->x2;
const float s0x3 = 2.0f * versor->s0 * versor->x3;
const float x1x2 = 2.0f * versor->x1 * versor->x2;
const float x1x3 = 2.0f * versor->x1 * versor->x3;
const float x2x3 = 2.0f * versor->x2 * versor->x3;
const float s0x1 = versor->_s0 * versor->_x1;
const float s0x2 = versor->_s0 * versor->_x2;
const float s0x3 = versor->_s0 * versor->_x3;
const float x1x2 = versor->_x1 * versor->_x2;
const float x1x3 = versor->_x1 * versor->_x3;
const float x2x3 = versor->_x2 * versor->_x3;
matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
matrix->r1c2 = x1x2 + s0x3;
matrix->r2c3 = x2x3 + s0x1;
matrix->r3c1 = x1x3 + s0x2;
matrix->r1c2 = 2.0f * (x1x2 + s0x3);
matrix->r2c3 = 2.0f * (x2x3 + s0x1);
matrix->r3c1 = 2.0f * (x1x3 + s0x2);
matrix->r2c1 = x1x2 - s0x3;
matrix->r3c2 = x2x3 - s0x1;
matrix->r1c3 = x1x3 - s0x2;
matrix->r2c1 = 2.0f * (x1x2 - s0x3);
matrix->r3c2 = 2.0f * (x2x3 - s0x1);
matrix->r1c3 = 2.0f * (x1x3 - s0x2);
}
inline void bgc_versor_get_reverse_matrix_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* matrix)
{
const double s0s0 = versor->s0 * versor->s0;
const double x1x1 = versor->x1 * versor->x1;
const double x2x2 = versor->x2 * versor->x2;
const double x3x3 = versor->x3 * versor->x3;
const double s0s0 = versor->_s0 * versor->_s0;
const double x1x1 = versor->_x1 * versor->_x1;
const double x2x2 = versor->_x2 * versor->_x2;
const double x3x3 = versor->_x3 * versor->_x3;
const double s0x1 = 2.0 * versor->s0 * versor->x1;
const double s0x2 = 2.0 * versor->s0 * versor->x2;
const double s0x3 = 2.0 * versor->s0 * versor->x3;
const double x1x2 = 2.0 * versor->x1 * versor->x2;
const double x1x3 = 2.0 * versor->x1 * versor->x3;
const double x2x3 = 2.0 * versor->x2 * versor->x3;
const double s0x1 = versor->_s0 * versor->_x1;
const double s0x2 = versor->_s0 * versor->_x2;
const double s0x3 = versor->_s0 * versor->_x3;
const double x1x2 = versor->_x1 * versor->_x2;
const double x1x3 = versor->_x1 * versor->_x3;
const double x2x3 = versor->_x2 * versor->_x3;
matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
matrix->r1c2 = x1x2 + s0x3;
matrix->r2c3 = x2x3 + s0x1;
matrix->r3c1 = x1x3 + s0x2;
matrix->r1c2 = 2.0 * (x1x2 + s0x3);
matrix->r2c3 = 2.0 * (x2x3 + s0x1);
matrix->r3c1 = 2.0 * (x1x3 + s0x2);
matrix->r2c1 = x1x2 - s0x3;
matrix->r3c2 = x2x3 - s0x1;
matrix->r1c3 = x1x3 - s0x2;
matrix->r2c1 = 2.0 * (x1x2 - s0x3);
matrix->r3c2 = 2.0 * (x2x3 - s0x1);
matrix->r1c3 = 2.0 * (x1x3 - s0x2);
}
// ============= Get Both Matrixes ============== //
inline void bgc_versor_get_both_matrixes_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* rotation, BgcMatrix3x3FP32* reverse)
inline void bgc_versor_get_both_matrices_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* rotation, BgcMatrix3x3FP32* reverse)
{
bgc_versor_get_reverse_matrix_fp32(versor, reverse);
bgc_matrix3x3_transpose_fp32(reverse, rotation);
}
inline void bgc_versor_get_both_matrixes_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* rotation, BgcMatrix3x3FP64* reverse)
inline void bgc_versor_get_both_matrices_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* rotation, BgcMatrix3x3FP64* reverse)
{
bgc_versor_get_reverse_matrix_fp64(versor, reverse);
bgc_matrix3x3_transpose_fp64(reverse, rotation);
@ -546,13 +574,13 @@ inline void bgc_versor_get_both_matrixes_fp64(const BgcVersorFP64* versor, BgcMa
inline void bgc_versor_turn_vector_fp32(const BgcVersorFP32* versor, const BgcVector3FP32* vector, BgcVector3FP32* result)
{
const float tx1 = 2.0f * (versor->x2 * vector->x3 - versor->x3 * vector->x2);
const float tx2 = 2.0f * (versor->x3 * vector->x1 - versor->x1 * vector->x3);
const float tx3 = 2.0f * (versor->x1 * vector->x2 - versor->x2 * vector->x1);
const float tx1 = 2.0f * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
const float tx2 = 2.0f * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
const float tx3 = 2.0f * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);
const float x1 = (vector->x1 + tx1 * versor->s0) + (versor->x2 * tx3 - versor->x3 * tx2);
const float x2 = (vector->x2 + tx2 * versor->s0) + (versor->x3 * tx1 - versor->x1 * tx3);
const float x3 = (vector->x3 + tx3 * versor->s0) + (versor->x1 * tx2 - versor->x2 * tx1);
const float x1 = (vector->x1 + tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
const float x2 = (vector->x2 + tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
const float x3 = (vector->x3 + tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);
result->x1 = x1;
result->x2 = x2;
@ -561,13 +589,13 @@ inline void bgc_versor_turn_vector_fp32(const BgcVersorFP32* versor, const BgcVe
inline void bgc_versor_turn_vector_fp64(const BgcVersorFP64* versor, const BgcVector3FP64* vector, BgcVector3FP64* result)
{
const double tx1 = 2.0 * (versor->x2 * vector->x3 - versor->x3 * vector->x2);
