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Переделка методов turn3_find_direction_difference, возврат функций матриц поворота для turn3

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Andrey Pokidov 2026-02-07 02:53:21 +07:00
parent 2ce4b64ca3
commit 78d1661c5d
2 changed files with 198 additions and 106 deletions
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131
basic-geometry/turn3.c
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@ -201,92 +201,95 @@ void bgc_fp64_turn3_set_rotation(BGC_FP64_Turn3* turn, const double x1, const do
} }
} }
// ========= Make Direction Difference ========== // // ========= Find Direction Difference ========== //
static int _bgc_fp32_turn3_make_direction_turn(BGC_FP32_Turn3* turn, const BGC_FP32_Vector3* start, const BGC_FP32_Vector3* end, const float square_modulus_product) int bgc_fp32_turn3_find_direction_difference(BGC_FP32_Turn3* turn, const BGC_FP32_Vector3* first, const BGC_FP32_Vector3* second)
{ {
BGC_FP32_Vector3 orthogonal_axis; const float first_square_modulus = bgc_fp32_vector3_get_square_modulus(first);
bgc_fp32_vector3_get_cross_product(&orthogonal_axis, start, end);
const float scalar_product = bgc_fp32_vector3_get_dot_product(start, end);
const float square_modulus = bgc_fp32_vector3_get_square_modulus(&orthogonal_axis);
const float square_sine = square_modulus / square_modulus_product;
if (square_sine > BGC_FP32_SQUARE_EPSILON) {
const float cosine = scalar_product / sqrtf(square_modulus_product);
const float angle = 0.5f * atan2f(sqrtf(square_sine), cosine);
const float multiplier = sinf(angle) * sqrtf(1.0f / square_modulus);
bgc_fp32_turn3_set_raw_values(turn, cosf(angle), orthogonal_axis.x1 * multiplier, orthogonal_axis.x2 * multiplier, orthogonal_axis.x3 * multiplier);
return BGC_SOME_TURN;
}
if (scalar_product < 0.0f) {
return BGC_OPPOSITE;
}
bgc_fp32_turn3_reset(turn); bgc_fp32_turn3_reset(turn);
return BGC_ZERO_TURN; if (first_square_modulus <= BGC_FP32_SQUARE_EPSILON) {
return BGC_ERROR_TURN3_FIRST_VECTOR_ZERO;
}
const float second_square_modulus = bgc_fp32_vector3_get_square_modulus(second);
if (second_square_modulus <= BGC_FP32_SQUARE_EPSILON) {
return BGC_ERROR_TURN3_SECOND_VECTOR_ZERO;
}
BGC_FP32_Vector3 axis;
bgc_fp32_vector3_get_cross_product(&axis, first, second);
const float square_product = first_square_modulus * second_square_modulus;
const float dot_product = bgc_fp32_vector3_get_dot_product(first, second);
const float axis_square_modulus = bgc_fp32_vector3_get_square_modulus(&axis);
if (axis_square_modulus <= BGC_FP32_SQUARE_EPSILON * square_product) {
if (dot_product < 0.0f) {
return BGC_ERROR_TURN3_VECTORS_OPPOSITE;
}
return BGC_SUCCESS;
}
const float axis_modulus = sqrtf(axis_square_modulus);
const float trigonometry_fix = sqrtf(1.0f / square_product);
const float angle = 0.5f * atan2f(axis_modulus * trigonometry_fix, dot_product * trigonometry_fix);
const float vector_multiplier = sinf(angle) / axis_modulus;
bgc_fp32_turn3_set_raw_values(turn, cosf(angle), axis.x1 * vector_multiplier, axis.x2 * vector_multiplier, axis.x3 * vector_multiplier);
return BGC_SUCCESS;
} }
