584 lines
26 KiB
C
584 lines
26 KiB
C
#include <math.h>
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#include "angle.h"
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#include "versor.h"
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const BgcVersorFP32 BGC_IDLE_VERSOR_FP32 = { 1.0f, 0.0f, 0.0f, 0.0f };
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const BgcVersorFP64 BGC_IDLE_VERSOR_FP64 = { 1.0, 0.0, 0.0, 0.0 };
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extern inline void bgc_versor_reset_fp32(BgcVersorFP32* versor);
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extern inline void bgc_versor_reset_fp64(BgcVersorFP64* versor);
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extern inline void bgc_versor_set_values_fp32(const float s0, const float x1, const float x2, const float x3, BgcVersorFP32* versor);
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extern inline void bgc_versor_set_values_fp64(const double s0, const double x1, const double x2, const double x3, BgcVersorFP64* versor);
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extern inline void bgc_versor_set_rotation_fp32(const BgcRotation3FP32* rotation, BgcVersorFP32* result);
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extern inline void bgc_versor_set_rotation_fp64(const BgcRotation3FP64* rotation, BgcVersorFP64* result);
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extern inline void bgc_versor_copy_fp32(const BgcVersorFP32* source, BgcVersorFP32* destination);
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extern inline void bgc_versor_copy_fp64(const BgcVersorFP64* source, BgcVersorFP64* destination);
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extern inline void bgc_versor_swap_fp32(BgcVersorFP32* versor1, BgcVersorFP32* versor2);
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extern inline void bgc_versor_swap_fp64(BgcVersorFP64* versor1, BgcVersorFP64* versor2);
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extern inline int bgc_versor_is_identity_fp32(const BgcVersorFP32* versor);
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extern inline int bgc_versor_is_identity_fp64(const BgcVersorFP64* versor);
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extern inline void bgc_versor_convert_fp64_to_fp32(const BgcVersorFP64* source, BgcVersorFP32* destination);
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extern inline void bgc_versor_convert_fp32_to_fp64(const BgcVersorFP32* source, BgcVersorFP64* destination);
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extern inline void bgc_versor_shorten_fp32(BgcVersorFP32* versor);
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extern inline void bgc_versor_shorten_fp64(BgcVersorFP64* versor);
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extern inline void bgc_versor_get_shortened_fp32(const BgcVersorFP32* versor, BgcVersorFP32* shortened);
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extern inline void bgc_versor_get_shortened_fp64(const BgcVersorFP64* versor, BgcVersorFP64* shortened);
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extern inline void bgc_versor_make_opposite_fp32(BgcVersorFP32* versor);
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extern inline void bgc_versor_make_opposite_fp64(BgcVersorFP64* versor);
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extern inline void bgc_versor_get_opposite_fp32(const BgcVersorFP32* versor, BgcVersorFP32* opposite);
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extern inline void bgc_versor_get_opposite_fp64(const BgcVersorFP64* versor, BgcVersorFP64* opposite);
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extern inline void bgc_versor_invert_fp32(BgcVersorFP32* versor);
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extern inline void bgc_versor_invert_fp64(BgcVersorFP64* versor);
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extern inline void bgc_versor_get_inverse_fp32(const BgcVersorFP32* versor, BgcVersorFP32* inverse);
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extern inline void bgc_versor_get_inverse_fp64(const BgcVersorFP64* versor, BgcVersorFP64* inverse);
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extern inline void bgc_versor_combine_fp32(const BgcVersorFP32* second, const BgcVersorFP32* first, BgcVersorFP32* result);
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extern inline void bgc_versor_combine_fp64(const BgcVersorFP64* second, const BgcVersorFP64* first, BgcVersorFP64* result);
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extern inline void bgc_versor_combine3_fp32(const BgcVersorFP32* third, const BgcVersorFP32* second, const BgcVersorFP32* first, BgcVersorFP32* result);
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extern inline void bgc_versor_combine3_fp64(const BgcVersorFP64* third, const BgcVersorFP64* second, const BgcVersorFP64* first, BgcVersorFP64* result);
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extern inline void bgc_versor_exclude_fp32(const BgcVersorFP32* base, const BgcVersorFP32* excludant, BgcVersorFP32* difference);
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extern inline void bgc_versor_exclude_fp64(const BgcVersorFP64* base, const BgcVersorFP64* excludant, BgcVersorFP64* difference);
