From 2ce4b64ca3b2865d4a5579ac2088bbd82be497a5 Mon Sep 17 00:00:00 2001 From: Andrey Pokidov Date: Fri, 6 Feb 2026 20:33:37 +0700 Subject: [PATCH] =?UTF-8?q?=D0=98=D1=81=D0=BF=D1=80=D0=B0=D0=B2=D0=BB?= =?UTF-8?q?=D0=B5=D0=BD=D0=B8=D0=B5=20=D1=84=D1=83=D0=BD=D0=BA=D1=86=D0=B8?= =?UTF-8?q?=D0=B8,=20=D0=BA=D0=BE=D1=82=D0=BE=D1=80=D0=B0=D1=8F=20=D0=BD?= =?UTF-8?q?=D0=B0=D1=85=D0=BE=D0=B4=D0=B8=D1=82=20=D1=82=D1=80=D1=91=D1=85?= =?UTF-8?q?=D0=BC=D0=B5=D1=80=D0=BD=D1=8B=D1=85=20=D0=BF=D0=BE=D0=B2=D0=BE?= =?UTF-8?q?=D1=80=D0=BE=D1=82=20=D0=BC=D0=B5=D0=B6=D0=B4=D1=83=20=D0=B4?= =?UTF-8?q?=D0=B2=D1=83=D0=BC=D1=8F=20=D0=BF=D0=B0=D1=80=D0=B0=D0=BC=D0=B8?= =?UTF-8?q?=20=D0=B2=D0=B5=D0=BA=D1=82=D0=BE=D1=80=D0=BE=D0=B2?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- basic-geometry-dev/main.c | 329 ++++++++++++++------------ basic-geometry/dual-quaternion.c | 8 +- basic-geometry/dual-quaternion.h | 20 +- basic-geometry/quaternion.c | 48 ++-- basic-geometry/quaternion.h | 271 +++++++++++++++++---- basic-geometry/turn3.c | 388 ++++++++++++++++++------------- basic-geometry/turn3.h | 108 ++++----- 7 files changed, 705 insertions(+), 467 deletions(-) diff --git a/basic-geometry-dev/main.c b/basic-geometry-dev/main.c index bef60f1..ae8a901 100644 --- a/basic-geometry-dev/main.c +++ b/basic-geometry-dev/main.c @@ -79,7 +79,7 @@ void list_work(const uint_fast32_t amount, structure_fp32_t* list) } } } - +/* int main() { const unsigned int amount = 1000000; @@ -121,7 +121,7 @@ int main() return 0; } - +*/ /* int main() { @@ -149,84 +149,84 @@ int main() { } */ -void test_basis_difference_fp32() +void test_pair_difference_fp32() { - BGC_FP32_Vector3 initial_primary, initial_auxiliary; - BGC_FP32_Vector3 final_primary, final_auxiliary; + BGC_FP32_Vector3 initial_main, initial_branch; + BGC_FP32_Vector3 final_main, final_branch; BGC_FP32_Turn3 turn; // No turn - bgc_fp32_vector3_make(&initial_primary, 1.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&initial_auxiliary, 0.0f, 1.0f, 0.0f); + bgc_fp32_vector3_make(&initial_main, 1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&initial_branch, 0.0f, 1.0f, 0.0f); - bgc_fp32_vector3_make(&final_primary, 1.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&final_auxiliary, 0.0f, 1.0f, 0.0f); + bgc_fp32_vector3_make(&final_main, 1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&final_branch, 0.0f, 1.0f, 0.0f); - bgc_fp32_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp32_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\nNo turn:\n"); print_quaternion_fp32(&turn._versor); // Turn around (1, 1, 0) axis on 180 degrees - bgc_fp32_vector3_make(&initial_primary, 1.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&initial_auxiliary, 0.0f, 1.0f, 0.0f); + bgc_fp32_vector3_make(&initial_main, 1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&initial_branch, 0.0f, 1.0f, 0.0f); - bgc_fp32_vector3_make(&final_primary, 0.0f, 1.0f, 0.0f); - bgc_fp32_vector3_make(&final_auxiliary, 1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&final_main, 0.0f, 1.0f, 0.0f); + bgc_fp32_vector3_make(&final_branch, 1.0f, 0.0f, 0.0f); - bgc_fp32_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp32_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\nTurn around (1, 1, 0) axis on 180 degrees:\n"); print_quaternion_fp32(&turn._versor); // 180 degree turn - bgc_fp32_vector3_make(&initial_primary, 1.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&initial_auxiliary, 0.0f, 1.0f, 0.0f); + bgc_fp32_vector3_make(&initial_main, 1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&initial_branch, 0.0f, 1.0f, 0.0f); - bgc_fp32_vector3_make(&final_primary, -1.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&final_auxiliary, 0.0f, 1.0f, 0.0f); + bgc_fp32_vector3_make(&final_main, -1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&final_branch, 0.0f, 1.0f, 0.0f); - bgc_fp32_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp32_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\n180 degree turn around (0, 1, 0):\n"); print_quaternion_fp32(&turn._versor); // 90 degree turn around x3 axis - bgc_fp32_vector3_make(&initial_primary, 2.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&initial_auxiliary, 0.0f, 3.1f, 0.0f); + bgc_fp32_vector3_make(&initial_main, 2.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&initial_branch, 0.0f, 3.1f, 0.0f); - bgc_fp32_vector3_make(&final_primary, 0.0f, 10.0f, 0.0f); - bgc_fp32_vector3_make(&final_auxiliary,-1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&final_main, 0.0f, 10.0f, 0.0f); + bgc_fp32_vector3_make(&final_branch,-1.0f, 0.0f, 0.0f); - bgc_fp32_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp32_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\n90 degree turn around (0, 0, 1):\n"); print_quaternion_fp32(&turn._versor); // Unorthogonal pairs turn at 90 degrees around x3 axis - bgc_fp32_vector3_make(&initial_primary, 2.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&initial_auxiliary, -2.0f, 3.1f, 0.0f); + bgc_fp32_vector3_make(&initial_main, 2.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&initial_branch, -2.0f, 3.1f, 0.0f); - bgc_fp32_vector3_make(&final_primary, 0.0f, 10.0f, 0.0f); - bgc_fp32_vector3_make(&final_auxiliary, -1.0f, 5.0f, 0.0f); + bgc_fp32_vector3_make(&final_main, 0.0f, 10.0f, 0.0f); + bgc_fp32_vector3_make(&final_branch, -1.0f, 5.0f, 0.0f); - bgc_fp32_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp32_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\nUnorthogonal pairs turn at 90 degrees around (0, 0, 1):\n"); print_quaternion_fp32(&turn._versor); // Zero vectors - bgc_fp32_vector3_make(&initial_primary, 0.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&initial_auxiliary, 0.0f, 1.0f, 0.0f); - bgc_fp32_vector3_make(&final_primary, 1.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&final_auxiliary, 0.0f, 1.0f, 0.0f); + bgc_fp32_vector3_make(&initial_main, 0.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&initial_branch, 0.0f, 1.0f, 0.0f); + bgc_fp32_vector3_make(&final_main, 1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&final_branch, 0.0f, 1.0f, 0.0f); int code; - code = bgc_fp32_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + code = bgc_fp32_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); - if (code >= 0) { + if (code == BGC_SUCCESS) { printf("\nZero vectors: this cannot be!\n"); print_quaternion_fp32(&turn._versor); } @@ -235,14 +235,14 @@ void test_basis_difference_fp32() } // Parallel vectors - bgc_fp32_vector3_make(&initial_primary, 1.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&initial_auxiliary, 2.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&final_primary, 1.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&final_auxiliary, 0.0f, 1.0f, 0.0f); + bgc_fp32_vector3_make(&initial_main, 1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&initial_branch, 2.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&final_main, 1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&final_branch, 0.0f, 1.0f, 0.0f); - code = bgc_fp32_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + code = bgc_fp32_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); - if (code >= 0) { + if (code == BGC_SUCCESS) { printf("\nParallel vectors: this cannot be!\n"); print_quaternion_fp32(&turn._versor); } @@ -251,141 +251,171 @@ void test_basis_difference_fp32() } // Small angle turn (about 1 degree): - bgc_fp32_vector3_make(&initial_primary, 1.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&initial_auxiliary, 0.0f, 1.0f, 0.0f); + bgc_fp32_vector3_make(&initial_main, 1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&initial_branch, 0.0f, 1.0f, 0.0f); - bgc_fp32_vector3_make(&final_primary, 0.999848f, 0.017452f, 0.0f); - bgc_fp32_vector3_make(&final_auxiliary, -0.017452f, 0.999848f, 0.0f); + bgc_fp32_vector3_make(&final_main, 0.999848f, 0.017452f, 0.0f); + bgc_fp32_vector3_make(&final_branch, -0.017452f, 0.999848f, 0.0f); - bgc_fp32_turn3_make_basis_difference(&turn , &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp32_turn3_find_pair_difference(&turn , &initial_main, &initial_branch, &final_main, &final_branch); printf("\nSmall angle turn (about 1 degree):\n"); print_quaternion_fp32(&turn._versor); // About 179 degrees turn - bgc_fp32_vector3_make(&initial_primary, 1.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&initial_auxiliary, 0.0f, 1.0f, 0.0f); + bgc_fp32_vector3_make(&initial_main, 1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&initial_branch, 0.0f, 1.0f, 0.0f); - bgc_fp32_vector3_make(&final_primary, -0.999848f, -0.017452f, 0.0f); - bgc_fp32_vector3_make(&final_auxiliary, 0.017452f, -0.999848f, 0.0f); + bgc_fp32_vector3_make(&final_main, -0.999848f, -0.017452f, 0.0f); + bgc_fp32_vector3_make(&final_branch, 0.017452f, -0.999848f, 0.0f); - bgc_fp32_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp32_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\nAbout 179 degrees turn:\n"); print_quaternion_fp32(&turn._versor); // 120 degrees around (-1, -1, 1) - bgc_fp32_vector3_make(&initial_primary, 1.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&initial_auxiliary, 0.0f, 1.0f, 0.0f); + bgc_fp32_vector3_make(&initial_main, 1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&initial_branch, 0.0f, 1.0f, 0.0f); - bgc_fp32_vector3_make(&final_primary, 0.0f, 1.0f, 0.0f); - bgc_fp32_vector3_make(&final_auxiliary, 0.0f, 0.0f, -1.0f); + bgc_fp32_vector3_make(&final_main, 0.0f, 1.0f, 0.0f); + bgc_fp32_vector3_make(&final_branch, 0.0f, 0.0f, -1.0f); - bgc_fp32_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp32_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\n120 degees turn:\n"); print_quaternion_fp32(&turn._versor); - // About 1 degree turn difference between initial_primary and initial_auxiliary directions - bgc_fp32_vector3_make(&initial_primary, 1.