static int _bgc_fp64_turn3_make_direction_turn(BGC_FP64_Turn3* versor, const BGC_FP64_Vector3* start, const BGC_FP64_Vector3* end, const double square_modulus_product) int bgc_fp64_turn3_find_direction_difference(BGC_FP64_Turn3* turn, const BGC_FP64_Vector3* first, const BGC_FP64_Vector3* second)
{ {
BGC_FP64_Vector3 orthogonal_axis; const double first_square_modulus = bgc_fp64_vector3_get_square_modulus(first);
bgc_fp64_vector3_get_cross_product(&orthogonal_axis, start, end); bgc_fp64_turn3_reset(turn);
const double scalar_product = bgc_fp64_vector3_get_dot_product(start, end); if (first_square_modulus <= BGC_FP64_SQUARE_EPSILON) {
const double square_modulus = bgc_fp64_vector3_get_square_modulus(&orthogonal_axis); return BGC_ERROR_TURN3_FIRST_VECTOR_ZERO;
const double square_sine = square_modulus / square_modulus_product;
if (square_sine > BGC_FP64_SQUARE_EPSILON) {
const double cosine = scalar_product / sqrt(square_modulus_product);
const double angle = 0.5 * atan2(sqrt(square_sine), cosine);
const double multiplier = sin(angle) * sqrt(1.0f / square_modulus);
bgc_fp64_turn3_set_raw_values(versor, cos(angle), orthogonal_axis.x1 * multiplier, orthogonal_axis.x2 * multiplier, orthogonal_axis.x3 * multiplier);
return BGC_SOME_TURN;
} }
if (scalar_product < 0.0) { const double second_square_modulus = bgc_fp64_vector3_get_square_modulus(second);
return BGC_OPPOSITE;
if (second_square_modulus <= BGC_FP64_SQUARE_EPSILON) {
return BGC_ERROR_TURN3_SECOND_VECTOR_ZERO;
} }
bgc_fp64_turn3_reset(versor); BGC_FP64_Vector3 axis;
return BGC_ZERO_TURN; bgc_fp64_vector3_get_cross_product(&axis, first, second);
}
// ========= Find Direction Difference ========== // const double square_product = first_square_modulus * second_square_modulus;
const double dot_product = bgc_fp64_vector3_get_dot_product(first, second);
const double axis_square_modulus = bgc_fp64_vector3_get_square_modulus(&axis);
int bgc_fp32_turn3_find_direction_difference(BGC_FP32_Turn3* difference, const BGC_FP32_Vector3* start, const BGC_FP32_Vector3* end) if (axis_square_modulus <= BGC_FP64_SQUARE_EPSILON * square_product) {
{ bgc_fp64_turn3_reset(turn);
const float start_square_modulus = bgc_fp32_vector3_get_square_modulus(start); if (dot_product < 0.0) {
const float end_square_modulus = bgc_fp32_vector3_get_square_modulus(end); return BGC_ERROR_TURN3_VECTORS_OPPOSITE;
}
if (start_square_modulus <= BGC_FP32_SQUARE_EPSILON || end_square_modulus <= BGC_FP32_SQUARE_EPSILON) { return BGC_SUCCESS;
bgc_fp32_turn3_reset(difference);
return BGC_ZERO_TURN;
} }
return _bgc_fp32_turn3_make_direction_turn(difference, start, end, start_square_modulus * end_square_modulus); const double axis_modulus = sqrt(axis_square_modulus);
} const double trigonometry_fix = sqrt(1.0 / square_product);
int bgc_fp64_turn3_find_direction_difference(BGC_FP64_Turn3* difference, const BGC_FP64_Vector3* start, const BGC_FP64_Vector3* end) const double angle = 0.5 * atan2(axis_modulus * trigonometry_fix, dot_product * trigonometry_fix);
{
const double start_square_modulus = bgc_fp64_vector3_get_square_modulus(start);
const double end_square_modulus = bgc_fp64_vector3_get_square_modulus(end);
if (start_square_modulus <= BGC_FP64_SQUARE_EPSILON || end_square_modulus <= BGC_FP64_SQUARE_EPSILON) { const double vector_multiplier = sin(angle) / axis_modulus;
bgc_fp64_turn3_reset(difference);
return BGC_ZERO_TURN;