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extern inline void bgc_versor_get_rotation_matrix_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* matrix);
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extern inline void bgc_versor_get_rotation_matrix_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* matrix);
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extern inline void bgc_versor_get_reverse_matrix_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* matrix);
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extern inline void bgc_versor_get_reverse_matrix_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* matrix);
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extern inline void bgc_versor_get_both_matrices_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* rotation, BgcMatrix3x3FP32* reverse);
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extern inline void bgc_versor_get_both_matrices_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* rotation, BgcMatrix3x3FP64* reverse);
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extern inline void bgc_versor_turn_vector_fp32(const BgcVersorFP32* versor, const BgcVector3FP32* vector, BgcVector3FP32* result);
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extern inline void bgc_versor_turn_vector_fp64(const BgcVersorFP64* versor, const BgcVector3FP64* vector, BgcVector3FP64* result);
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extern inline void bgc_versor_turn_vector_back_fp32(const BgcVersorFP32* versor, const BgcVector3FP32* vector, BgcVector3FP32* result);
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extern inline void bgc_versor_turn_vector_back_fp64(const BgcVersorFP64* versor, const BgcVector3FP64* vector, BgcVector3FP64* result);
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extern inline int bgc_versor_are_close_fp32(const BgcVersorFP32* versor1, const BgcVersorFP32* versor2);
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extern inline int bgc_versor_are_close_fp64(const BgcVersorFP64* versor1, const BgcVersorFP64* versor2);
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// ================= Normalize ================== //
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void _bgc_versor_normalize_fp32(const float square_modulus, BgcVersorFP32* versor)
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{
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// (square_modulus != square_modulus) is true when square_modulus is NaN
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if (square_modulus <= BGC_SQUARE_EPSYLON_FP32 || square_modulus != square_modulus) {
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versor->_s0 = 1.0f;
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versor->_x1 = 0.0f;
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versor->_x2 = 0.0f;
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versor->_x3 = 0.0f;
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return;
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}
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const float multiplier = sqrtf(1.0f / square_modulus);
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versor->_s0 *= multiplier;
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versor->_x1 *= multiplier;
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versor->_x2 *= multiplier;
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versor->_x3 *= multiplier;
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}
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void _bgc_versor_normalize_fp64(const double square_modulus, BgcVersorFP64* versor)
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{
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// (square_modulus != square_modulus) is true when square_modulus is NaN
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if (square_modulus <= BGC_SQUARE_EPSYLON_FP64 || square_modulus != square_modulus) {
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versor->_s0 = 1.0;
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versor->_x1 = 0.0;
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versor->_x2 = 0.0;
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versor->_x3 = 0.0;
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return;
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}
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const double multiplier = sqrt(1.0 / square_modulus);
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versor->_s0 *= multiplier;
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versor->_x1 *= multiplier;
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versor->_x2 *= multiplier;
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versor->_x3 *= multiplier;
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}
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// ================== Set Turn ================== //
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void bgc_versor_set_turn_fp32(const float x1, const float x2, const float x3, const float angle, const BgcAngleUnitEnum unit, BgcVersorFP32* result)
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{
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const float square_vector = x1 * x1 + x2 * x2 + x3 * x3;