const double tx2 = 2.0 * (versor->x3 * vector->x1 - versor->x1 * vector->x3);
const double tx3 = 2.0 * (versor->x1 * vector->x2 - versor->x2 * vector->x1);
const double tx1 = 2.0 * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
const double tx2 = 2.0 * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
const double tx3 = 2.0 * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);
const double x1 = (vector->x1 + tx1 * versor->s0) + (versor->x2 * tx3 - versor->x3 * tx2);
const double x2 = (vector->x2 + tx2 * versor->s0) + (versor->x3 * tx1 - versor->x1 * tx3);
const double x3 = (vector->x3 + tx3 * versor->s0) + (versor->x1 * tx2 - versor->x2 * tx1);
const double x1 = (vector->x1 + tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
const double x2 = (vector->x2 + tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
const double x3 = (vector->x3 + tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);
result->x1 = x1;
result->x2 = x2;
@ -578,13 +606,13 @@ inline void bgc_versor_turn_vector_fp64(const BgcVersorFP64* versor, const BgcVe
inline void bgc_versor_turn_vector_back_fp32(const BgcVersorFP32* versor, const BgcVector3FP32* vector, BgcVector3FP32* result)
{
const float tx1 = 2.0f * (versor->x2 * vector->x3 - versor->x3 * vector->x2);
const float tx2 = 2.0f * (versor->x3 * vector->x1 - versor->x1 * vector->x3);
const float tx3 = 2.0f * (versor->x1 * vector->x2 - versor->x2 * vector->x1);
const float tx1 = 2.0f * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
const float tx2 = 2.0f * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
const float tx3 = 2.0f * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);
const float x1 = (vector->x1 - tx1 * versor->s0) + (versor->x2 * tx3 - versor->x3 * tx2);
const float x2 = (vector->x2 - tx2 * versor->s0) + (versor->x3 * tx1 - versor->x1 * tx3);
const float x3 = (vector->x3 - tx3 * versor->s0) + (versor->x1 * tx2 - versor->x2 * tx1);
const float x1 = (vector->x1 - tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
const float x2 = (vector->x2 - tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
const float x3 = (vector->x3 - tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);
result->x1 = x1;
result->x2 = x2;
@ -593,13 +621,13 @@ inline void bgc_versor_turn_vector_back_fp32(const BgcVersorFP32* versor, const
inline void bgc_versor_turn_vector_back_fp64(const BgcVersorFP64* versor, const BgcVector3FP64* vector, BgcVector3FP64* result)
{
const double tx1 = 2.0 * (versor->x2 * vector->x3 - versor->x3 * vector->x2);
const double tx2 = 2.0 * (versor->x3 * vector->x1 - versor->x1 * vector->x3);
const double tx3 = 2.0 * (versor->x1 * vector->x2 - versor->x2 * vector->x1);
const double tx1 = 2.0 * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
const double tx2 = 2.0 * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
const double tx3 = 2.0 * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);
const double x1 = (vector->x1 - tx1 * versor->s0) + (versor->x2 * tx3 - versor->x3 * tx2);
const double x2 = (vector->x2 - tx2 * versor->s0) + (versor->x3 * tx1 - versor->x1 * tx3);
const double x3 = (vector->x3 - tx3 * versor->s0) + (versor->x1 * tx2 - versor->x2 * tx1);
const double x1 = (vector->x1 - tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
const double x2 = (vector->x2 - tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
const double x3 = (vector->x3 - tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);
result->x1 = x1;
result->x2 = x2;
@ -610,20 +638,20 @@ inline void bgc_versor_turn_vector_back_fp64(const BgcVersorFP64* versor, const
inline int bgc_versor_are_close_fp32(const BgcVersorFP32* versor1, const BgcVersorFP32* versor2)
{
const float ds0 = versor1->s0 - versor2->s0;
const float dx1 = versor1->x1 - versor2->x1;
const float dx2 = versor1->x2 - versor2->x2;
const float dx3 = versor1->x3 - versor2->x3;
const float ds0 = versor1->_s0 - versor2->_s0;
const float dx1 = versor1->_x1 - versor2->_x1;
const float dx2 = versor1->_x2 - versor2->_x2;
const float dx3 = versor1->_x3 - versor2->_x3;
return (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3) <= BGC_SQUARE_EPSYLON_FP32;
}
inline int bgc_versor_are_close_fp64(const BgcVersorFP64* versor1, const BgcVersorFP64* versor2)
{
const double ds0 = versor1->s0 - versor2->s0;
const double dx1 = versor1->x1 - versor2->x1;
const double dx2 = versor1->x2 - versor2->x2;
const double dx3 = versor1->x3 - versor2->x3;
const double ds0 = versor1->_s0 - versor2->_s0;
const double dx1 = versor1->_x1 - versor2->_x1;
const double dx2 = versor1->_x2 - versor2->_x2;
const double dx3 = versor1->_x3 - versor2->_x3;
return (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3) <= BGC_SQUARE_EPSYLON_FP64;
}