}
return _bgc_fp64_turn3_make_direction_turn(difference, start, end, start_square_modulus * end_square_modulus); bgc_fp64_turn3_set_raw_values(turn, cos(angle), axis.x1 * vector_multiplier, axis.x2 * vector_multiplier, axis.x3 * vector_multiplier);
return BGC_SUCCESS;
} }
// ============ Make Orthogonal Pair ============ // // ============ Make Orthogonal Pair ============ //
@ -334,7 +337,7 @@ static inline int _bgc_fp64_turn3_get_orthogonal_pair(BGC_FP64_Vector3* unit_mai
return _BGC_ERROR_TURN3_EMPTY_BRANCH; return _BGC_ERROR_TURN3_EMPTY_BRANCH;
} }
bgc_fp64_vector3_multiply(unit_main, main, sqrtf(1.0 / main_square_modulus)); bgc_fp64_vector3_multiply(unit_main, main, sqrt(1.0 / main_square_modulus));
bgc_fp64_vector3_add_scaled(unit_branch, branch, unit_main, -bgc_fp64_vector3_get_dot_product(branch, unit_main)); bgc_fp64_vector3_add_scaled(unit_branch, branch, unit_main, -bgc_fp64_vector3_get_dot_product(branch, unit_main));

151
basic-geometry/turn3.h
View file

@ -9,32 +9,23 @@
#include "matrix3x3.h" #include "matrix3x3.h"
#include "quaternion.h" #include "quaternion.h"
#define BGC_SOME_TURN 1 #define BGC_ERROR_TURN3_FIRST_VECTOR_ZERO -3010
#define BGC_ZERO_TURN 0 #define BGC_ERROR_TURN3_SECOND_VECTOR_ZERO -3011
#define BGC_OPPOSITE -1 #define BGC_ERROR_TURN3_VECTORS_OPPOSITE -3012
#define _BGC_ERROR_TURN3_FIRST_PAIR 3000 #define _BGC_ERROR_TURN3_FIRST_PAIR -3020
#define _BGC_ERROR_TURN3_SECOND_PAIR 3010 #define _BGC_ERROR_TURN3_SECOND_PAIR -3030
#define _BGC_ERROR_TURN3_EMPTY_MAIN 1 #define _BGC_ERROR_TURN3_EMPTY_MAIN -1
#define _BGC_ERROR_TURN3_EMPTY_BRANCH 2 #define _BGC_ERROR_TURN3_EMPTY_BRANCH -2
#define _BGC_ERROR_TURN3_PAIR_PARALLEL 3 #define _BGC_ERROR_TURN3_PAIR_PARALLEL -3
#define BGC_ERROR_TURN3_FIRST_PAIR_EMPTY_MAIN 3001 #define BGC_ERROR_TURN3_FIRST_PAIR_ZERO_MAIN -3021
#define BGC_ERROR_TURN3_FIRST_PAIR_EMPTY_BRANCH 3002 #define BGC_ERROR_TURN3_FIRST_PAIR_ZERO_BRANCH -3022
#define BGC_ERROR_TURN3_FIRST_PAIR_PARALLEL 3003 #define BGC_ERROR_TURN3_FIRST_PAIR_PARALLEL -3023
#define BGC_ERROR_TURN3_SECOND_PAIR_EMPTY_MAIN 3011 #define BGC_ERROR_TURN3_SECOND_PAIR_ZERO_MAIN -3031
#define BGC_ERROR_TURN3_SECOND_PAIR_EMPTY_BRANCH 3012 #define BGC_ERROR_TURN3_SECOND_PAIR_ZERO_BRANCH -3032
#define BGC_ERROR_TURN3_SECOND_PAIR_PARALLEL 3013 #define BGC_ERROR_TURN3_SECOND_PAIR_PARALLEL -3033
#define BGC_ERROR_PRIMARY_DIRECTION_UNKNOWN -3001
#define BGC_ERROR_PRIMARY_VECTOR_IS_ZERO -3002
#define BGC_ERROR_AUXILIARY_DIRECTION_UNKNOWN -3011
#define BGC_ERROR_AUXILIARY_VECTOR_IS_ZERO -3012
#define BGC_ERROR_DIRECTIONS_PARALLEL -3021
#define BGC_ERROR_VECTORS_PARALLEL -3022
// =================== Types ==================== // // =================== Types ==================== //
@ -143,9 +134,9 @@ void bgc_fp64_turn3_set_rotation(BGC_FP64_Turn3* turn, const double x1, const do
// ========= Find Direction Difference ========== // // ========= Find Direction Difference ========== //
int bgc_fp32_turn3_find_direction_difference(BGC_FP32_Turn3* difference, const BGC_FP32_Vector3* start, const BGC_FP32_Vector3* end); int bgc_fp32_turn3_find_direction_difference(BGC_FP32_Turn3* turn, const BGC_FP32_Vector3* start, const BGC_FP32_Vector3* end);