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if (square_vector <= BGC_SQUARE_EPSYLON_FP32) {
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bgc_versor_reset_fp32(result);
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return;
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}
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const float half_angle = bgc_angle_to_radians_fp32(0.5f * angle, unit);
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const float sine = sinf(half_angle);
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if (bgc_is_zero_fp32(sine)) {
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bgc_versor_reset_fp32(result);
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return;
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}
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const float multiplier = sine / sqrtf(square_vector);
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bgc_versor_set_values_fp32(cosf(half_angle), x1 * multiplier, x2 * multiplier, x3 * multiplier, result);
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}
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void bgc_versor_set_turn_fp64(const double x1, const double x2, const double x3, const double angle, const BgcAngleUnitEnum unit, BgcVersorFP64* result)
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{
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const double square_vector = x1 * x1 + x2 * x2 + x3 * x3;
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if (square_vector <= BGC_SQUARE_EPSYLON_FP64) {
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bgc_versor_reset_fp64(result);
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return;
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}
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const double half_angle = bgc_angle_to_radians_fp64(0.5 * angle, unit);
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const double sine = sin(half_angle);
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if (bgc_is_zero_fp64(sine)) {
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bgc_versor_reset_fp64(result);
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return;
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}
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const double multiplier = sine / sqrt(square_vector);
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bgc_versor_set_values_fp64(cos(half_angle), x1 * multiplier, x2 * multiplier, x3 * multiplier, result);
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}
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// ========= Make Direction Difference ========== //
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static int _bgc_versor_make_direction_turn_fp32(const BgcVector3FP32* start, const BgcVector3FP32* end, const float square_modulus_product, BgcVersorFP32* result)
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{
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BgcVector3FP32 orthogonal_axis;
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bgc_vector3_get_cross_product_fp32(start, end, &orthogonal_axis);
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const float scalar_product = bgc_vector3_get_scalar_product_fp32(start, end);
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const float square_modulus = bgc_vector3_get_square_modulus_fp32(&orthogonal_axis);
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const float square_sine = square_modulus / square_modulus_product;
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if (square_sine > BGC_SQUARE_EPSYLON_FP32) {
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const float cosine = scalar_product / sqrtf(square_modulus_product);
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const float angle = 0.5f * atan2f(sqrtf(square_sine), cosine);
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const float multiplier = sinf(angle) * sqrtf(1.0f / square_modulus);
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bgc_versor_set_values_fp32(cosf(angle), orthogonal_axis.x1 * multiplier, orthogonal_axis.x2 * multiplier, orthogonal_axis.x3 * multiplier, result);
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return BGC_SOME_TURN;
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}
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if (scalar_product < 0.0f) {
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return BGC_OPPOSITE;
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}
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bgc_versor_reset_fp32(result);
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return BGC_ZERO_TURN;
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}
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static int _bgc_versor_make_direction_turn_fp64(const BgcVector3FP64* start, const BgcVector3FP64* end, const double square_modulus_product, BgcVersorFP64* result)
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{
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BgcVector3FP64 orthogonal_axis;
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bgc_vector3_get_cross_product_fp64(start, end, &orthogonal_axis);
