643 lines
27 KiB
C
643 lines
27 KiB
C
#include <math.h>
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#include "angle.h"
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#include "turn3.h"
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const BGC_FP32_Turn3 BGC_FP32_IDLE_TURN3 = {{ 1.0f, 0.0f, 0.0f, 0.0f }};
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const BGC_FP64_Turn3 BGC_FP64_IDLE_TURN3 = {{ 1.0, 0.0, 0.0, 0.0 }};
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extern inline void bgc_fp32_turn3_reset(BGC_FP32_Turn3* turn);
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extern inline void bgc_fp64_turn3_reset(BGC_FP64_Turn3* turn);
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extern inline void bgc_fp32_turn3_set_raw_values(BGC_FP32_Turn3* turn, const float s0, const float x1, const float x2, const float x3);
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extern inline void bgc_fp64_turn3_set_raw_values(BGC_FP64_Turn3* turn, const double s0, const double x1, const double x2, const double x3);
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extern inline void bgc_fp32_turn3_get_quaternion(BGC_FP32_Quaternion* quaternion, const BGC_FP32_Turn3* turn);
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extern inline void bgc_fp64_turn3_get_quaternion(BGC_FP64_Quaternion* quaternion, const BGC_FP64_Turn3* turn);
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extern inline void bgc_fp32_turn3_set_quaternion(BGC_FP32_Turn3* turn, const BGC_FP32_Quaternion* quaternion);
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extern inline void bgc_fp64_turn3_set_quaternion(BGC_FP64_Turn3* turn, const BGC_FP64_Quaternion* quaternion);
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extern inline void bgc_fp32_turn3_copy(BGC_FP32_Turn3* destination, const BGC_FP32_Turn3* source);
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extern inline void bgc_fp64_turn3_copy(BGC_FP64_Turn3* destination, const BGC_FP64_Turn3* source);
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extern inline void bgc_fp32_turn3_swap(BGC_FP32_Turn3* turn1, BGC_FP32_Turn3* turn2);
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extern inline void bgc_fp64_turn3_swap(BGC_FP64_Turn3* turn1, BGC_FP64_Turn3* turn2);
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extern inline int bgc_fp32_turn3_is_idle(const BGC_FP32_Turn3* turn);
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extern inline int bgc_fp64_turn3_is_idle(const BGC_FP64_Turn3* turn);
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extern inline void bgc_fp32_turn3_convert_to_fp64(BGC_FP64_Turn3* destination, const BGC_FP32_Turn3* source);
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extern inline void bgc_fp64_turn3_convert_to_fp32(BGC_FP32_Turn3* destination, const BGC_FP64_Turn3* source);
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extern inline void bgc_fp32_turn3_shorten(BGC_FP32_Turn3* turn);
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extern inline void bgc_fp64_turn3_shorten(BGC_FP64_Turn3* turn);
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extern inline void bgc_fp32_turn3_get_shortened(BGC_FP32_Turn3* shortened, const BGC_FP32_Turn3* turn);
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extern inline void bgc_fp64_turn3_get_shortened(BGC_FP64_Turn3* shortened, const BGC_FP64_Turn3* turn);
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extern inline void bgc_fp32_turn3_alternate(BGC_FP32_Turn3* turn);
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extern inline void bgc_fp64_turn3_alternate(BGC_FP64_Turn3* turn);
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extern inline void bgc_fp32_turn3_get_alternative(BGC_FP32_Turn3* alternative, const BGC_FP32_Turn3* turn);
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extern inline void bgc_fp64_turn3_get_alternative(BGC_FP64_Turn3* alternative, const BGC_FP64_Turn3* turn);
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extern inline void bgc_fp32_turn3_revert(BGC_FP32_Turn3* turn);
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extern inline void bgc_fp64_turn3_revert(BGC_FP64_Turn3* turn);
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extern inline void bgc_fp32_turn3_get_reverse(BGC_FP32_Turn3* inverse, const BGC_FP32_Turn3* turn);
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extern inline void bgc_fp64_turn3_get_reverse(BGC_FP64_Turn3* inverse, const BGC_FP64_Turn3* turn);
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extern inline void bgc_fp32_turn3_combine(BGC_FP32_Turn3* combination, const BGC_FP32_Turn3* first, const BGC_FP32_Turn3* second);
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extern inline void bgc_fp64_turn3_combine(BGC_FP64_Turn3* combination, const BGC_FP64_Turn3* first, const BGC_FP64_Turn3* second);
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extern inline void bgc_fp32_turn3_combine3(BGC_FP32_Turn3* combination, const BGC_FP32_Turn3* first, const BGC_FP32_Turn3* second, const BGC_FP32_Turn3* third);
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extern inline void bgc_fp64_turn3_combine3(BGC_FP64_Turn3* combination, const BGC_FP64_Turn3* first, const BGC_FP64_Turn3* second, const BGC_FP64_Turn3* third);