int bgc_fp64_turn3_find_direction_difference(BGC_FP64_Turn3* difference, const BGC_FP64_Vector3* start, const BGC_FP64_Vector3* end); int bgc_fp64_turn3_find_direction_difference(BGC_FP64_Turn3* turn, const BGC_FP64_Vector3* start, const BGC_FP64_Vector3* end);
// ======= Find Direction Pair Difference ======= // // ======= Find Direction Pair Difference ======= //
@ -401,36 +392,134 @@ void bgc_fp64_turn3_spherically_interpolate(BGC_FP64_Turn3* interpolation, const
inline void bgc_fp32_turn3_get_rotation_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_Turn3* turn) inline void bgc_fp32_turn3_get_rotation_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_Turn3* turn)
{ {
bgc_fp32_quaternion_get_rotation_matrix(matrix, &turn->_versor); const float s0s0 = turn->_versor.s0 * turn->_versor.s0;
const float x1x1 = turn->_versor.x1 * turn->_versor.x1;
const float x2x2 = turn->_versor.x2 * turn->_versor.x2;
const float x3x3 = turn->_versor.x3 * turn->_versor.x3;
const float s0x1 = turn->_versor.s0 * turn->_versor.x1;
const float s0x2 = turn->_versor.s0 * turn->_versor.x2;
const float s0x3 = turn->_versor.s0 * turn->_versor.x3;
const float x1x2 = turn->_versor.x1 * turn->_versor.x2;
const float x1x3 = turn->_versor.x1 * turn->_versor.x3;
const float x2x3 = turn->_versor.x2 * turn->_versor.x3;
matrix->r1c1 = ((s0s0 + x1x1) - (x2x2 + x3x3));
matrix->r2c2 = ((s0s0 + x2x2) - (x1x1 + x3x3));
matrix->r3c3 = ((s0s0 + x3x3) - (x1x1 + x2x2));
matrix->r1c2 = 2.0f * (x1x2 - s0x3);
matrix->r2c3 = 2.0f * (x2x3 - s0x1);
matrix->r3c1 = 2.0f * (x1x3 - s0x2);
matrix->r2c1 = 2.0f * (x1x2 + s0x3);
matrix->r3c2 = 2.0f * (x2x3 + s0x1);
matrix->r1c3 = 2.0f * (x1x3 + s0x2);
} }
inline void bgc_fp64_turn3_get_rotation_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_Turn3* turn) inline void bgc_fp64_turn3_get_rotation_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_Turn3* turn)
{ {
bgc_fp64_quaternion_get_rotation_matrix(matrix, &turn->_versor); const double s0s0 = turn->_versor.s0 * turn->_versor.s0;
const double x1x1 = turn->_versor.x1 * turn->_versor.x1;
const double x2x2 = turn->_versor.x2 * turn->_versor.x2;
const double x3x3 = turn->_versor.x3 * turn->_versor.x3;
const double s0x1 = turn->_versor.s0 * turn->_versor.x1;
const double s0x2 = turn->_versor.s0 * turn->_versor.x2;
const double s0x3 = turn->_versor.s0 * turn->_versor.x3;
const double x1x2 = turn->_versor.x1 * turn->_versor.x2;
const double x1x3 = turn->_versor.x1 * turn->_versor.x3;
const double x2x3 = turn->_versor.x2 * turn->_versor.x3;
matrix->r1c1 = ((s0s0 + x1x1) - (x2x2 + x3x3));
matrix->r2c2 = ((s0s0 + x2x2) - (x1x1 + x3x3));
matrix->r3c3 = ((s0s0 + x3x3) - (x1x1 + x2x2));
matrix->r1c2 = 2.0 * (x1x2 - s0x3);
matrix->r2c3 = 2.0 * (x2x3 - s0x1);
matrix->r3c1 = 2.0 * (x1x3 - s0x2);
matrix->r2c1 = 2.0 * (x1x2 + s0x3);
matrix->r3c2 = 2.0 * (x2x3 + s0x1);
matrix->r1c3 = 2.0 * (x1x3 + s0x2);
} }
// ============= Get Reverse Matrix ============= // // ============= Get Reverse Matrix ============= //
inline void bgc_fp32_turn3_get_reverse_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_Turn3* turn) inline void bgc_fp32_turn3_get_reverse_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_Turn3* turn)
{ {
bgc_fp32_quaternion_get_reverse_matrix(matrix, &turn->_versor); const float s0s0 = turn->_versor.s0 * turn->_versor.s0;