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const double scalar_product = bgc_vector3_get_scalar_product_fp64(start, end);
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const double square_modulus = bgc_vector3_get_square_modulus_fp64(&orthogonal_axis);
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const double square_sine = square_modulus / square_modulus_product;
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if (square_sine > BGC_SQUARE_EPSYLON_FP64) {
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const double cosine = scalar_product / sqrt(square_modulus_product);
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const double angle = 0.5 * atan2(sqrt(square_sine), cosine);
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const double multiplier = sin(angle) * sqrt(1.0f / square_modulus);
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bgc_versor_set_values_fp64(cos(angle), orthogonal_axis.x1 * multiplier, orthogonal_axis.x2 * multiplier, orthogonal_axis.x3 * multiplier, result);
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return BGC_SOME_TURN;
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}
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if (scalar_product < 0.0) {
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return BGC_OPPOSITE;
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}
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bgc_versor_reset_fp64(result);
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return BGC_ZERO_TURN;
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}
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int bgc_versor_make_direction_difference_fp32(const BgcVector3FP32* start, const BgcVector3FP32* end, BgcVersorFP32* result)
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{
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const float start_square_modulus = bgc_vector3_get_square_modulus_fp32(start);
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const float end_square_modulus = bgc_vector3_get_square_modulus_fp32(end);
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if (start_square_modulus <= BGC_SQUARE_EPSYLON_FP32 || end_square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
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bgc_versor_reset_fp32(result);
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return BGC_ZERO_TURN;
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}
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return _bgc_versor_make_direction_turn_fp32(start, end, start_square_modulus * end_square_modulus, result);
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}
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int bgc_versor_make_direction_difference_fp64(const BgcVector3FP64* start, const BgcVector3FP64* end, BgcVersorFP64* result)
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{
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const double start_square_modulus = bgc_vector3_get_square_modulus_fp64(start);
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const double end_square_modulus = bgc_vector3_get_square_modulus_fp64(end);
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if (start_square_modulus <= BGC_SQUARE_EPSYLON_FP64 || end_square_modulus <= BGC_SQUARE_EPSYLON_FP64) {
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bgc_versor_reset_fp64(result);
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return BGC_ZERO_TURN;
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}
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return _bgc_versor_make_direction_turn_fp64(start, end, start_square_modulus * end_square_modulus, result);
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}
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// =============== Set Directions =============== //
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static int _bgc_versor_validate_basis_fp32(const float primary_square_modulus, const float auxiliary_square_modulus, const float orthogonal_square_modulus)
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{
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if (primary_square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
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//TODO: add error code for: primary_vector is zero
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return BGC_FAILED;
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}
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if (auxiliary_square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
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//TODO: add error code for: auxiliary_vector is zero
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return BGC_FAILED;
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}
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if (orthogonal_square_modulus <= BGC_SQUARE_EPSYLON_FP32 * primary_square_modulus * auxiliary_square_modulus) {
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//TODO: add error code for: primary_vector and auxiliary_vector are parallel
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return BGC_FAILED;
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}
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return BGC_SUCCESS;