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&initial_auxiliary, 0.999848f, 0.017452f, 0.0f); - bgc_fp32_vector3_make(&final_primary, 0.0f, 1.0f, 0.0f); - bgc_fp32_vector3_make(&final_auxiliary, -1.0f, 0.0f, 0.0f); + // About 1 degree turn difference between initial_main and initial_branch directions + bgc_fp32_vector3_make(&initial_main, 1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&initial_branch, 0.999848f, 0.017452f, 0.0f); + bgc_fp32_vector3_make(&final_main, 0.0f, 1.0f, 0.0f); + bgc_fp32_vector3_make(&final_branch, -1.0f, 0.0f, 0.0f); - bgc_fp32_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp32_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); - printf("\nAbout 1 degree turn difference between initial_primary and initial_auxiliary directions:\n"); + printf("\nAbout 1 degree turn difference between initial_main and initial_branch directions:\n"); print_quaternion_fp32(&turn._versor); - // About 0.01 degree turn difference between initial_primary and initial_auxiliary directions - bgc_fp32_vector3_make(&initial_primary, 1.0f, 0.0f, 0.0f); - bgc_fp32_vector3_make(&initial_auxiliary, 1.0f, 0.000001f, 0.0f); - bgc_fp32_vector3_make(&final_primary, 0.0f, -1.0f, 0.0f); - bgc_fp32_vector3_make(&final_auxiliary, 1.0f, 0.0f, 0.0f); + // About 0.01 degree turn difference between initial_main and initial_branch directions + bgc_fp32_vector3_make(&initial_main, 1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&initial_branch, 1.0f, 0.000001f, 0.0f); + bgc_fp32_vector3_make(&final_main, 0.0f, -1.0f, 0.0f); + bgc_fp32_vector3_make(&final_branch, 1.0f, 0.0f, 0.0f); - bgc_fp32_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp32_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); - printf("\nAbout 0.01 degree turn difference between initial_primary and initial_auxiliary directions:\n"); + printf("\nAbout 0.01 degree turn difference between initial_main and initial_branch directions:\n"); print_quaternion_fp32(&turn._versor); + + bgc_fp32_vector3_make(&initial_main, 1.0f, 0.0f, 0.0f); + bgc_fp32_vector3_make(&initial_branch, 0.0f, 0.999999f, 0.00014142f); // почти (0,1,0), но крошечный z + + bgc_fp32_vector3_make(&final_main, -0.999999f, 0.0f, 0.00014142f); + bgc_fp32_vector3_make(&final_branch, 0.0f, 0.999999f, -0.00014142f); + + bgc_fp32_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); + printf("\nNear 180° with tiny branch deviation:\n"); + print_quaternion_fp32(&turn._versor); + + bgc_fp32_vector3_make(&initial_main, 1.0f, 0.2f, 0.1f); + bgc_fp32_vector3_make(&initial_branch, 0.1f, 1.0f, 0.3f); // почти (0,1,0), но крошечный z + + BGC_FP32_Turn3 known; + + bgc_fp32_turn3_set_rotation(&known, 0.0f, 0.0f, 1.0f, 90.0f, BGC_ANGLE_UNIT_DEGREES); + + bgc_fp32_vector3_make(&initial_main, -0.999999f, 0.0f, 0.00014142f); + bgc_fp32_vector3_make(&initial_branch, 0.0f, 0.999999f, -0.00014142f); + + bgc_fp32_turn3_vector(&final_main, &known, &initial_main); + bgc_fp32_turn3_vector(&final_branch, &known, &initial_branch); + + bgc_fp32_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); + printf("\nRecover known 90° Z rotation:\n"); + print_quaternion_fp32(&turn._versor); + + printf("Known was: "); + print_quaternion_fp32(&known._versor); } -void test_basis_difference_fp64() +void test_pair_difference_fp64() { - BGC_FP64_Vector3 initial_primary, initial_auxiliary; - BGC_FP64_Vector3 final_primary, final_auxiliary; + BGC_FP64_Vector3 initial_main, initial_branch; + BGC_FP64_Vector3 final_main, final_branch; BGC_FP64_Turn3 turn; // No turn - bgc_fp64_vector3_make(&initial_primary, 1.0, 0.0, 0.0); - bgc_fp64_vector3_make(&initial_auxiliary, 0.0, 1.0, 0.0); - bgc_fp64_vector3_make(&final_primary, 1.0, 0.0, 0.0); - bgc_fp64_vector3_make(&final_auxiliary, 0.0, 1.0, 0.0); + bgc_fp64_vector3_make(&initial_main, 1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&initial_branch, 0.0, 1.0, 0.0); + bgc_fp64_vector3_make(&final_main, 1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&final_branch, 0.0, 1.0, 0.0); - bgc_fp64_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp64_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\nNo turn:\n"); print_quaternion_fp64(&turn._versor); // Turn around (1, 1, 0) axis on 180 degrees - bgc_fp64_vector3_make(&initial_primary, 1.0, 0.0, 0.0); - bgc_fp64_vector3_make(&initial_auxiliary, 0.0, 1.0, 0.0); - bgc_fp64_vector3_make(&final_primary, 0.0, 1.0, 0.0); - bgc_fp64_vector3_make(&final_auxiliary, 1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&initial_main, 1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&initial_branch, 0.0, 1.0, 0.0); + bgc_fp64_vector3_make(&final_main, 0.0, 1.0, 0.0); + bgc_fp64_vector3_make(&final_branch, 1.0, 0.0, 0.0); - bgc_fp64_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp64_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\nTurn around (1, 1, 0) axis on 180 degrees:\n"); print_quaternion_fp64(&turn._versor); // 180 degree turn - bgc_fp64_vector3_make(&initial_primary, 1.0, 0.0, 0.0); - bgc_fp64_vector3_make(&initial_auxiliary, 0.0, 1.0, 0.0); + bgc_fp64_vector3_make(&initial_main, 1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&initial_branch, 0.0, 1.0, 0.0); - bgc_fp64_vector3_make(&initial_auxiliary, -1.0, 0.0, 0.0); - bgc_fp64_vector3_make(&final_auxiliary, 0.0, 1.0, 0.0); + bgc_fp64_vector3_make(&initial_branch, -1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&final_branch, 0.0, 1.0, 0.0); - bgc_fp64_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp64_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\n180 degree turn around (0, 1, 0):\n"); print_quaternion_fp64(&turn._versor); // 90 degree turn around x3 axis - bgc_fp64_vector3_make(&initial_primary, 2.0, 0.0, 0.0); - bgc_fp64_vector3_make(&initial_auxiliary, 0.0, 3.1, 0.0); + bgc_fp64_vector3_make(&initial_main, 2.0, 0.0, 0.0); + bgc_fp64_vector3_make(&initial_branch, 0.0, 3.1, 0.0); - bgc_fp64_vector3_make(&final_primary, 0.0, 10.0, 0.0); - bgc_fp64_vector3_make(&final_auxiliary, -1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&final_main, 0.0, 10.0, 0.0); + bgc_fp64_vector3_make(&final_branch, -1.0, 0.0, 0.0); - bgc_fp64_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp64_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\n90 degree turn around (0, 0, 1):\n"); print_quaternion_fp64(&turn._versor); // Unorthogonal pairs turn at 90 degrees around x3 axis - bgc_fp64_vector3_make(&initial_primary, 2.0, 0.0, 0.0); - bgc_fp64_vector3_make(&initial_auxiliary, -2.0, 3.1, 0.0); + bgc_fp64_vector3_make(&initial_main, 2.0, 0.0, 0.0); + bgc_fp64_vector3_make(&initial_branch, -2.0, 3.1, 0.0); - bgc_fp64_vector3_make(&final_primary, 0.0, 10.0, 0.0); - bgc_fp64_vector3_make(&final_auxiliary, -1.0, 5.0, 0.0); + bgc_fp64_vector3_make(&final_main, 0.0, 10.0, 0.0); + bgc_fp64_vector3_make(&final_branch, -1.0, 5.0, 0.0); - bgc_fp64_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp64_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\nUnorthogonal pairs turn at 90 degrees around (0, 0, 1):\n"); print_quaternion_fp64(&turn._versor); // Zero vectors - bgc_fp64_vector3_make(&initial_primary, 0.0, 0.0, 0.0); - bgc_fp64_vector3_make(&initial_auxiliary, 0.0, 1.0, 0.0); - bgc_fp64_vector3_make(&final_primary, 1.0, 0.0, 0.0); - bgc_fp64_vector3_make(&final_auxiliary, 0.0, 1.0, 0.0); + bgc_fp64_vector3_make(&initial_main, 0.0, 0.0, 0.0); + bgc_fp64_vector3_make(&initial_branch, 0.0, 1.0, 0.0); + bgc_fp64_vector3_make(&final_main, 1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&final_branch, 0.0, 1.0, 0.0); int code; - code = bgc_fp64_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + code = bgc_fp64_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); - if (code >= 0) { + if (code == BGC_SUCCESS) { printf("\nZero vectors: this cannot be!\n"); print_quaternion_fp64(&turn._versor); } @@ -394,14 +424,14 @@ void test_basis_difference_fp64() } // Parallel vectors - bgc_fp64_vector3_make(&initial_primary, 1.0, 0.0, 0.0); - bgc_fp64_vector3_make(&initial_auxiliary, 2.0, 0.0, 0.0); - bgc_fp64_vector3_make(&final_primary, 1.0, 0.0, 0.0); - bgc_fp64_vector3_make(&final_auxiliary, 0.0, 1.0, 0.0); + bgc_fp64_vector3_make(&initial_main, 1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&initial_branch, 2.0, 0.0, 0.0); + bgc_fp64_vector3_make(&final_main, 1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&final_branch, 0.0, 1.0, 0.0); - code = bgc_fp64_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + code = bgc_fp64_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); - if (code >= 0) { + if (code == BGC_SUCCESS) { printf("\nParallel vectors: this cannot be!\n"); print_quaternion_fp64(&turn._versor); } @@ -410,82 +440,71 @@ void test_basis_difference_fp64() } // Small angle turn (about 1 degree): - bgc_fp64_vector3_make(&initial_primary, 1.0, 0.0, 0.0); - bgc_fp64_vector3_make(&initial_auxiliary, 0.0, 1.0, 0.0); + bgc_fp64_vector3_make(&initial_main, 1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&initial_branch, 0.0, 1.0, 0.0); - bgc_fp64_vector3_make(&final_primary, 0.999848, 0.017452, 0.0); - bgc_fp64_vector3_make(&final_auxiliary, -0.017452, 0.999848, 0.0); + bgc_fp64_vector3_make(&final_main, 0.999848, 0.017452, 0.0); + bgc_fp64_vector3_make(&final_branch, -0.017452, 0.999848, 0.0); - bgc_fp64_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp64_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\nSmall angle turn (about 1 degree):\n"); print_quaternion_fp64(&turn._versor); // About 179 degrees turn - bgc_fp64_vector3_make(&initial_primary, 1.0, 0.0, 0.0); - bgc_fp64_vector3_make(&initial_auxiliary, 0.0, 1.0, 0.0); + bgc_fp64_vector3_make(&initial_main, 1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&initial_branch, 0.0, 1.0, 0.0); - bgc_fp64_vector3_make(&final_primary, -0.999848, -0.017452, 0.0); - bgc_fp64_vector3_make(&final_auxiliary, 0.017452, -0.999848, 0.0); + bgc_fp64_vector3_make(&final_main, -0.999848, -0.017452, 0.0); + bgc_fp64_vector3_make(&final_branch, 0.017452, -0.999848, 0.0); - bgc_fp64_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp64_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\nAbout 179 degrees turn:\n"); print_quaternion_fp64(&turn._versor); // 120 degrees around (-1, -1, 1) - bgc_fp64_vector3_make(&initial_primary, 1.0, 0.0, 0.0); - bgc_fp64_vector3_make(&initial_auxiliary, 0.0, 1.0, 0.0); + bgc_fp64_vector3_make(&initial_main, 1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&initial_branch, 0.0, 1.0, 0.0); - bgc_fp64_vector3_make(&final_primary, 0.0, 1.0, 0.0); - bgc_fp64_vector3_make(&final_auxiliary, 0.0, 0.0, -1.0); + bgc_fp64_vector3_make(&final_main, 0.0, 1.0, 0.0); + bgc_fp64_vector3_make(&final_branch, 0.0, 0.0, -1.0); - bgc_fp64_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp64_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); printf("\n120 degees turn:\n"); print_quaternion_fp64(&turn._versor); - // About 1 degree turn difference between initial_primary and initial_auxiliary directions - bgc_fp64_vector3_make(&initial_primary, 1.0, 0.0, 0.0); - bgc_fp64_vector3_make(&initial_auxiliary, 0.999848, 0.017452, 0.0); - bgc_fp64_vector3_make(&final_primary, 0.0, 1.0, 0.0); - bgc_fp64_vector3_make(&final_auxiliary, -1.0, 0.0, 0.0); + // About 1 degree turn difference between initial_main and initial_branch directions + bgc_fp64_vector3_make(&initial_main, 1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&initial_branch, 0.999848, 0.017452, 0.0); + bgc_fp64_vector3_make(&final_main, 0.0, 1.0, 0.0); + bgc_fp64_vector3_make(&final_branch, -1.0, 0.0, 0.0); - bgc_fp64_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp64_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); - printf("\nAbout 