const float x1x1 = turn->_versor.x1 * turn->_versor.x1;
const float x2x2 = turn->_versor.x2 * turn->_versor.x2;
const float x3x3 = turn->_versor.x3 * turn->_versor.x3;
const float s0x1 = turn->_versor.s0 * turn->_versor.x1;
const float s0x2 = turn->_versor.s0 * turn->_versor.x2;
const float s0x3 = turn->_versor.s0 * turn->_versor.x3;
const float x1x2 = turn->_versor.x1 * turn->_versor.x2;
const float x1x3 = turn->_versor.x1 * turn->_versor.x3;
const float x2x3 = turn->_versor.x2 * turn->_versor.x3;
matrix->r1c1 = ((s0s0 + x1x1) - (x2x2 + x3x3));
matrix->r2c2 = ((s0s0 + x2x2) - (x1x1 + x3x3));
matrix->r3c3 = ((s0s0 + x3x3) - (x1x1 + x2x2));
matrix->r1c2 = 2.0f * (x1x2 + s0x3);
matrix->r2c3 = 2.0f * (x2x3 + s0x1);
matrix->r3c1 = 2.0f * (x1x3 + s0x2);
matrix->r2c1 = 2.0f * (x1x2 - s0x3);
matrix->r3c2 = 2.0f * (x2x3 - s0x1);
matrix->r1c3 = 2.0f * (x1x3 - s0x2);
} }
inline void bgc_fp64_turn3_get_reverse_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_Turn3* turn) inline void bgc_fp64_turn3_get_reverse_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_Turn3* turn)
{ {
bgc_fp64_quaternion_get_reverse_matrix(matrix, &turn->_versor); const double s0s0 = turn->_versor.s0 * turn->_versor.s0;
const double x1x1 = turn->_versor.x1 * turn->_versor.x1;
const double x2x2 = turn->_versor.x2 * turn->_versor.x2;
const double x3x3 = turn->_versor.x3 * turn->_versor.x3;
const double s0x1 = turn->_versor.s0 * turn->_versor.x1;
const double s0x2 = turn->_versor.s0 * turn->_versor.x2;
const double s0x3 = turn->_versor.s0 * turn->_versor.x3;
const double x1x2 = turn->_versor.x1 * turn->_versor.x2;
const double x1x3 = turn->_versor.x1 * turn->_versor.x3;
const double x2x3 = turn->_versor.x2 * turn->_versor.x3;
matrix->r1c1 = ((s0s0 + x1x1) - (x2x2 + x3x3));
matrix->r2c2 = ((s0s0 + x2x2) - (x1x1 + x3x3));
matrix->r3c3 = ((s0s0 + x3x3) - (x1x1 + x2x2));
matrix->r1c2 = 2.0 * (x1x2 + s0x3);
matrix->r2c3 = 2.0 * (x2x3 + s0x1);
matrix->r3c1 = 2.0 * (x1x3 + s0x2);
matrix->r2c1 = 2.0 * (x1x2 - s0x3);
matrix->r3c2 = 2.0 * (x2x3 - s0x1);
matrix->r1c3 = 2.0 * (x1x3 - s0x2);
} }
// ============= Get Both Matrixes ============== // // ============= Get Both Matrixes ============== //
inline void bgc_fp32_turn3_get_both_matrices(BGC_FP32_Matrix3x3* rotation, BGC_FP32_Matrix3x3* reverse, const BGC_FP32_Turn3* turn) inline void bgc_fp32_turn3_get_both_matrices(BGC_FP32_Matrix3x3* rotation, BGC_FP32_Matrix3x3* reverse, const BGC_FP32_Turn3* turn)
{ {
bgc_fp32_quaternion_get_both_matrices(rotation, reverse, &turn->_versor); bgc_fp32_turn3_get_reverse_matrix(reverse, turn);
bgc_fp32_matrix3x3_get_transposed(rotation, reverse);
} }
inline void bgc_fp64_turn3_get_both_matrices(BGC_FP64_Matrix3x3* rotation, BGC_FP64_Matrix3x3* reverse, const BGC_FP64_Turn3* turn) inline void bgc_fp64_turn3_get_both_matrices(BGC_FP64_Matrix3x3* rotation, BGC_FP64_Matrix3x3* reverse, const BGC_FP64_Turn3* turn)
{ {
bgc_fp64_quaternion_get_both_matrices(rotation, reverse, &turn->_versor); bgc_fp64_turn3_get_reverse_matrix(reverse, turn);
bgc_fp64_matrix3x3_get_transposed(rotation, reverse);
} }
// ================ Turn Vector ================= // // ================ Turn Vector ================= //