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}
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static int _bgc_versor_validate_basis_fp64(const double primary_square_modulus, const double auxiliary_square_modulus, const double orthogonal_square_modulus)
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{
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if (primary_square_modulus <= BGC_SQUARE_EPSYLON_FP64) {
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//TODO: add error code for: primary_vector is zero
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return BGC_FAILED;
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}
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if (auxiliary_square_modulus <= BGC_SQUARE_EPSYLON_FP64) {
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//TODO: add error code for: auxiliary_vector is zero
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return BGC_FAILED;
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}
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if (orthogonal_square_modulus <= BGC_SQUARE_EPSYLON_FP64 * primary_square_modulus * auxiliary_square_modulus) {
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//TODO: add error code for: primary_vector and auxiliary_vector are parallel
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return BGC_FAILED;
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}
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return BGC_SUCCESS;
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}
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int bgc_versor_make_basis_difference_fp32(
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const BgcVector3FP32* initial_primary_direction,
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const BgcVector3FP32* initial_auxiliary_direction,
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const BgcVector3FP32* final_primary_direction,
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const BgcVector3FP32* final_auxiliary_direction,
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BgcVersorFP32* result
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)
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{
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BgcVector3FP32 initial_orthogonal_direction, turned_orthogonal_direction, final_orthogonal_direction;
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// Step 1: Validate initial basis:
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bgc_vector3_get_cross_product_fp32(initial_primary_direction, initial_auxiliary_direction, &initial_orthogonal_direction);
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const float initial_primary_square_modulus = bgc_vector3_get_square_modulus_fp32(initial_primary_direction);
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const float initial_auxiliary_square_modulus = bgc_vector3_get_square_modulus_fp32(initial_auxiliary_direction);
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const float initial_orthogonal_square_modulus = bgc_vector3_get_square_modulus_fp32(&initial_orthogonal_direction);
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const int initial_basis_valudation = _bgc_versor_validate_basis_fp32(initial_primary_square_modulus, initial_auxiliary_square_modulus, initial_orthogonal_square_modulus);
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if (initial_basis_valudation != BGC_SUCCESS) {
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return initial_basis_valudation;
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}
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// Step 1: Validate final basis:
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bgc_vector3_get_cross_product_fp32(final_primary_direction, final_auxiliary_direction, &final_orthogonal_direction);
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const float final_primary_square_modulus = bgc_vector3_get_square_modulus_fp32(final_primary_direction);
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const float final_auxiliary_square_modulus = bgc_vector3_get_square_modulus_fp32(final_auxiliary_direction);
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const float final_orthogonal_square_modulus = bgc_vector3_get_square_modulus_fp32(&final_orthogonal_direction);
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const int final_basis_valudation = _bgc_versor_validate_basis_fp32(final_primary_square_modulus, final_auxiliary_square_modulus, final_orthogonal_square_modulus);
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if (final_basis_valudation != BGC_SUCCESS) {
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return final_basis_valudation;
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}
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// Step 3: Validate normalize orthogonal vectors:
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bgc_vector3_divide_fp32(&initial_orthogonal_direction, sqrtf(initial_orthogonal_square_modulus), &initial_orthogonal_direction);
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bgc_vector3_divide_fp32(&final_orthogonal_direction, sqrtf(final_orthogonal_square_modulus), &final_orthogonal_direction);
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BgcVersorFP32 turn1, turn2;