1 degree turn difference between initial_primary and initial_auxiliary directions:\n"); + printf("\nAbout 1 degree turn difference between initial_main and initial_branch directions:\n"); print_quaternion_fp64(&turn._versor); - // About 0.001 degree turn difference between initial_primary and initial_auxiliary directions - bgc_fp64_vector3_make(&initial_primary, 1.0, 0.0, 0.0); - bgc_fp64_vector3_make(&initial_auxiliary, 1.0, 0.000001, 0.0); - bgc_fp64_vector3_make(&final_primary, 0.0, -1.0, 0.0); - bgc_fp64_vector3_make(&final_auxiliary, 1.0, 0.0, 0.0); + // About 0.001 degree turn difference between initial_main and initial_branch directions + bgc_fp64_vector3_make(&initial_main, 1.0, 0.0, 0.0); + bgc_fp64_vector3_make(&initial_branch, 1.0, 0.000001, 0.0); + bgc_fp64_vector3_make(&final_main, 0.0, -1.0, 0.0); + bgc_fp64_vector3_make(&final_branch, 1.0, 0.0, 0.0); - bgc_fp64_turn3_make_basis_difference(&turn, &initial_primary, &initial_auxiliary, &final_primary, &final_auxiliary); + bgc_fp64_turn3_find_pair_difference(&turn, &initial_main, &initial_branch, &final_main, &final_branch); - printf("\nAbout 0.01 degree turn difference between initial_primary and initial_auxiliary directions:\n"); + printf("\nAbout 0.01 degree turn difference between initial_main and initial_branch directions:\n"); print_quaternion_fp64(&turn._versor); } -/* + #include "affine3.h" int main() { - //BGC_FP32_Turn3 start = { 1.0f, 0.0f, 0.0f, 0.0f }; - //BGC_FP32_Turn3 end = { 0.0f, 1.0f, 0.0f, 0.0f }; - - BGC_FP32_Turn3 start = { 1.0f, 0.0f, 0.0f, 0.0f }; - BGC_FP32_Turn3 end = { 0.9999f, 0.01414f, 0.0f, 0.0f }; - BGC_FP32_Slerp slerp; - BGC_FP32_Turn3 result; - bgc_fp32_slerp_make_full(&slerp, &start, &end); - bgc_fp32_slerp_get_phase_versor(&result, &slerp, 0.5f); - - //print_quaternion_fp32(&result); - - test_basis_difference_fp64(); + //test_pair_difference_fp32(); + test_pair_difference_fp64(); //printf("Affine3 performance test: %f\n", test_bgc_affine3_performance(10000000, 10)); @@ -495,4 +514,4 @@ int main() return 0; } -*/ + diff --git a/basic-geometry/dual-quaternion.c b/basic-geometry/dual-quaternion.c index 4db7e44..506e06a 100644 --- a/basic-geometry/dual-quaternion.c +++ b/basic-geometry/dual-quaternion.c @@ -21,11 +21,11 @@ extern inline void bgc_fp64_dual_quaternion_add_scaled(BGC_FP64_DualQuaternion* extern inline void bgc_fp32_dual_quaternion_subtract(BGC_FP32_DualQuaternion* difference, const BGC_FP32_DualQuaternion* minuend, const BGC_FP32_DualQuaternion* subtrahend); extern inline void bgc_fp64_dual_quaternion_subtract(BGC_FP64_DualQuaternion* difference, const BGC_FP64_DualQuaternion* minuend, const BGC_FP64_DualQuaternion* subtrahend); -extern inline void bgc_fp32_dual_quaternion_multiply(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const float multipier); -extern inline void bgc_fp64_dual_quaternion_multiply(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const double multipier); +extern inline void bgc_fp32_dual_quaternion_multiply_by_number(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const float multipier); +extern inline void bgc_fp64_dual_quaternion_multiply_by_number(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const double multipier); -extern inline void bgc_fp32_dual_quaternion_divide(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* divident, const float divisor); -extern inline void bgc_fp64_dual_quaternion_divide(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* divident, const double divisor); +extern inline void bgc_fp32_dual_quaternion_divide_by_number(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* divident, const float divisor); +extern inline void bgc_fp64_dual_quaternion_divide_by_number(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* divident, const double divisor); extern inline void bgc_fp32_dual_quaternion_get_mean2(BGC_FP32_DualQuaternion* mean, const BGC_FP32_DualQuaternion* quaternion1, const BGC_FP32_DualQuaternion* quaternion2); extern inline void bgc_fp64_dual_quaternion_get_mean2(BGC_FP64_DualQuaternion* mean, const BGC_FP64_DualQuaternion* quaternion1, const BGC_FP64_DualQuaternion* quaternion2); diff --git a/basic-geometry/dual-quaternion.h b/basic-geometry/dual-quaternion.h index e3f3357..122653c 100644 --- a/basic-geometry/dual-quaternion.h +++ b/basic-geometry/dual-quaternion.h @@ -113,28 +113,28 @@ inline void bgc_fp64_dual_quaternion_subtract(BGC_FP64_DualQuaternion* differenc // ================== Multiply ================== // -inline void bgc_fp32_dual_quaternion_multiply(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const float multipier) +inline void bgc_fp32_dual_quaternion_multiply_by_number(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const float multipier) { - bgc_fp32_quaternion_multiply(&product->real, &multiplicand->real, multipier); - bgc_fp32_quaternion_multiply(&product->dual, &multiplicand->dual, multipier); + bgc_fp32_quaternion_multiply_by_number(&product->real, &multiplicand->real, multipier); + bgc_fp32_quaternion_multiply_by_number(&product->dual, &multiplicand->dual, multipier); } -inline void bgc_fp64_dual_quaternion_multiply(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const double multipier) +inline void bgc_fp64_dual_quaternion_multiply_by_number(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const double multipier) { - bgc_fp64_quaternion_multiply(&product->real, &multiplicand->real, multipier); - bgc_fp64_quaternion_multiply(&product->dual, &multiplicand->dual, multipier); + bgc_fp64_quaternion_multiply_by_number(&product->real, &multiplicand->real, multipier); + bgc_fp64_quaternion_multiply_by_number(&product->dual, &multiplicand->dual, multipier); } // =================== Divide =================== // -inline void bgc_fp32_dual_quaternion_divide(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* divident, const float divisor) +inline void bgc_fp32_dual_quaternion_divide_by_number(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* divident, const float divisor) { - bgc_fp32_dual_quaternion_multiply(quotient, divident, 1.0f / divisor); + bgc_fp32_dual_quaternion_multiply_by_number(quotient, divident, 1.0f / divisor); } -inline void bgc_fp64_dual_quaternion_divide(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* divident, const double divisor) +inline void bgc_fp64_dual_quaternion_divide_by_number(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* divident, const double divisor) { - bgc_fp64_dual_quaternion_multiply(quotient, divident, 1.0 / divisor); + bgc_fp64_dual_quaternion_multiply_by_number(quotient, divident, 1.0 / divisor); } // ================ Mean of Two ================= // diff --git a/basic-geometry/quaternion.c b/basic-geometry/quaternion.c index 3f74252..e04fcdc 100644 --- a/basic-geometry/quaternion.c +++ b/basic-geometry/quaternion.c @@ -40,20 +40,20 @@ extern inline void bgc_fp64_quaternion_add_scaled(BGC_FP64_Quaternion* sum, cons extern inline void bgc_fp32_quaternion_subtract(BGC_FP32_Quaternion* difference, const BGC_FP32_Quaternion* minuend, const BGC_FP32_Quaternion* subtrahend); extern inline void bgc_fp64_quaternion_subtract(BGC_FP64_Quaternion* difference, const BGC_FP64_Quaternion* minuend, const BGC_FP64_Quaternion* subtrahend); -extern inline void bgc_fp32_quaternion_get_product(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* left, const BGC_FP32_Quaternion* right); -extern inline void bgc_fp64_quaternion_get_product(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* left, const BGC_FP64_Quaternion* right); +extern inline void bgc_fp32_quaternion_multiply_by_quaternion(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* left, const BGC_FP32_Quaternion* right); +extern inline void bgc_fp64_quaternion_multiply_by_quaternion(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* left, const BGC_FP64_Quaternion* right); -extern inline void bgc_fp32_quaternion_get_product_by_conjugate(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* left, const BGC_FP32_Quaternion* right); -extern inline void bgc_fp64_quaternion_get_product_by_conjugate(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* left, const BGC_FP64_Quaternion* right); +extern inline void bgc_fp32_quaternion_multiply_by_conjugate(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* left, const BGC_FP32_Quaternion* right); +extern inline void bgc_fp64_quaternion_multiply_by_conjugate(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* left, const BGC_FP64_Quaternion* right); -extern inline void bgc_fp32_quaternion_multiply(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* multiplicand, const float multipier); -extern inline void bgc_fp64_quaternion_multiply(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* multiplicand, const double multipier); +extern inline void bgc_fp32_quaternion_multiply_by_number(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* multiplicand, const float multipier); +extern inline void bgc_fp64_quaternion_multiply_by_number(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* multiplicand, const double multipier); -extern inline int bgc_fp32_quaternion_get_ratio(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* divident, const BGC_FP32_Quaternion* divisor); -extern inline int bgc_fp64_quaternion_get_ratio(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* divident, const BGC_FP64_Quaternion* divisor); +extern inline int bgc_fp32_quaternion_divide_by_quaternion(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* divident, const BGC_FP32_Quaternion* divisor); +extern inline int bgc_fp64_quaternion_divide_by_quaternion(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* divident, const BGC_FP64_Quaternion* divisor); -extern inline void bgc_fp32_quaternion_divide(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* dividend, const float divisor); -extern inline void bgc_fp64_quaternion_divide(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* dividend, const double divisor); +extern inline void bgc_fp32_quaternion_divide_by_number(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* dividend, const float divisor); +extern inline void bgc_fp64_quaternion_divide_by_number(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* dividend, const double divisor); extern inline void bgc_fp32_quaternion_get_mean2(BGC_FP32_Quaternion* mean, const BGC_FP32_Quaternion* quaternion1, const BGC_FP32_Quaternion* quaternion2); extern inline void bgc_fp64_quaternion_get_mean2(BGC_FP64_Quaternion* mean, const BGC_FP64_Quaternion* quaternion1, const BGC_FP64_Quaternion* quaternion2); @@ -88,6 +88,18 @@ extern inline int bgc_fp64_quaternion_normalize(BGC_FP64_Quaternion* quaternion) extern inline int bgc_fp32_quaternion_get_normalized(BGC_FP32_Quaternion* normalized, const