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Развитие SLERP для трёхмерных пространств, а также развитие дуальных чисел, векторов и кватернионов

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Andrey Pokidov 2026-02-13 20:34:11 +07:00
parent 053af33444
commit 86ea23de7d
23 changed files with 1063 additions and 830 deletions
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104
basic-geometry/slerp3.c Normal file
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#include "./slerp3.h"
extern inline void bgc_fp32_slerp_reset(BGC_FP32_Slerp3* slerp);
extern inline void bgc_fp64_slerp_reset(BGC_FP64_Slerp3* slerp);
extern inline void bgc_fp32_slerp_make_full(BGC_FP32_Slerp3* slerp, const BGC_FP32_Turn3* start, const BGC_FP32_Turn3* end);
extern inline void bgc_fp64_slerp_make_full(BGC_FP64_Slerp3* slerp, const BGC_FP64_Turn3* start, const BGC_FP64_Turn3* end);
extern inline void bgc_fp32_slerp_make_shortened(BGC_FP32_Slerp3* slerp, const BGC_FP32_Turn3* start, const BGC_FP32_Turn3* end);
extern inline void bgc_fp64_slerp_make_shortened(BGC_FP64_Slerp3* slerp, const BGC_FP64_Turn3* start, const BGC_FP64_Turn3* end);
extern inline void bgc_fp32_slerp_get_phase_turn(BGC_FP32_Turn3* versor, const BGC_FP32_Slerp3* slerp, const float phase);
extern inline void bgc_fp64_slerp_get_phase_turn(BGC_FP64_Turn3* versor, const BGC_FP64_Slerp3* slerp, const double phase);
extern inline void bgc_fp32_slerp_get_phase_rotation_matrix(BGC_FP32_Matrix3x3* rotation_matrix, const BGC_FP32_Slerp3* slerp, const float phase);
extern inline void bgc_fp64_slerp_get_phase_rotation_matrix(BGC_FP64_Matrix3x3* rotation_matrix, const BGC_FP64_Slerp3* slerp, const double phase);
extern inline void bgc_fp32_slerp_get_phase_reverse_matrix(BGC_FP32_Matrix3x3* reverse_matrix, const BGC_FP32_Slerp3* slerp, const float phase);
extern inline void bgc_fp64_slerp_get_phase_rotation_matrix(BGC_FP64_Matrix3x3* reverse_matrix, const BGC_FP64_Slerp3* slerp, const double phase);
extern inline void bgc_fp32_slerp_get_phase_both_matrices(BGC_FP32_Matrix3x3* rotation_matrix, BGC_FP32_Matrix3x3* reverse_matrix, const BGC_FP32_Slerp3* slerp, const float phase);
extern inline void bgc_fp64_slerp_get_phase_both_matrices(BGC_FP64_Matrix3x3* rotation_matrix, BGC_FP64_Matrix3x3* reverse_matrix, const BGC_FP64_Slerp3* slerp, const double phase);
void bgc_fp32_slerp_make(BGC_FP32_Slerp3* slerp, const BGC_FP32_Turn3* start, const BGC_FP32_Turn3* augment)
{
const float square_vector = augment->_versor.x1 * augment->_versor.x1 + augment->_versor.x2 * augment->_versor.x2 + augment->_versor.x3 * augment->_versor.x3;
if (isnan(square_vector)) {
bgc_fp32_slerp_reset(slerp);
return;
}
if (square_vector <= BGC_FP32_SQUARE_EPSILON) {
slerp->_cosine_weight.s0 = start->_versor.s0;
slerp->_cosine_weight.x1 = start->_versor.x1;
slerp->_cosine_weight.x2 = start->_versor.x2;
slerp->_cosine_weight.x3 = start->_versor.x3;
slerp->_sine_weight.s0 = 0.0f;
slerp->_sine_weight.x1 = 0.0f;
slerp->_sine_weight.x2 = 0.0f;
slerp->_sine_weight.x3 = 0.0f;
slerp->radians = 0.0f;
return;
}
const float vector_modulus = sqrtf(square_vector);
slerp->radians = atan2f(vector_modulus, augment->_versor.s0);
const float multiplier = 1.0f / vector_modulus;
slerp->_cosine_weight.s0 = start->_versor.s0;
slerp->_cosine_weight.x1 = start->_versor.x1;
slerp->_cosine_weight.x2 = start->_versor.x2;
slerp->_cosine_weight.x3 = start->_versor.x3;
slerp->_sine_weight.s0 = -multiplier * (augment->_versor.x1 * start->_versor.x1 + augment->_versor.x2 * start->_versor.x2 + augment->_versor.x3 * start->_versor.x3);
slerp->_sine_weight.x1 = multiplier * (augment->_versor.x1 * start->_versor.s0 + augment->_versor.x2 * start->_versor.x3 - augment->_versor.x3 * start->_versor.x2);
slerp->_sine_weight.x2 = multiplier * (augment->_versor.x2 * start->_versor.s0 - augment->_versor.x1 * start->_versor.x3 + augment->_versor.x3 * start->_versor.x1);
slerp->_sine_weight.x3 = multiplier * (augment->_versor.x3 * start->_versor.s0 - augment->_versor.x2 * start->_versor.x1 + augment->_versor.x1 * start->_versor.x2);
}
void bgc_fp64_slerp_make(BGC_FP64_Slerp3* slerp, const BGC_FP64_Turn3* start, const BGC_FP64_Turn3* augment)
{
const double square_vector = augment->_versor.x1 * augment->_versor.x1 + augment->_versor.x2 * augment->_versor.x2 + augment->_versor.x3 * augment->_versor.x3;
if (isnan(square_vector)) {
bgc_fp64_slerp_reset(slerp);
return;
}
if (square_vector <= BGC_FP64_SQUARE_EPSILON) {
slerp->_cosine_weight.s0 = start->_versor.s0;
slerp->_cosine_weight.x1 = start->_versor.x1;
slerp->_cosine_weight.x2 = start->_versor.x2;
slerp->_cosine_weight.x3 = start->_versor.x3;
slerp->_sine_weight.s0 = 0.0;
slerp->_sine_weight.x1 = 0.0;
slerp->_sine_weight.x2 = 0.0;
slerp->_sine_weight.x3 = 0.0;
slerp->radians = 0.0;
return;
}
const double vector_modulus = sqrt(square_vector);
slerp->radians = atan2(vector_modulus, augment->_versor.s0);
const double multiplier = 1.0 / vector_modulus;
slerp->_cosine_weight.s0 = start->_versor.s0;
slerp->_cosine_weight.x1 = start->_versor.x1;
slerp->_cosine_weight.x2 = start->_versor.x2;
slerp->_cosine_weight.x3 = start->_versor.x3;
slerp->_sine_weight.s0 = -multiplier * (augment->_versor.x1 * start->_versor.x1 + augment->_versor.x2 * start->_versor.x2 + augment->_versor.x3 * start->_versor.x3);
slerp->_sine_weight.x1 = multiplier * (augment->_versor.x1 * start->_versor.s0 + augment->_versor.x2 * start->_versor.x3 - augment->_versor.x3 * start->_versor.x2);
slerp->_sine_weight.x2 = multiplier * (augment->_versor.x2 * start->_versor.s0 - augment->_versor.x1 * start->_versor.x3 + augment->_versor.x3 * start->_versor.x1);
slerp->_sine_weight.x3 = multiplier * (augment->_versor.x3 * start->_versor.s0 - augment->_versor.x2 * start->_versor.x1 + augment->_versor.x1 * start->_versor.x2);
}