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// Step 4: Find turn1
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int turn1_code = _bgc_versor_make_direction_turn_fp32(initial_primary_direction, final_primary_direction, initial_primary_square_modulus * final_primary_square_modulus, &turn1);
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if (turn1_code == BGC_OPPOSITE) {
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bgc_versor_set_values_fp32(0.0f, initial_orthogonal_direction.x1, initial_orthogonal_direction.x2, initial_orthogonal_direction.x3, &turn1);
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}
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bgc_versor_turn_vector_fp32(&turn1, &initial_orthogonal_direction, &turned_orthogonal_direction);
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// Step 5: Find turn2:
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int turn2_code = _bgc_versor_make_direction_turn_fp32(&turned_orthogonal_direction, &final_orthogonal_direction, 1.0f, &turn2);
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if (turn2_code == BGC_OPPOSITE) {
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const float turn2_multiplier = sqrtf(1.0f / final_primary_square_modulus);
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bgc_versor_set_values_fp32(0.0f,
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final_primary_direction->x1 * turn2_multiplier,
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final_primary_direction->x2 * turn2_multiplier,
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final_primary_direction->x3 * turn2_multiplier,
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&turn2
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);
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}
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// Step 6: Combine turn1 and turn2:
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bgc_versor_combine_fp32(&turn2, &turn1, result);
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return BGC_SUCCESS;
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}
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int bgc_versor_make_basis_difference_fp64(
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const BgcVector3FP64* initial_primary_direction,
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const BgcVector3FP64* initial_auxiliary_direction,
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const BgcVector3FP64* final_primary_direction,
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const BgcVector3FP64* final_auxiliary_direction,
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BgcVersorFP64* result
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)
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{
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BgcVector3FP64 initial_orthogonal_direction, turned_orthogonal_direction, final_orthogonal_direction;
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// Step 1: Validate initial basis:
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bgc_vector3_get_cross_product_fp64(initial_primary_direction, initial_auxiliary_direction, &initial_orthogonal_direction);
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const double initial_primary_square_modulus = bgc_vector3_get_square_modulus_fp64(initial_primary_direction);
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const double initial_auxiliary_square_modulus = bgc_vector3_get_square_modulus_fp64(initial_auxiliary_direction);
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const double initial_orthogonal_square_modulus = bgc_vector3_get_square_modulus_fp64(&initial_orthogonal_direction);
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const int initial_basis_valudation = _bgc_versor_validate_basis_fp64(initial_primary_square_modulus, initial_auxiliary_square_modulus, initial_orthogonal_square_modulus);
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|
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if (initial_basis_valudation != BGC_SUCCESS) {
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return initial_basis_valudation;
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}
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|
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// Step 1: Validate final basis:
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bgc_vector3_get_cross_product_fp64(final_primary_direction, final_auxiliary_direction, &final_orthogonal_direction);
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const double final_primary_square_modulus = bgc_vector3_get_square_modulus_fp64(final_primary_direction);
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const double final_auxiliary_square_modulus = bgc_vector3_get_square_modulus_fp64(final_auxiliary_direction);
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const double final_orthogonal_square_modulus = bgc_vector3_get_square_modulus_fp64(&final_orthogonal_direction);
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const int final_basis_valudation = _bgc_versor_validate_basis_fp64(final_primary_square_modulus, final_auxiliary_square_modulus, final_orthogonal_square_modulus);
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|