BGC_FP32_Quaternion* quaternion); extern inline int bgc_fp64_quaternion_get_normalized(BGC_FP64_Quaternion* normalized, const BGC_FP64_Quaternion* quaternion); +extern inline void _bgc_fp32_quaternion_turn_vector_roughly(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Quaternion* quaternion, const BGC_FP32_Vector3* original_vector); +extern inline void _bgc_fp64_quaternion_turn_vector_roughly(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Quaternion* quaternion, const BGC_FP64_Vector3* original_vector); + +extern inline void _bgc_fp32_quaternion_turn_vector_back_roughly(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Quaternion* quaternion, const BGC_FP32_Vector3* original_vector); +extern inline void _bgc_fp64_quaternion_turn_vector_back_roughly(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Quaternion* quaternion, const BGC_FP64_Vector3* original_vector); + +extern inline int bgc_fp32_quaternion_turn_vector(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Quaternion* quaternion, const BGC_FP32_Vector3* original_vector); +extern inline int bgc_fp64_quaternion_turn_vector(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Quaternion* quaternion, const BGC_FP64_Vector3* original_vector); + +extern inline int bgc_fp32_quaternion_turn_vector_back(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Quaternion* quaternion, const BGC_FP32_Vector3* original_vector); +extern inline int bgc_fp64_quaternion_turn_vector_back(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Quaternion* quaternion, const BGC_FP64_Vector3* original_vector); + extern inline int bgc_fp32_quaternion_get_rotation_matrix(BGC_FP32_Matrix3x3* rotation, const BGC_FP32_Quaternion* quaternion); extern inline int bgc_fp64_quaternion_get_rotation_matrix(BGC_FP64_Matrix3x3* rotation, const BGC_FP64_Quaternion* quaternion); @@ -114,12 +126,12 @@ int bgc_fp32_quaternion_get_exponation(BGC_FP32_Quaternion* power, const BGC_FP3 // isnan(square_modulus) means checking for NaN value at square_modulus if (isnan(square_modulus)) { - return 0; + return BGC_FAILED; } if (square_vector <= BGC_FP32_SQUARE_EPSILON) { if (base->s0 < 0.0f) { - return 0; + return BGC_FAILED; } power->s0 = powf(base->s0, exponent); @@ -127,7 +139,7 @@ int bgc_fp32_quaternion_get_exponation(BGC_FP32_Quaternion* power, const BGC_FP3 power->x2 = 0.0f; power->x3 = 0.0f; - return 1; + return BGC_SUCCESS; } const float vector_modulus = sqrtf(square_vector); @@ -140,7 +152,7 @@ int bgc_fp32_quaternion_get_exponation(BGC_FP32_Quaternion* power, const BGC_FP3 power->x2 = base->x2 * multiplier; power->x3 = base->x3 * multiplier; - return 1; + return BGC_SUCCESS; } int bgc_fp64_quaternion_get_exponation(BGC_FP64_Quaternion* power, const BGC_FP64_Quaternion* base, const double exponent) @@ -155,12 +167,12 @@ int bgc_fp64_quaternion_get_exponation(BGC_FP64_Quaternion* power, const BGC_FP6 // isnan(square_modulus) means checking for NaN value at square_modulus if (isnan(square_modulus)) { - return 0; + return BGC_FAILED; } if (square_vector <= BGC_FP64_SQUARE_EPSILON) { if (base->s0 < 0.0) { - return 0; + return BGC_FAILED; } power->s0 = pow(base->s0, exponent); @@ -168,7 +180,7 @@ int bgc_fp64_quaternion_get_exponation(BGC_FP64_Quaternion* power, const BGC_FP6 power->x2 = 0.0; power->x3 = 0.0; - return 1; + return BGC_SUCCESS; } const double vector_modulus = sqrt(square_vector); @@ -181,5 +193,5 @@ int bgc_fp64_quaternion_get_exponation(BGC_FP64_Quaternion* power, const BGC_FP6 power->x2 = base->x2 * multiplier; power->x3 = base->x3 * multiplier; - return 1; + return BGC_SUCCESS; } diff --git a/basic-geometry/quaternion.h b/basic-geometry/quaternion.h index 8de1ccc..0eddc57 100644 --- a/basic-geometry/quaternion.h +++ b/basic-geometry/quaternion.h @@ -5,6 +5,7 @@ #include "utilities.h" #include "angle.h" +#include "vector3.h" #include "matrix3x3.h" typedef struct { @@ -247,7 +248,7 @@ inline void bgc_fp64_quaternion_subtract(BGC_FP64_Quaternion* difference, const // ================== Multiply ================== // -inline void bgc_fp32_quaternion_get_product(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* left, const BGC_FP32_Quaternion* right) +inline void bgc_fp32_quaternion_multiply_by_quaternion(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* left, const BGC_FP32_Quaternion* right) { 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); @@ -260,7 +261,7 @@ inline void bgc_fp32_quaternion_get_product(BGC_FP32_Quaternion* product, const product->x3 = x3; } -inline void bgc_fp64_quaternion_get_product(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* left, const BGC_FP64_Quaternion* right) +inline void bgc_fp64_quaternion_multiply_by_quaternion(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* left, const BGC_FP64_Quaternion* right) { 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); @@ -273,7 +274,7 @@ inline void bgc_fp64_quaternion_get_product(BGC_FP64_Quaternion* product, const product->x3 = x3; } -inline void bgc_fp32_quaternion_get_product_by_conjugate(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* left, const BGC_FP32_Quaternion* right) +inline void bgc_fp32_quaternion_multiply_by_conjugate(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* left, const BGC_FP32_Quaternion* right) { 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->x3 * right->x2) - (left->s0 * right->x1 + left->x2 * right->x3); @@ -286,7 +287,7 @@ inline void bgc_fp32_quaternion_get_product_by_conjugate(BGC_FP32_Quaternion* pr product->x3 = x3; } -inline void bgc_fp64_quaternion_get_product_by_conjugate(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* left, const BGC_FP64_Quaternion* right) +inline void bgc_fp64_quaternion_multiply_by_conjugate(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* left, const BGC_FP64_Quaternion* right) { 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->x3 * right->x2) - (left->s0 * right->x1 + left->x2 * right->x3); @@ -299,7 +300,7 @@ inline void bgc_fp64_quaternion_get_product_by_conjugate(BGC_FP64_Quaternion* pr product->x3 = x3; } -inline void bgc_fp32_quaternion_multiply(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* multiplicand, const float multipier) +inline void bgc_fp32_quaternion_multiply_by_number(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* multiplicand, const float multipier) { product->s0 = multiplicand->s0 * multipier; product->x1 = multiplicand->x1 * multipier; @@ -307,7 +308,7 @@ inline void bgc_fp32_quaternion_multiply(BGC_FP32_Quaternion* product, const BGC product->x3 = multiplicand->x3 * multipier; } -inline void bgc_fp64_quaternion_multiply(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* multiplicand, const double multipier) +inline void bgc_fp64_quaternion_multiply_by_number(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* multiplicand, const double multipier) { product->s0 = multiplicand->s0 * multipier; product->x1 = multiplicand->x1 * multipier; @@ -317,12 +318,12 @@ inline void bgc_fp64_quaternion_multiply(BGC_FP64_Quaternion* product, const BGC // =================== Divide =================== // -inline int bgc_fp32_quaternion_get_ratio(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* divident, const BGC_FP32_Quaternion* divisor) +inline int bgc_fp32_quaternion_divide_by_quaternion(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* divident, const BGC_FP32_Quaternion* divisor) { const float square_modulus = bgc_fp32_quaternion_get_square_modulus(divisor); if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) { - return 0; + return BGC_FAILED; } const float s0 = (divident->s0 * divisor->s0 + divident->x1 * divisor->x1) + (divident->x2 * divisor->x2 + divident->x3 * divisor->x3); @@ -337,15 +338,15 @@ inline int bgc_fp32_quaternion_get_ratio(BGC_FP32_Quaternion* quotient, const BG quotient->x2 = x2 * multiplicand; quotient->x3 = x3 * multiplicand; - return 1; + return BGC_SUCCESS; } -inline int bgc_fp64_quaternion_get_ratio(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* divident, const BGC_FP64_Quaternion* divisor) +inline int bgc_fp64_quaternion_divide_by_quaternion(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* divident, const BGC_FP64_Quaternion* divisor) { const double square_modulus = bgc_fp64_quaternion_get_square_modulus(divisor); if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) { - return 0; + return BGC_FAILED; } const double s0 = (divident->s0 * divisor->s0 + divident->x1 * divisor->x1) + (divident->x2 * divisor->x2 + divident->x3 * divisor->x3); @@ -360,17 +361,17 @@ inline int bgc_fp64_quaternion_get_ratio(BGC_FP64_Quaternion* quotient, const BG quotient->x2 = x2 * multiplicand; quotient->x3 = x3 * multiplicand; - return 1; + return BGC_SUCCESS; } -inline void bgc_fp32_quaternion_divide(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* dividend, const float divisor) +inline void bgc_fp32_quaternion_divide_by_number(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* dividend, const float divisor) { - bgc_fp32_quaternion_multiply(quotient, dividend, 1.0f / divisor); + bgc_fp32_quaternion_multiply_by_number(quotient, dividend, 1.0f / divisor); } -inline void bgc_fp64_quaternion_divide(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* dividend, const double divisor) +inline void bgc_fp64_quaternion_divide_by_number(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* dividend, const double divisor) { - bgc_fp64_quaternion_multiply(quotient, dividend, 1.0 / divisor); + bgc_fp64_quaternion_multiply_by_number(quotient, dividend, 1.0 / divisor); } // ================ Mean of Two ================= // @@ -504,7 +505,7 @@ inline int bgc_fp32_quaternion_get_inverse(BGC_FP32_Quaternion* inverse, const B const float square_modulus = bgc_fp32_quaternion_get_square_modulus(quaternion); if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) { - return 0; + return BGC_FAILED; } const float multiplicand = 1.0f / square_modulus; @@ -514,7 +515,7 @@ inline int bgc_fp32_quaternion_get_inverse(BGC_FP32_Quaternion* inverse, const B inverse->x2 = -quaternion->x2 * multiplicand; inverse->x3 = -quaternion->x3 * multiplicand; - return 1; + return BGC_SUCCESS; } inline int bgc_fp64_quaternion_get_inverse(BGC_FP64_Quaternion* inverse, const BGC_FP64_Quaternion* quaternion) @@ -522,7 +523,7 @@ inline int bgc_fp64_quaternion_get_inverse(BGC_FP64_Quaternion* inverse, const B const double square_modulus = bgc_fp64_quaternion_get_square_modulus(quaternion); if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) { - return 0; + return BGC_FAILED; } const double multiplicand = 1.0 / square_modulus; @@ -532,7 +533,7 @@ inline int bgc_fp64_quaternion_get_inverse(BGC_FP64_Quaternion* inverse, const B inverse->x2 = -quaternion->x2 * multiplicand; inverse->x3 = -quaternion->x3 * multiplicand; - return 1; + return BGC_SUCCESS; } inline int bgc_fp32_quaternion_invert(BGC_FP32_Quaternion* quaternion) @@ -552,11 +553,11 @@ inline int bgc_fp32_quaternion_normalize(BGC_FP32_Quaternion* quaternion) const float square_modulus = bgc_fp32_quaternion_get_square_modulus(quaternion); if (bgc_fp32_is_square_unit(square_modulus)) { - return 1; + return BGC_SUCCESS; } if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) { - return 0; + return BGC_FAILED; } const float multiplier = sqrtf(1.0f / square_modulus); @@ -566,7 +567,7 @@ inline int bgc_fp32_quaternion_normalize(BGC_FP32_Quaternion* quaternion) quaternion->x2 *= multiplier; quaternion->x3 *= multiplier; - return 1; + return BGC_SUCCESS; } inline int bgc_fp64_quaternion_normalize(BGC_FP64_Quaternion* quaternion) @@ -574,11 +575,11 @@ inline int bgc_fp64_quaternion_normalize(BGC_FP64_Quaternion* quaternion) const double square_modulus = bgc_fp64_quaternion_get_square_modulus(quaternion); if (bgc_fp64_is_square_unit(square_modulus)) { - return 1; + return BGC_SUCCESS; } if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) { - return 0; + return BGC_FAILED; } const double multiplier = sqrt(1.0 / square_modulus); @@ -588,7 +589,7 @@ inline int bgc_fp64_quaternion_normalize(BGC_FP64_Quaternion* quaternion) quaternion->x2 *= multiplier; quaternion->x3 *= multiplier; - return 1; + return BGC_SUCCESS; } inline int bgc_fp32_quaternion_get_normalized(BGC_FP32_Quaternion* normalized, const BGC_FP32_Quaternion* quaternion) @@ -597,16 +598,16 @@ inline int bgc_fp32_quaternion_get_normalized(BGC_FP32_Quaternion* normalized, c if (bgc_fp32_is_square_unit(square_modulus)) { bgc_fp32_quaternion_copy(normalized, quaternion); - return 1; + return BGC_SUCCESS; } if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) { bgc_fp32_quaternion_reset(normalized); - return 0; + return BGC_FAILED; } - bgc_fp32_quaternion_multiply(normalized, quaternion, sqrtf(1.0f / square_modulus)); - return 1; + bgc_fp32_quaternion_multiply_by_number(normalized, quaternion, sqrtf(1.0f / square_modulus)); + return BGC_SUCCESS; } inline int bgc_fp64_quaternion_get_normalized(BGC_FP64_Quaternion* normalized, const BGC_FP64_Quaternion* quaternion) @@ -615,16 +616,16 @@ inline int bgc_fp64_quaternion_get_normalized(BGC_FP64_Quaternion* normalized, c if (bgc_fp64_is_square_unit(square_modulus)) { bgc_fp64_quaternion_copy(normalized, quaternion); - return 1; + return BGC_SUCCESS; } if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) { bgc_fp64_quaternion_reset(normalized); - return 0; + return BGC_FAILED; } - bgc_fp64_quaternion_multiply(normalized, quaternion, sqrt(1.0 / square_modulus)); - return 1; + bgc_fp64_quaternion_multiply_by_number(normalized, quaternion, sqrt(1.0 / square_modulus)); + return BGC_SUCCESS; } // =============== Get Exponation =============== // @@ -633,6 +634,182 @@ int bgc_fp32_quaternion_get_exponation(BGC_FP32_Quaternion* power, const BGC_FP3 int bgc_fp64_quaternion_get_exponation(BGC_FP64_Quaternion* power, const BGC_FP64_Quaternion* base, const double exponent); +// ============== Raw Turn Vector3 ============== // + +// An internal function +inline void _bgc_fp32_quaternion_turn_vector_roughly(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Quaternion* quaternion, const BGC_FP32_Vector3* original_vector) +{ + const float tx1 = 2.0f * (quaternion->x2 * original_vector->x3 - quaternion->x3 * original_vector->x2); + const float tx2 = 2.0f * (quaternion->x3 * original_vector->x1 - quaternion->x1 * original_vector->x3); + const float tx3 = 2.0f * (quaternion->x1 * original_vector->x2 - quaternion->x2 * original_vector->x1); + + const float x1 = (original_vector->x1 + tx1 * quaternion->s0) + (quaternion->x2 * tx3 - quaternion->x3 * tx2); + const float x2 = (original_vector->x2 + tx2 * quaternion->s0) + (quaternion->x3 * tx1 - quaternion->x1 * tx3); + const float x3 = (original_vector->x3 + tx3 * quaternion->s0) + (quaternion->x1 * tx2 - quaternion->x2 * tx1); + + turned_vector->x1 = x1; + turned_vector->x2 = x2; + turned_vector->x3 = x3; +} + +// An internal function +inline void _bgc_fp64_quaternion_turn_vector_roughly(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Quaternion* quaternion, const BGC_FP64_Vector3* original_vector) +{ + const double tx1 = 2.0f * (quaternion->x2 * original_vector->x3 - quaternion->x3 * original_vector->x2); + const double tx2 = 2.0f * (quaternion->x3 * original_vector->x1 - quaternion->x1 * original_vector->x3); + const double tx3 = 2.0f * (quaternion->x1 * original_vector->x2 - quaternion->x2 * original_vector->x1); + + const double x1 = (original_vector->x1 + tx1 * quaternion->s0) + (quaternion->x2 * tx3 - quaternion->x3 * tx2); + const double x2 = (original_vector->x2 + tx2 * quaternion->s0) + (quaternion->x3 * tx1 - quaternion->x1 * tx3); + const double x3 = (original_vector->x3 + tx3 * quaternion->s0) + (quaternion->x1 * tx2 - quaternion->x2 * tx1); + + turned_vector->x1 = x1; + turned_vector->x2 = x2; + turned_vector->x3 = x3; +} + +// ========= Raw Turn Vector3 Backwards ========= // + +// An internal function +inline void _bgc_fp32_quaternion_turn_vector_back_roughly(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Quaternion* quaternion, const BGC_FP32_Vector3* original_vector) +{ + const float tx1 = 2.0f * (quaternion->x2 * original_vector->x3 - quaternion->x3 * original_vector->x2); + const float tx2 = 2.0f * (quaternion->x3 * original_vector->x1 - quaternion->x1 * original_vector->x3); + const float tx3 = 2.0f * (quaternion->x1 * original_vector->x2 - quaternion->x2 * original_vector->x1); + + const float x1 = (original_vector->x1 + tx1 * quaternion->s0) + (quaternion->x2 * tx3 - quaternion->x3 * tx2); + const float x2 = (original_vector->x2 + tx2 * quaternion->s0) + (quaternion->x3 * tx1 - quaternion->x1 * tx3); + const float x3 = (original_vector->x3 + tx3 * quaternion->s0) + (quaternion->x1 * tx2 - quaternion->x2 * tx1); + + turned_vector->x1 = x1; + turned_vector->x2 = x2; + turned_vector->x3 = x3; +} + +// An internal function +inline void _bgc_fp64_quaternion_turn_vector_back_roughly(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Quaternion* quaternion, const BGC_FP64_Vector3* original_vector) +{ + const double tx1 = 2.0f * (quaternion->x2 * original_vector->x3 - quaternion->x3 * original_vector->x2); + const double tx2 = 2.0f * (quaternion->x3 * original_vector->x1 - quaternion->x1 * original_vector->x3); + const double tx3 = 2.0f * (quaternion->x1 * original_vector->x2 - quaternion->x2 * original_vector->x1); + + const double x1 = (original_vector->x1 + tx1 * quaternion->s0) + (quaternion->x2 * tx3 - quaternion->x3 * tx2); + const double x2 = (original_vector->x2 + tx2 * quaternion->s0) + (quaternion->x3 * tx1 - quaternion->x1 * tx3); + const double x3 = (original_vector->x3 + tx3 * quaternion->s0) + (quaternion->x1 * tx2 - quaternion->x2 * tx1); + + turned_vector->x1 = x1; + turned_vector->x2 = x2; + turned_vector->x3 = x3; +} + +// ================ Turn Vector3 ================ // + +inline int bgc_fp32_quaternion_turn_vector(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Quaternion* quaternion, const BGC_FP32_Vector3* original_vector) +{ + const float square_modulus = bgc_fp32_quaternion_get_square_modulus(quaternion); + + if (square_modulus < BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) { + return BGC_FAILED; + } + + const float multiplier = 2.0f / square_modulus; + + const float tx1 = multiplier * (quaternion->x2 * original_vector->x3 - quaternion->x3 * original_vector->x2); + const float tx2 = multiplier * (quaternion->x3 * original_vector->x1 - quaternion->x1 * original_vector->x3); + const float tx3 = multiplier * (quaternion->x1 * original_vector->x2 - quaternion->x2 * original_vector->x1); + + const float x1 = (original_vector->x1 + tx1 * quaternion->s0) + (quaternion->x2 * tx3 - quaternion->x3 * tx2); + const float x2 = (original_vector->x2 + tx2 * quaternion->s0) + (quaternion->x3 * tx1 - quaternion->x1 * tx3); + const float x3 = (original_vector->x3 + tx3 * quaternion->s0) + (quaternion->x1 * tx2 - quaternion->x2 * tx1); + + turned_vector->x1 = x1; + turned_vector->x2 = x2; + turned_vector->x3 = x3; + + + return BGC_SUCCESS; +} + +inline int bgc_fp64_quaternion_turn_vector(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Quaternion* quaternion, const BGC_FP64_Vector3* original_vector) +{ + const double square_modulus = bgc_fp64_quaternion_get_square_modulus(quaternion); + + if (square_modulus < BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) { + return BGC_FAILED; + } + + const double multiplier = 2.0 / square_modulus; + + const double tx1 = multiplier * (quaternion->x2 * original_vector->x3 - quaternion->x3 * original_vector->x2); + const double tx2 = multiplier * (quaternion->x3 * original_vector->x1 - quaternion->x1 * original_vector->x3); + const double tx3 = multiplier * (quaternion->x1 * original_vector->x2 - quaternion->x2 * original_vector->x1); + + const double x1 = (original_vector->x1 + tx1 * quaternion->s0) + (quaternion->x2 * tx3 - quaternion->x3 * tx2); + const double x2 = (original_vector->x2 + tx2 * quaternion->s0) + (quaternion->x3 * tx1 - quaternion->x1 * tx3); + const double x3 = (original_vector->x3 + tx3 * quaternion->s0) + (quaternion->x1 * tx2 - quaternion->x2 * tx1); + + turned_vector->x1 = x1; + turned_vector->x2 = x2; + turned_vector->x3 = x3; + + + return BGC_SUCCESS; +} + +// =========== Turn Vector3 Backwards =========== // + +inline int bgc_fp32_quaternion_turn_vector_back(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Quaternion* quaternion, const BGC_FP32_Vector3* original_vector) +{ + const float square_modulus = bgc_fp32_quaternion_get_square_modulus(quaternion); + + if (square_modulus < BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) { + return BGC_FAILED; + } + + const float multiplier = 2.0f / square_modulus; + + const float tx1 = multiplier * (quaternion->x2 * original_vector->x3 - quaternion->x3 * original_vector->x2); + const float tx2 = multiplier * (quaternion->x3 * original_vector->x1 - quaternion->x1 * original_vector->x3); + const float tx3 = multiplier * (quaternion->x1 * original_vector->x2 - quaternion->x2 * original_vector->x1); + + const float x1 = (original_vector->x1 - tx1 * quaternion->s0) + (quaternion->x2 * tx3 - quaternion->x3 * tx2); + const float x2 = (original_vector->x2 - tx2 * quaternion->s0) + (quaternion->x3 * tx1 - quaternion->x1 * tx3); + const float x3 = (original_vector->x3 - tx3 * quaternion->s0) + (quaternion->x1 * tx2 - quaternion->x2 * tx1); + + turned_vector->x1 = x1; + turned_vector->x2 = x2; + turned_vector->x3 = x3; + + + return BGC_SUCCESS; +} + +inline int bgc_fp64_quaternion_turn_vector_back(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Quaternion* quaternion, const