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if (final_basis_valudation != BGC_SUCCESS) {
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return final_basis_valudation;
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}
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|
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// Step 3: Validate normalize orthogonal vectors:
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bgc_vector3_divide_fp64(&initial_orthogonal_direction, sqrt(initial_orthogonal_square_modulus), &initial_orthogonal_direction);
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bgc_vector3_divide_fp64(&final_orthogonal_direction, sqrt(final_orthogonal_square_modulus), &final_orthogonal_direction);
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BgcVersorFP64 turn1, turn2;
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// Step 4: Find turn1
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int turn1_code = _bgc_versor_make_direction_turn_fp64(initial_primary_direction, final_primary_direction, initial_primary_square_modulus * final_primary_square_modulus, &turn1);
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|
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if (turn1_code == BGC_OPPOSITE) {
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bgc_versor_set_values_fp64(0.0, initial_orthogonal_direction.x1, initial_orthogonal_direction.x2, initial_orthogonal_direction.x3, &turn1);
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}
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|
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bgc_versor_turn_vector_fp64(&turn1, &initial_orthogonal_direction, &turned_orthogonal_direction);
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|
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// Step 5: Find turn2:
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int turn2_code = _bgc_versor_make_direction_turn_fp64(&turned_orthogonal_direction, &final_orthogonal_direction, 1.0f, &turn2);
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if (turn2_code == BGC_OPPOSITE) {
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const double turn2_multiplier = sqrt(1.0 / final_primary_square_modulus);
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bgc_versor_set_values_fp64(0.0,
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final_primary_direction->x1 * turn2_multiplier,
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final_primary_direction->x2 * turn2_multiplier,
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final_primary_direction->x3 * turn2_multiplier,
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&turn2
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|
);
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}
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|
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// Step 6: Combine turn1 and turn2:
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bgc_versor_combine_fp64(&turn2, &turn1, result);
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|
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return BGC_SUCCESS;
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}
|
|
|
|
// =============== Get Exponation =============== //
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|
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void bgc_versor_get_exponation_fp32(const BgcVersorFP32* base, const float exponent, BgcVersorFP32* power)
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|
{
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const float square_vector = base->_x1 * base->_x1 + base->_x2 * base->_x2 + base->_x3 * base->_x3;
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|
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if (square_vector <= BGC_SQUARE_EPSYLON_FP32 || square_vector != square_vector) {
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bgc_versor_reset_fp32(power);
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return;
|
|
}
|
|
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const float vector_modulus = sqrtf(square_vector);
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|
|
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const float angle = atan2f(vector_modulus, base->_s0) * exponent;
|
|
|
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const float multiplier = sinf(angle) / vector_modulus;
|
|
|
|
bgc_versor_set_values_fp32(cosf(angle), base->_x1 * multiplier, base->_x2 * multiplier, base->_x3 * multiplier, power);
|
|
}
|
|
|
|
void bgc_versor_get_exponation_fp64(const BgcVersorFP64* base, const double exponent, BgcVersorFP64* power)
|
|
{
|
|
const double square_vector = base->_x1 * base->_x1 + base->_x2 * base->_x2 + base->_x3 * base->_x3;
|
|
|
|
if (square_vector <= BGC_SQUARE_EPSYLON_FP64 || square_vector != square_vector) {
|
|
bgc_versor_reset_fp64(power);
|
|
return;
|
|
}
|
|
|
|
const double vector_modulus = sqrt(square_vector);
|
|
|
|
const double angle = atan2(vector_modulus, base->_s0) * exponent;
|
|
|
|
const double multiplier = sin(angle) / vector_modulus;
|
|
|
|
bgc_versor_set_values_fp64(cos(angle), base->_x1 * multiplier, base->_x2 * multiplier, base->_x3 * multiplier, power);
|
|
}
|
|
|
|