BGC_FP64_Vector3* original_vector) +{ + const double square_modulus = bgc_fp64_quaternion_get_square_modulus(quaternion); + + if (square_modulus < BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) { + return BGC_FAILED; + } + + const double multiplier = 2.0 / square_modulus; + + const double tx1 = multiplier * (quaternion->x2 * original_vector->x3 - quaternion->x3 * original_vector->x2); + const double tx2 = multiplier * (quaternion->x3 * original_vector->x1 - quaternion->x1 * original_vector->x3); + const double tx3 = multiplier * (quaternion->x1 * original_vector->x2 - quaternion->x2 * original_vector->x1); + + const double x1 = (original_vector->x1 - tx1 * quaternion->s0) + (quaternion->x2 * tx3 - quaternion->x3 * tx2); + const double x2 = (original_vector->x2 - tx2 * quaternion->s0) + (quaternion->x3 * tx1 - quaternion->x1 * tx3); + const double x3 = (original_vector->x3 - tx3 * quaternion->s0) + (quaternion->x1 * tx2 - quaternion->x2 * tx1); + + turned_vector->x1 = x1; + turned_vector->x2 = x2; + turned_vector->x3 = x3; + + + return BGC_SUCCESS; +} + // ============ Get Rotation Matrix ============= // inline int bgc_fp32_quaternion_get_rotation_matrix(BGC_FP32_Matrix3x3* rotation, const BGC_FP32_Quaternion* quaternion) @@ -647,7 +824,7 @@ inline int bgc_fp32_quaternion_get_rotation_matrix(BGC_FP32_Matrix3x3* rotation, if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) { bgc_fp32_matrix3x3_make_identity(rotation); - return 0; + return BGC_FAILED; } const float corrector1 = 1.0f / square_modulus; @@ -673,7 +850,7 @@ inline int bgc_fp32_quaternion_get_rotation_matrix(BGC_FP32_Matrix3x3* rotation, rotation->r3c2 = corrector2 * (x2x3 + s0x1); rotation->r1c3 = corrector2 * (x1x3 + s0x2); - return 1; + return BGC_SUCCESS; } inline int bgc_fp64_quaternion_get_rotation_matrix(BGC_FP64_Matrix3x3* rotation, const BGC_FP64_Quaternion* quaternion) @@ -688,7 +865,7 @@ inline int bgc_fp64_quaternion_get_rotation_matrix(BGC_FP64_Matrix3x3* rotation, if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) { bgc_fp64_matrix3x3_make_identity(rotation); - return 0; + return BGC_FAILED; } const double corrector1 = 1.0f / square_modulus; @@ -714,7 +891,7 @@ inline int bgc_fp64_quaternion_get_rotation_matrix(BGC_FP64_Matrix3x3* rotation, rotation->r3c2 = corrector2 * (x2x3 + s0x1); rotation->r1c3 = corrector2 * (x1x3 + s0x2); - return 1; + return BGC_SUCCESS; } // ============= Get Reverse Matrix ============= // @@ -731,7 +908,7 @@ inline int bgc_fp32_quaternion_get_reverse_matrix(BGC_FP32_Matrix3x3* reverse, c if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) { bgc_fp32_matrix3x3_make_identity(reverse); - return 0; + return BGC_FAILED; } const float corrector1 = 1.0f / square_modulus; @@ -757,7 +934,7 @@ inline int bgc_fp32_quaternion_get_reverse_matrix(BGC_FP32_Matrix3x3* reverse, c reverse->r3c2 = corrector2 * (x2x3 - s0x1); reverse->r1c3 = corrector2 * (x1x3 - s0x2); - return 1; + return BGC_SUCCESS; } inline int bgc_fp64_quaternion_get_reverse_matrix(BGC_FP64_Matrix3x3* reverse, const BGC_FP64_Quaternion* quaternion) @@ -772,7 +949,7 @@ inline int bgc_fp64_quaternion_get_reverse_matrix(BGC_FP64_Matrix3x3* reverse, c if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) { bgc_fp64_matrix3x3_make_identity(reverse); - return 0; + return BGC_FAILED; } const double corrector1 = 1.0f / square_modulus; @@ -805,22 +982,22 @@ inline int bgc_fp64_quaternion_get_reverse_matrix(BGC_FP64_Matrix3x3* reverse, c inline int bgc_fp32_quaternion_get_both_matrices(BGC_FP32_Matrix3x3* rotation, BGC_FP32_Matrix3x3* reverse, const BGC_FP32_Quaternion* quaternion) { - if (bgc_fp32_quaternion_get_reverse_matrix(reverse, quaternion)) { + if (bgc_fp32_quaternion_get_reverse_matrix(reverse, quaternion) == BGC_SUCCESS) { bgc_fp32_matrix3x3_get_transposed(rotation, reverse); - return 1; + return BGC_SUCCESS; } - return 0; + return BGC_FAILED; } inline int bgc_fp64_quaternion_get_both_matrices(BGC_FP64_Matrix3x3* rotation, BGC_FP64_Matrix3x3* reverse, const BGC_FP64_Quaternion* quaternion) { - if (bgc_fp64_quaternion_get_reverse_matrix(reverse, quaternion)) { + if (bgc_fp64_quaternion_get_reverse_matrix(reverse, quaternion) == BGC_SUCCESS) { bgc_fp64_matrix3x3_get_transposed(rotation, reverse); - return 1; + return BGC_SUCCESS; } - return 0; + return BGC_FAILED; } // ================== Are Close ================= // diff --git a/basic-geometry/turn3.c b/basic-geometry/turn3.c index 21570f1..0050c64 100644 --- a/basic-geometry/turn3.c +++ b/basic-geometry/turn3.c @@ -85,7 +85,7 @@ void _bgc_fp32_turn3_normalize(BGC_FP32_Turn3* turn, const float square_modulus) return; } - bgc_fp32_quaternion_multiply(&turn->_versor, &turn->_versor, sqrtf(1.0f / square_modulus)); + bgc_fp32_quaternion_multiply_by_number(&turn->_versor, &turn->_versor, sqrtf(1.0f / square_modulus)); } void _bgc_fp64_turn3_normalize(BGC_FP64_Turn3* turn, const double square_modulus) @@ -95,7 +95,7 @@ void _bgc_fp64_turn3_normalize(BGC_FP64_Turn3* turn, const double square_modulus return; } - bgc_fp64_quaternion_multiply(&turn->_versor, &turn->_versor, sqrt(1.0 / square_modulus)); + bgc_fp64_quaternion_multiply_by_number(&turn->_versor, &turn->_versor, sqrt(1.0 / square_modulus)); } @@ -289,190 +289,246 @@ int bgc_fp64_turn3_find_direction_difference(BGC_FP64_Turn3* difference, const B return _bgc_fp64_turn3_make_direction_turn(difference, start, end, start_square_modulus * end_square_modulus); } -// =============== Set Directions =============== // +// ============ Make Orthogonal Pair ============ // -static int _bgc_fp32_turn3_validate_basis(const float primary_square_modulus, const float auxiliary_square_modulus, const float orthogonal_square_modulus) +static inline int _bgc_fp32_turn3_get_orthogonal_pair(BGC_FP32_Vector3* unit_main, BGC_FP32_Vector3* unit_branch, const BGC_FP32_Vector3* main, const BGC_FP32_Vector3* branch) { - if (primary_square_modulus <= BGC_FP32_SQUARE_EPSILON) { - //TODO: add error code for: primary_vector is zero - return BGC_FAILED; + const float main_square_modulus = bgc_fp32_vector3_get_square_modulus(main); + + if (main_square_modulus <= BGC_FP32_SQUARE_EPSILON) { + return _BGC_ERROR_TURN3_EMPTY_MAIN; } - if (auxiliary_square_modulus <= BGC_FP32_SQUARE_EPSILON) { - //TODO: add error code for: auxiliary_vector is zero - return BGC_FAILED; + const float branch_square_modulus = bgc_fp32_vector3_get_square_modulus(branch); + + if (branch_square_modulus <= BGC_FP32_SQUARE_EPSILON) { + return _BGC_ERROR_TURN3_EMPTY_BRANCH; } - if (orthogonal_square_modulus <= BGC_FP32_SQUARE_EPSILON * primary_square_modulus * auxiliary_square_modulus) { - //TODO: add error code for: primary_vector and auxiliary_vector are parallel - return BGC_FAILED; + bgc_fp32_vector3_multiply(unit_main, main, sqrtf(1.0f / main_square_modulus)); + + bgc_fp32_vector3_add_scaled(unit_branch, branch, unit_main, -bgc_fp32_vector3_get_dot_product(branch, unit_main)); + + const float orthogonal_square_modulus = bgc_fp32_vector3_get_square_modulus(unit_branch); + + if (orthogonal_square_modulus <= BGC_FP32_SQUARE_EPSILON) { + return _BGC_ERROR_TURN3_PAIR_PARALLEL; + } + + bgc_fp32_vector3_multiply(unit_branch, unit_branch, sqrtf(1.0f / orthogonal_square_modulus)); + + return BGC_SUCCESS; +} + +static inline int _bgc_fp64_turn3_get_orthogonal_pair(BGC_FP64_Vector3* unit_main, BGC_FP64_Vector3* unit_branch, const BGC_FP64_Vector3* main, const BGC_FP64_Vector3* branch) +{ + const double main_square_modulus = bgc_fp64_vector3_get_square_modulus(main); + + if (main_square_modulus <= BGC_FP64_SQUARE_EPSILON) { + return _BGC_ERROR_TURN3_EMPTY_MAIN; + } + + const double branch_square_modulus = bgc_fp64_vector3_get_square_modulus(branch); + + if (branch_square_modulus <= BGC_FP64_SQUARE_EPSILON) { + return _BGC_ERROR_TURN3_EMPTY_BRANCH; + } + + bgc_fp64_vector3_multiply(unit_main, main, sqrtf(1.0 / main_square_modulus)); + + bgc_fp64_vector3_add_scaled(unit_branch, branch, unit_main, -bgc_fp64_vector3_get_dot_product(branch, unit_main)); + + const double orthogonal_square_modulus = bgc_fp64_vector3_get_square_modulus(unit_branch); + + if (orthogonal_square_modulus <= BGC_FP64_SQUARE_EPSILON) { + return _BGC_ERROR_TURN3_PAIR_PARALLEL; + } + + bgc_fp64_vector3_multiply(unit_branch, unit_branch, sqrt(1.0 / orthogonal_square_modulus)); + + return BGC_SUCCESS; +} + +// ========= Make Direction Difference ========== // + +static inline void _bgc_fp32_turn3_get_turning_quaternion(BGC_FP32_Quaternion* quaternion, const BGC_FP32_Vector3* unit_start, const BGC_FP32_Vector3* unit_end, const BGC_FP32_Vector3* unit_orthogonal) +{ + BGC_FP32_Vector3 axis; + + bgc_fp32_vector3_get_cross_product(&axis, unit_start, unit_end); + + const float dot_product = bgc_fp32_vector3_get_dot_product(unit_start, unit_end); + + const float axis_square_modulus = bgc_fp32_vector3_get_square_modulus(&axis); + + // unit_start and unit_end are parallel + if (axis_square_modulus <= BGC_FP32_SQUARE_EPSILON) { + // unit_start and unit_end are co-directional, angle = 180 degrees + if (dot_product >= 0.0f) { + quaternion->s0 = 1.0f; + quaternion->x1 = 0.0f; + quaternion->x2 = 0.0f; + quaternion->x3 = 0.0f; + return; + } + + // unit_start and unit_end are opposite, angle = 180 degrees + quaternion->s0 = 0.0f; + quaternion->x1 = unit_orthogonal->x1; + quaternion->x2 = unit_orthogonal->x2; + quaternion->x3 = unit_orthogonal->x3; + return; + } + + const float axis_modulus = sqrtf(axis_square_modulus); + + const float angle = 0.5f * atan2f(axis_modulus, dot_product); + + const float multiplier = sinf(angle) / axis_modulus; + + quaternion->s0 = cosf(angle); + quaternion->x1 = axis.x1 * multiplier; + quaternion->x2 = axis.x2 * multiplier; + quaternion->x3 = axis.x3 * multiplier; +} + +static inline void _bgc_fp64_turn3_get_turning_quaternion(BGC_FP64_Quaternion* quaternion, const BGC_FP64_Vector3* unit_start, const BGC_FP64_Vector3* unit_end, const BGC_FP64_Vector3* unit_orthogonal) +{ + BGC_FP64_Vector3 axis; + + bgc_fp64_vector3_get_cross_product(&axis, unit_start, unit_end); + + const double dot_product = bgc_fp64_vector3_get_dot_product(unit_start, unit_end); + + const double axis_square_modulus = bgc_fp64_vector3_get_square_modulus(&axis); + + // unit_start and unit_end are parallel + if (axis_square_modulus <= BGC_FP64_SQUARE_EPSILON) { + // unit_start and unit_end are co-directional, angle = 180 degrees + if (dot_product >= 0.0) { + quaternion->s0 = 1.0; + quaternion->x1 = 0.0; + quaternion->x2 = 0.0; + quaternion->x3 = 0.0; + return; + } + + // unit_start and unit_end are opposite, angle = 180 degrees + quaternion->s0 = 0.0; + quaternion->x1 = unit_orthogonal->x1; + quaternion->x2 = unit_orthogonal->x2; + quaternion->x3 = unit_orthogonal->x3; + return; + } + + const double axis_modulus = sqrt(axis_square_modulus); + + const double angle = 0.5 * atan2(axis_modulus, dot_product); + + const double multiplier = sin(angle) / axis_modulus; + + quaternion->s0 = cos(angle); + quaternion->x1 = axis.x1 * multiplier; + quaternion->x2 = axis.x2 * multiplier; + quaternion->x3 = axis.x3 * multiplier; +} + +// ============ Make Pair Difference ============ // + +int bgc_fp32_turn3_find_pair_difference( + BGC_FP32_Turn3* turn, + const BGC_FP32_Vector3* first_pair_main, + const BGC_FP32_Vector3* first_pair_branch, + const BGC_FP32_Vector3* second_pair_main, + const BGC_FP32_Vector3* second_pair_branch +) { + BGC_FP32_Vector3 first_fixed_main, first_fixed_branch, first_turned_branch, second_fixed_main, second_fixed_branch; + + int status = _bgc_fp32_turn3_get_orthogonal_pair(&first_fixed_main, &first_fixed_branch, first_pair_main, first_pair_branch); + + if (status != BGC_SUCCESS) { + bgc_fp32_turn3_reset(turn); + return status + _BGC_ERROR_TURN3_FIRST_PAIR; + } + + status = _bgc_fp32_turn3_get_orthogonal_pair(&second_fixed_main, &second_fixed_branch, second_pair_main, second_pair_branch); + + if (status != BGC_SUCCESS) { + bgc_fp32_turn3_reset(turn); + return status + _BGC_ERROR_TURN3_SECOND_PAIR; + } + + BGC_FP32_Quaternion q1, q2; + + // Calculation of a turn (q1) which turns first_fixed_main into second_fixed_main + _bgc_fp32_turn3_get_turning_quaternion(&q1, &first_fixed_main, &second_fixed_main, &first_fixed_branch); + + // Roughly turn first_fixed_branch with q1 turn + _bgc_fp32_quaternion_turn_vector_roughly(&first_turned_branch, &q1, &first_fixed_branch); + + // Calculation of a turn (q2) which turns first_turned_branch into second_fixed_branch + _bgc_fp32_turn3_get_turning_quaternion(&q2, &first_turned_branch, &second_fixed_branch, &second_fixed_main); + + // Composing two turns with multiplication of quaterntions (q2 * q1) + bgc_fp32_quaternion_multiply_by_quaternion(&turn->_versor, &q2, &q1); + + // Making a final versor (a normalized quaternion) + const float square_modulus = bgc_fp32_quaternion_get_square_modulus(&turn->_versor); + + if (!bgc_fp32_is_square_unit(square_modulus)) { + _bgc_fp32_turn3_normalize(turn, square_modulus); } return BGC_SUCCESS; } -static int _bgc_fp64_turn3_validate_basis(const double primary_square_modulus, const double auxiliary_square_modulus, const double orthogonal_square_modulus) -{ - if (primary_square_modulus <= BGC_FP64_SQUARE_EPSILON) { - //TODO: add error code for: primary_vector is zero - return BGC_FAILED; +int bgc_fp64_turn3_find_pair_difference( + BGC_FP64_Turn3* turn, + const BGC_FP64_Vector3* first_pair_main, + const BGC_FP64_Vector3* first_pair_branch, + const BGC_FP64_Vector3* second_pair_main, + const BGC_FP64_Vector3* second_pair_branch +) { + BGC_FP64_Vector3 first_fixed_main, first_fixed_branch, first_turned_branch, second_fixed_main, second_fixed_branch; + + int status = _bgc_fp64_turn3_get_orthogonal_pair(&first_fixed_main, &first_fixed_branch, first_pair_main, first_pair_branch); + + if (status != BGC_SUCCESS) { + bgc_fp64_turn3_reset(turn); + return status + _BGC_ERROR_TURN3_FIRST_PAIR; } - if (auxiliary_square_modulus <= BGC_FP64_SQUARE_EPSILON) { - //TODO: add error code for: auxiliary_vector is zero - return BGC_FAILED; + status = _bgc_fp64_turn3_get_orthogonal_pair(&second_fixed_main, &second_fixed_branch, second_pair_main, second_pair_branch); + + if (status != BGC_SUCCESS) { + bgc_fp64_turn3_reset(turn); + return status + _BGC_ERROR_TURN3_SECOND_PAIR; } - if (orthogonal_square_modulus <= BGC_FP64_SQUARE_EPSILON * primary_square_modulus * auxiliary_square_modulus) { - //TODO: add error code for: primary_vector and auxiliary_vector are parallel - return BGC_FAILED; + BGC_FP64_Quaternion q1, q2; + + // Calculation of a turn (q1) which turns first_fixed_main into second_fixed_main + _bgc_fp64_turn3_get_turning_quaternion(&q1, &first_fixed_main, &second_fixed_main, &first_fixed_branch); + + // Roughly turn first_fixed_branch with q1 turn + _bgc_fp64_quaternion_turn_vector_roughly(&first_turned_branch, &q1, &first_fixed_branch); + + // Calculation of a turn (q2) which turns first_turned_branch into second_fixed_branch + _bgc_fp64_turn3_get_turning_quaternion(&q2, &first_turned_branch, &second_fixed_branch, &second_fixed_main); + + // Composing two turns with multiplication of quaterntions (q2 * q1) + bgc_fp64_quaternion_multiply_by_quaternion(&turn->_versor, &q2, &q1); + + // Making a final versor (a normalized quaternion) + const double square_modulus = bgc_fp64_quaternion_get_square_modulus(&turn->_versor); + + if (!bgc_fp64_is_square_unit(square_modulus)) { + _bgc_fp64_turn3_normalize(turn, square_modulus); } return BGC_SUCCESS; } -int bgc_fp32_turn3_make_basis_difference( - BGC_FP32_Turn3* versor, - const BGC_FP32_Vector3* initial_primary_direction, - const BGC_FP32_Vector3* initial_auxiliary_direction, - const BGC_FP32_Vector3* final_primary_direction, - const BGC_FP32_Vector3* final_auxiliary_direction -) -{ - BGC_FP32_Vector3 initial_orthogonal_direction, turned_orthogonal_direction, final_orthogonal_direction; - - // Step 1: Validate initial basis: - bgc_fp32_vector3_get_cross_product(&initial_orthogonal_direction, initial_primary_direction, initial_auxiliary_direction); - - const float initial_primary_square_modulus = bgc_fp32_vector3_get_square_modulus(initial_primary_direction); - const float initial_auxiliary_square_modulus = bgc_fp32_vector3_get_square_modulus(initial_auxiliary_direction); - const float initial_orthogonal_square_modulus = bgc_fp32_vector3_get_square_modulus(&initial_orthogonal_direction); - - const int initial_basis_valudation = _bgc_fp32_turn3_validate_basis(initial_primary_square_modulus, initial_auxiliary_square_modulus, initial_orthogonal_square_modulus); - - if (initial_basis_valudation != BGC_SUCCESS) { - return initial_basis_valudation; - } - - // Step 1: Validate final basis: - bgc_fp32_vector3_get_cross_product(&final_orthogonal_direction, final_primary_direction, final_auxiliary_direction); - - const float final_primary_square_modulus = bgc_fp32_vector3_get_square_modulus(final_primary_direction); - const float final_auxiliary_square_modulus = bgc_fp32_vector3_get_square_modulus(final_auxiliary_direction); - const float final_orthogonal_square_modulus = bgc_fp32_vector3_get_square_modulus(&final_orthogonal_direction); - - const int final_basis_valudation = _bgc_fp32_turn3_validate_basis(final_primary_square_modulus, final_auxiliary_square_modulus, final_orthogonal_square_modulus); - - if (final_basis_valudation != BGC_SUCCESS) { - return final_basis_valudation; - } - - // Step 3: Validate normalize orthogonal vectors: - bgc_fp32_vector3_divide(&initial_orthogonal_direction, &initial_orthogonal_direction, sqrtf(initial_orthogonal_square_modulus)); - bgc_fp32_vector3_divide(&final_orthogonal_direction, &final_orthogonal_direction, sqrtf(final_orthogonal_square_modulus)); - - BGC_FP32_Turn3 turn1, turn2; - - // Step 4: Find turn1 - int turn1_code = _bgc_fp32_turn3_make_direction_turn(&turn1, initial_primary_direction, final_primary_direction, initial_primary_square_modulus * final_primary_square_modulus); - - if (turn1_code == BGC_OPPOSITE) { - bgc_fp32_turn3_set_raw_values(&turn1, 0.0f, initial_orthogonal_direction.x1, initial_orthogonal_direction.x2, initial_orthogonal_direction.x3); - } - - bgc_fp32_turn3_vector(&turned_orthogonal_direction, &turn1, &initial_orthogonal_direction); - - // Step 5: Find turn2: - int turn2_code = _bgc_fp32_turn3_make_direction_turn(&turn2, &turned_orthogonal_direction, &final_orthogonal_direction, 1.0f); - - if (turn2_code == BGC_OPPOSITE) { - const float turn2_multiplier = sqrtf(1.0f / final_primary_square_modulus); - - bgc_fp32_turn3_set_raw_values(&turn2, - 0.0f, - final_primary_direction->x1 * turn2_multiplier, - final_primary_direction->x2 * turn2_multiplier, - final_primary_direction->x3 * turn2_multiplier - ); - } - - // Step 6: Combine turn1 and turn2: - bgc_fp32_turn3_combine(versor, &turn1, &turn2); - - return BGC_SUCCESS; -} - -int bgc_fp64_turn3_make_basis_difference( - BGC_FP64_Turn3* versor, - const BGC_FP64_Vector3* initial_primary_direction, - const BGC_FP64_Vector3* initial_auxiliary_direction, - const BGC_FP64_Vector3* final_primary_direction, - const BGC_FP64_Vector3* final_auxiliary_direction -) -{ - BGC_FP64_Vector3 initial_orthogonal_direction, turned_orthogonal_direction, final_orthogonal_direction; - - // Step 1: Validate initial basis: - bgc_fp64_vector3_get_cross_product(&initial_orthogonal_direction, initial_primary_direction, initial_auxiliary_direction); - - const double initial_primary_square_modulus = bgc_fp64_vector3_get_square_modulus(initial_primary_direction); - const double initial_auxiliary_square_modulus = bgc_fp64_vector3_get_square_modulus(initial_auxiliary_direction); - const double initial_orthogonal_square_modulus = bgc_fp64_vector3_get_square_modulus(&initial_orthogonal_direction); - - const int initial_basis_valudation = _bgc_fp64_turn3_validate_basis(initial_primary_square_modulus, initial_auxiliary_square_modulus, initial_orthogonal_square_modulus); - - if (initial_basis_valudation != BGC_SUCCESS) { - return initial_basis_valudation; - } - - // Step 1: Validate final basis: - bgc_fp64_vector3_get_cross_product(&final_orthogonal_direction, final_primary_direction, final_auxiliary_direction); - - const double final_primary_square_modulus = bgc_fp64_vector3_get_square_modulus(final_primary_direction); - const double final_auxiliary_square_modulus = bgc_fp64_vector3_get_square_modulus(final_auxiliary_direction); - const double final_orthogonal_square_modulus = bgc_fp64_vector3_get_square_modulus(&final_orthogonal_direction); - - const int final_basis_valudation = _bgc_fp64_turn3_validate_basis(final_primary_square_modulus, final_auxiliary_square_modulus, final_orthogonal_square_modulus); - - if (final_basis_valudation != BGC_SUCCESS) { - return final_basis_valudation; - } - - // Step 3: Validate normalize orthogonal vectors: - bgc_fp64_vector3_divide(&initial_orthogonal_direction, &initial_orthogonal_direction, sqrt(initial_orthogonal_square_modulus)); - bgc_fp64_vector3_divide(&final_orthogonal_direction, &final_orthogonal_direction, sqrt(final_orthogonal_square_modulus)); - - BGC_FP64_Turn3 turn1, turn2; - - // Step 4: Find turn1 - int turn1_code = _bgc_fp64_turn3_make_direction_turn(&turn1, initial_primary_direction, final_primary_direction, initial_primary_square_modulus * final_primary_square_modulus); - - if (turn1_code == BGC_OPPOSITE) { - bgc_fp64_turn3_set_raw_values(&turn1, 0.0, initial_orthogonal_direction.x1, initial_orthogonal_direction.x2, initial_orthogonal_direction.x3); - } - - bgc_fp64_turn3_vector(&turned_orthogonal_direction, &turn1, &initial_orthogonal_direction); - - // Step 