// ============ Sphere Interpolation ============ //
|
|
|
|
void bgc_versor_spherically_interpolate_fp32(const BgcVersorFP32* start, const BgcVersorFP32* end, const float phase, BgcVersorFP32* result)
|
|
{
|
|
const float delta_s0 = (end->_s0 * start->_s0 + end->_x1 * start->_x1) + (end->_x2 * start->_x2 + end->_x3 * start->_x3);
|
|
const float delta_x1 = (end->_x1 * start->_s0 + end->_x3 * start->_x2) - (end->_s0 * start->_x1 + end->_x2 * start->_x3);
|
|
const float delta_x2 = (end->_x2 * start->_s0 + end->_x1 * start->_x3) - (end->_s0 * start->_x2 + end->_x3 * start->_x1);
|
|
const float delta_x3 = (end->_x3 * start->_s0 + end->_x2 * start->_x1) - (end->_s0 * start->_x3 + end->_x1 * start->_x2);
|
|
|
|
const float square_vector = delta_x1 * delta_x1 + delta_x2 * delta_x2 + delta_x3 * delta_x3;
|
|
|
|
// square_vector != square_vector means checking for NaN value at square_vector
|
|
if (square_vector <= BGC_SQUARE_EPSYLON_FP32 || square_vector != square_vector) {
|
|
bgc_versor_copy_fp32(end, result);
|
|
return;
|
|
}
|
|
|
|
// Calculating of the turning which fits the phase:
|
|
const float vector_modulus = sqrtf(square_vector);
|
|
const float angle = atan2f(vector_modulus, delta_s0) * phase;
|
|
const float multiplier = sinf(angle) / vector_modulus;
|
|
|
|
const float turn_s0 = cosf(angle);
|
|
const float turn_x1 = delta_x1 * multiplier;
|
|
const float turn_x2 = delta_x2 * multiplier;
|
|
const float turn_x3 = delta_x3 * multiplier;
|
|
|
|
// Combining of starting orientation with the turning
|
|
bgc_versor_set_values_fp32(
|
|
(turn_s0 * start->_s0 - turn_x1 * start->_x1) - (turn_x2 * start->_x2 + turn_x3 * start->_x3),
|
|
(turn_x1 * start->_s0 + turn_s0 * start->_x1) - (turn_x3 * start->_x2 - turn_x2 * start->_x3),
|
|
(turn_x2 * start->_s0 + turn_s0 * start->_x2) - (turn_x1 * start->_x3 - turn_x3 * start->_x1),
|
|
(turn_x3 * start->_s0 + turn_s0 * start->_x3) - (turn_x2 * start->_x1 - turn_x1 * start->_x2),
|
|
result
|
|
);
|
|
}
|
|
|
|
void bgc_versor_spherically_interpolate_fp64(const BgcVersorFP64* start, const BgcVersorFP64* end, const double phase, BgcVersorFP64* result)
|
|
{
|
|
const double delta_s0 = (end->_s0 * start->_s0 + end->_x1 * start->_x1) + (end->_x2 * start->_x2 + end->_x3 * start->_x3);
|
|
const double delta_x1 = (end->_x1 * start->_s0 + end->_x3 * start->_x2) - (end->_s0 * start->_x1 + end->_x2 * start->_x3);
|
|
const double delta_x2 = (end->_x2 * start->_s0 + end->_x1 * start->_x3) - (end->_s0 * start->_x2 + end->_x3 * start->_x1);
|
|
const double delta_x3 = (end->_x3 * start->_s0 + end->_x2 * start->_x1) - (end->_s0 * start->_x3 + end->_x1 * start->_x2);
|
|
|
|
const double square_vector = delta_x1 * delta_x1 + delta_x2 * delta_x2 + delta_x3 * delta_x3;
|
|
|
|
// square_vector != square_vector means checking for NaN value at square_vector
|
|
if (square_vector <= BGC_SQUARE_EPSYLON_FP64 || square_vector != square_vector) {
|
|
bgc_versor_copy_fp64(end, result);
|
|
return;
|
|
}
|
|
|
|
// Calculating of the turning which fits the phase:
|
|
const double vector_modulus = sqrt(square_vector);
|
|
const double angle = atan2(vector_modulus, delta_s0) * phase;
|
|
const double multiplier = sin(angle) / vector_modulus;
|
|
|
|
const double turn_s0 = cos(angle);
|
|
const double turn_x1 = delta_x1 * multiplier;
|
|
const double turn_x2 = delta_x2 * multiplier;
|
|
const double turn_x3 = delta_x3 * multiplier;
|
|
|
|
// Combining of starting orientation with the turning
|
|
bgc_versor_set_values_fp64(
|
|
(turn_s0 * start->_s0 - turn_x1 * start->_x1) - (turn_x2 * start->_x2 + turn_x3 * start->_x3),
|
|
(turn_x1 * start->_s0 + turn_s0 * start->_x1) - (turn_x3 * start->_x2 - turn_x2 * start->_x3),
|
|
(turn_x2 * start->_s0 + turn_s0 * start->_x2) - (turn_x1 * start->_x3 - turn_x3 * start->_x1),
|
|
(turn_x3 * start->_s0 + turn_s0 * start->_x3) - (turn_x2 * start->_x1 - turn_x1 * start->_x2),
|
|
result
|
|
);
|
|
}
|
|
|
|
// ================ Get Rotation ================ //
|
|
|
|
void bgc_versor_get_rotation_fp32(const BgcVersorFP32* versor, BgcRotation3FP32* result)
|
|
{
|
|
const float square_modulus = versor->_x1 * versor->_x1 + versor->_x2 * versor->_x2 + versor->_x3 * versor->_x3;
|
|
|
|
if (square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
|
|
bgc_rotation3_reset_fp32(result);
|
|
return;
|
|
}
|
|
|
|
const float vector_modulus = sqrtf(square_modulus);
|
|
|
|
const float multiplier = 1.0f / vector_modulus;
|
|
|
|
result->radians = 2.0f * atan2f(vector_modulus, versor->_s0);
|
|
|
|
result->axis.x1 = versor->_x1 * multiplier;
|
|
result->axis.x2 = versor->_x2 * multiplier;
|
|
result->axis.x3 = versor->_x3 * multiplier;
|
|
}
|
|
|
|
void bgc_versor_get_rotation_fp64(const BgcVersorFP64* versor, BgcRotation3FP64* result)
|
|
{
|
|
const double square_modulus = versor->_x1 * versor->_x1 + versor->_x2 * versor->_x2 + versor->_x3 * versor->_x3;
|
|
|
|
if (square_modulus <= BGC_SQUARE_EPSYLON_FP64) {
|
|
bgc_rotation3_reset_fp64(result);
|
|
return;
|
|
}
|
|
|
|
const double vector_modulus = sqrt(square_modulus);
|
|
|
|
const double multiplier = 1.0 / vector_modulus;
|
|
|
|
result->radians = 2.0 * atan2(vector_modulus, versor->_s0);
|
|
|
|
result->axis.x1 = versor->_x1 * multiplier;
|
|
result->axis.x2 = versor->_x2 * multiplier;
|
|
result->axis.x3 = versor->_x3 * multiplier;
|
|
}
|