5: Find turn2: - int turn2_code = _bgc_fp64_turn3_make_direction_turn(&turn2, &turned_orthogonal_direction, &final_orthogonal_direction, 1.0f); - - if (turn2_code == BGC_OPPOSITE) { - const double turn2_multiplier = sqrt(1.0 / final_primary_square_modulus); - - bgc_fp64_turn3_set_raw_values(&turn2, - 0.0, - final_primary_direction->x1 * turn2_multiplier, - final_primary_direction->x2 * turn2_multiplier, - final_primary_direction->x3 * turn2_multiplier - ); - } - - // Step 6: Combine turn1 and turn2: - bgc_fp64_turn3_combine(versor, &turn1, &turn2); - - return BGC_SUCCESS; -} - // =============== Get Exponation =============== // void bgc_fp32_turn3_get_exponation(BGC_FP32_Turn3* power, const BGC_FP32_Turn3* base, const float exponent) diff --git a/basic-geometry/turn3.h b/basic-geometry/turn3.h index 13d02fe..f4ea1ce 100644 --- a/basic-geometry/turn3.h +++ b/basic-geometry/turn3.h @@ -13,6 +13,20 @@ #define BGC_ZERO_TURN 0 #define BGC_OPPOSITE -1 +#define _BGC_ERROR_TURN3_FIRST_PAIR 3000 +#define _BGC_ERROR_TURN3_SECOND_PAIR 3010 +#define _BGC_ERROR_TURN3_EMPTY_MAIN 1 +#define _BGC_ERROR_TURN3_EMPTY_BRANCH 2 +#define _BGC_ERROR_TURN3_PAIR_PARALLEL 3 + +#define BGC_ERROR_TURN3_FIRST_PAIR_EMPTY_MAIN 3001 +#define BGC_ERROR_TURN3_FIRST_PAIR_EMPTY_BRANCH 3002 +#define BGC_ERROR_TURN3_FIRST_PAIR_PARALLEL 3003 + +#define BGC_ERROR_TURN3_SECOND_PAIR_EMPTY_MAIN 3011 +#define BGC_ERROR_TURN3_SECOND_PAIR_EMPTY_BRANCH 3012 +#define BGC_ERROR_TURN3_SECOND_PAIR_PARALLEL 3013 + #define BGC_ERROR_PRIMARY_DIRECTION_UNKNOWN -3001 #define BGC_ERROR_PRIMARY_VECTOR_IS_ZERO -3002 @@ -133,22 +147,22 @@ int bgc_fp32_turn3_find_direction_difference(BGC_FP32_Turn3* difference, const B int bgc_fp64_turn3_find_direction_difference(BGC_FP64_Turn3* difference, const BGC_FP64_Vector3* start, const BGC_FP64_Vector3* end); -// =============== Set Directions =============== // +// ======= Find Direction Pair Difference ======= // -int bgc_fp32_turn3_make_basis_difference( +int bgc_fp32_turn3_find_pair_difference( BGC_FP32_Turn3* turn, - const BGC_FP32_Vector3* initial_primary_direction, - const BGC_FP32_Vector3* initial_auxiliary_direction, - const BGC_FP32_Vector3* final_primary_direction, - const BGC_FP32_Vector3* final_auxiliary_direction + const BGC_FP32_Vector3* first_pair_main, + const BGC_FP32_Vector3* first_pair_branch, + const BGC_FP32_Vector3* second_pair_main, + const BGC_FP32_Vector3* second_pair_branch ); -int bgc_fp64_turn3_make_basis_difference( +int bgc_fp64_turn3_find_pair_difference( BGC_FP64_Turn3* turn, - const BGC_FP64_Vector3* initial_primary_direction, - const BGC_FP64_Vector3* initial_auxiliary_direction, - const BGC_FP64_Vector3* final_primary_direction, - const BGC_FP64_Vector3* final_auxiliary_direction + const BGC_FP64_Vector3* first_pair_main, + const BGC_FP64_Vector3* first_pair_branch, + const BGC_FP64_Vector3* second_pair_main, + const BGC_FP64_Vector3* second_pair_branch ); // ==================== Copy ==================== // @@ -301,7 +315,7 @@ void bgc_fp64_turn3_get_exponation(BGC_FP64_Turn3* power, const BGC_FP64_Turn3* inline void bgc_fp32_turn3_combine(BGC_FP32_Turn3* combination, const BGC_FP32_Turn3* first, const BGC_FP32_Turn3* second) { - bgc_fp32_quaternion_get_product(&combination->_versor, &second->_versor, &first->_versor); + bgc_fp32_quaternion_multiply_by_quaternion(&combination->_versor, &second->_versor, &first->_versor); const float square_modulus = bgc_fp32_quaternion_get_square_modulus(&combination->_versor); @@ -312,7 +326,7 @@ inline void bgc_fp32_turn3_combine(BGC_FP32_Turn3* combination, const BGC_FP32_T inline void bgc_fp64_turn3_combine(BGC_FP64_Turn3* combination, const BGC_FP64_Turn3* first, const BGC_FP64_Turn3* second) { - bgc_fp64_quaternion_get_product(&combination->_versor, &second->_versor, &first->_versor); + bgc_fp64_quaternion_multiply_by_quaternion(&combination->_versor, &second->_versor, &first->_versor); const double square_modulus = bgc_fp64_quaternion_get_square_modulus(&combination->_versor); @@ -327,9 +341,9 @@ inline void bgc_fp32_turn3_combine3(BGC_FP32_Turn3* combination, const BGC_FP32_ { BGC_FP32_Quaternion product; - bgc_fp32_quaternion_get_product(&product, &second->_versor, &first->_versor); + bgc_fp32_quaternion_multiply_by_quaternion(&product, &second->_versor, &first->_versor); - bgc_fp32_quaternion_get_product(&combination->_versor, &third->_versor, &product); + bgc_fp32_quaternion_multiply_by_quaternion(&combination->_versor, &third->_versor, &product); const float square_modulus = bgc_fp32_quaternion_get_square_modulus(&combination->_versor); @@ -342,9 +356,9 @@ inline void bgc_fp64_turn3_combine3(BGC_FP64_Turn3* combination, const BGC_FP64_ { BGC_FP64_Quaternion product; - bgc_fp64_quaternion_get_product(&product, &second->_versor, &first->_versor); + bgc_fp64_quaternion_multiply_by_quaternion(&product, &second->_versor, &first->_versor); - bgc_fp64_quaternion_get_product(&combination->_versor, &third->_versor, &product); + bgc_fp64_quaternion_multiply_by_quaternion(&combination->_versor, &third->_versor, &product); const double square_modulus = bgc_fp64_quaternion_get_square_modulus(&combination->_versor); @@ -357,7 +371,7 @@ inline void bgc_fp64_turn3_combine3(BGC_FP64_Turn3* combination, const BGC_FP64_ inline void bgc_fp32_turn3_exclude(BGC_FP32_Turn3* difference, const BGC_FP32_Turn3* base, const BGC_FP32_Turn3* excludant) { - bgc_fp32_quaternion_get_product_by_conjugate(&difference->_versor, &base->_versor, &excludant->_versor); + bgc_fp32_quaternion_multiply_by_conjugate(&difference->_versor, &base->_versor, &excludant->_versor); const float square_modulus = bgc_fp32_quaternion_get_square_modulus(&difference->_versor); @@ -368,7 +382,7 @@ inline void bgc_fp32_turn3_exclude(BGC_FP32_Turn3* difference, const BGC_FP32_Tu inline void bgc_fp64_turn3_exclude(BGC_FP64_Turn3* difference, const BGC_FP64_Turn3* base, const BGC_FP64_Turn3* excludant) { - bgc_fp64_quaternion_get_product_by_conjugate(&difference->_versor, &base->_versor, &excludant->_versor); + bgc_fp64_quaternion_multiply_by_conjugate(&difference->_versor, &base->_versor, &excludant->_versor); const double square_modulus = bgc_fp64_quaternion_get_square_modulus(&difference->_versor); @@ -421,66 +435,26 @@ inline void bgc_fp64_turn3_get_both_matrices(BGC_FP64_Matrix3x3* rotation, BGC_F // ================ Turn Vector ================= // -inline void bgc_fp32_turn3_vector(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Turn3* versor, const BGC_FP32_Vector3* vector) +inline void bgc_fp32_turn3_vector(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Turn3* turn, const BGC_FP32_Vector3* original_vector) { - const float tx1 = 2.0f * (versor->_versor.x2 * vector->x3 - versor->_versor.x3 * vector->x2); - const float tx2 = 2.0f * (versor->_versor.x3 * vector->x1 - versor->_versor.x1 * vector->x3); - const float tx3 = 2.0f * (versor->_versor.x1 * vector->x2 - versor->_versor.x2 * vector->x1); - - const float x1 = (vector->x1 + tx1 * versor->_versor.s0) + (versor->_versor.x2 * tx3 - versor->_versor.x3 * tx2); - const float x2 = (vector->x2 + tx2 * versor->_versor.s0) + (versor->_versor.x3 * tx1 - versor->_versor.x1 * tx3); - const float x3 = (vector->x3 + tx3 * versor->_versor.s0) + (versor->_versor.x1 * tx2 - versor->_versor.x2 * tx1); - - turned_vector->x1 = x1; - turned_vector->x2 = x2; - turned_vector->x3 = x3; + _bgc_fp32_quaternion_turn_vector_roughly(turned_vector, &turn->_versor, original_vector); } -inline void bgc_fp64_turn3_vector(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Turn3* turn, const BGC_FP64_Vector3* vector) +inline void bgc_fp64_turn3_vector(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Turn3* turn, const BGC_FP64_Vector3* original_vector) { - const double tx1 = 2.0 * (turn->_versor.x2 * vector->x3 - turn->_versor.x3 * vector->x2); - const double tx2 = 2.0 * (turn->_versor.x3 * vector->x1 - turn->_versor.x1 * vector->x3); - const double tx3 = 2.0 * (turn->_versor.x1 * vector->x2 - turn->_versor.x2 * vector->x1); - - const double x1 = (vector->x1 + tx1 * turn->_versor.s0) + (turn->_versor.x2 * tx3 - turn->_versor.x3 * tx2); - const double x2 = (vector->x2 + tx2 * turn->_versor.s0) + (turn->_versor.x3 * tx1 - turn->_versor.x1 * tx3); - const double x3 = (vector->x3 + tx3 * turn->_versor.s0) + (turn->_versor.x1 * tx2 - turn->_versor.x2 * tx1); - - turned_vector->x1 = x1; - turned_vector->x2 = x2; - turned_vector->x3 = x3; + _bgc_fp64_quaternion_turn_vector_roughly(turned_vector, &turn->_versor, original_vector); } // ============== Turn Vector Back ============== // -inline void bgc_fp32_turn3_vector_back(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Turn3* turn, const BGC_FP32_Vector3* vector) +inline void bgc_fp32_turn3_vector_back(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Turn3* turn, const BGC_FP32_Vector3* original_vector) { - const float tx1 = 2.0f * (turn->_versor.x2 * vector->x3 - turn->_versor.x3 * vector->x2); - const float tx2 = 2.0f * (turn->_versor.x3 * vector->x1 - turn->_versor.x1 * vector->x3); - const float tx3 = 2.0f * (turn->_versor.x1 * vector->x2 - turn->_versor.x2 * vector->x1); - - const float x1 = (vector->x1 - tx1 * turn->_versor.s0) + (turn->_versor.x2 * tx3 - turn->_versor.x3 * tx2); - const float x2 = (vector->x2 - tx2 * turn->_versor.s0) + (turn->_versor.x3 * tx1 - turn->_versor.x1 * tx3); - const float x3 = (vector->x3 - tx3 * turn->_versor.s0) + (turn->_versor.x1 * tx2 - turn->_versor.x2 * tx1); - - turned_vector->x1 = x1; - turned_vector->x2 = x2; - turned_vector->x3 = x3; + _bgc_fp32_quaternion_turn_vector_back_roughly(turned_vector, &turn->_versor, original_vector); } -inline void bgc_fp64_turn3_vector_back(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Turn3* turn, const BGC_FP64_Vector3* vector) +inline void bgc_fp64_turn3_vector_back(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Turn3* turn, const BGC_FP64_Vector3* original_vector) { - const double tx1 = 2.0 * (turn->_versor.x2 * vector->x3 - turn->_versor.x3 * vector->x2); - const double tx2 = 2.0 * (turn->_versor.x3 * vector->x1 - turn->_versor.x1 * vector->x3); - const double tx3 = 2.0 * (turn->_versor.x1 * vector->x2 - turn->_versor.x2 * vector->x1); - - const double x1 = (vector->x1 - tx1 * turn->_versor.s0) + (turn->_versor.x2 * tx3 - turn->_versor.x3 * tx2); - const double x2 = (vector->x2 - tx2 * turn->_versor.s0) + (turn->_versor.x3 * tx1 - turn->_versor.x1 * tx3); - const double x3 = (vector->x3 - tx3 * turn->_versor.s0) + (turn->_versor.x1 * tx2 - turn->_versor.x2 * tx1); - - turned_vector->x1 = x1; - turned_vector->x2 = x2; - turned_vector->x3 = x3; + _bgc_fp64_quaternion_turn_vector_back_roughly(turned_vector, &turn->_versor, original_vector); } // ================== Are Close ================= //