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extern inline void bgc_fp32_turn3_exclude(BGC_FP32_Turn3* difference, const BGC_FP32_Turn3* base, const BGC_FP32_Turn3* excludant);
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extern inline void bgc_fp64_turn3_exclude(BGC_FP64_Turn3* difference, const BGC_FP64_Turn3* base, const BGC_FP64_Turn3* excludant);
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extern inline void bgc_fp32_turn3_get_rotation_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_Turn3* turn);
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extern inline void bgc_fp64_turn3_get_rotation_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_Turn3* turn);
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extern inline void bgc_fp32_turn3_get_reverse_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_Turn3* turn);
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extern inline void bgc_fp64_turn3_get_reverse_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_Turn3* turn);
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extern inline void bgc_fp32_turn3_get_both_matrices(BGC_FP32_Matrix3x3* rotation, BGC_FP32_Matrix3x3* reverse, const BGC_FP32_Turn3* turn);
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extern inline void bgc_fp64_turn3_get_both_matrices(BGC_FP64_Matrix3x3* rotation, BGC_FP64_Matrix3x3* reverse, const BGC_FP64_Turn3* turn);
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extern inline void bgc_fp32_turn3_vector(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Turn3* turn, const BGC_FP32_Vector3* vector);
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extern inline void bgc_fp64_turn3_vector(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Turn3* turn, const BGC_FP64_Vector3* vector);
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extern inline void bgc_fp32_turn3_vector_back(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Turn3* turn, const BGC_FP32_Vector3* vector);
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extern inline void bgc_fp64_turn3_vector_back(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Turn3* turn, const BGC_FP64_Vector3* vector);
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extern inline int bgc_fp32_turn3_are_close(const BGC_FP32_Turn3* turn1, const BGC_FP32_Turn3* turn2);
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extern inline int bgc_fp64_turn3_are_close(const BGC_FP64_Turn3* turn1, const BGC_FP64_Turn3* turn2);
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// ================= Normalize ================== //
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void _bgc_fp32_turn3_normalize(BGC_FP32_Turn3* turn, const float square_modulus)
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{
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if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
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bgc_fp32_turn3_reset(turn);
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return;
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}
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bgc_fp32_quaternion_multiply_by_real(&turn->_versor, &turn->_versor, sqrtf(1.0f / square_modulus));
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}
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void _bgc_fp64_turn3_normalize(BGC_FP64_Turn3* turn, const double square_modulus)
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{
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if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
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bgc_fp64_turn3_reset(turn);
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return;
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}
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bgc_fp64_quaternion_multiply_by_real(&turn->_versor, &turn->_versor, sqrt(1.0 / square_modulus));
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}
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// ================ Get Rotation ================ //
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float bgc_fp32_turn3_get_rotation(BGC_FP32_Vector3* axis, const BGC_FP32_Turn3* turn, const int angle_unit)
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{
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const float square_vector_modulus = turn->_versor.x1 * turn->_versor.x1 + turn->_versor.x2 * turn->_versor.x2 + turn->_versor.x3 * turn->_versor.x3;
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if (square_vector_modulus <= BGC_FP32_SQUARE_EPSILON) {
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bgc_fp32_vector3_reset(axis);
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return 0.0f;
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}
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const float vector_modulus = sqrtf(square_vector_modulus);
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const float multiplier = 1.0f / vector_modulus;
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axis->x1 = turn->_versor.x1 * multiplier;
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axis->x2 = turn->_versor.x2 * multiplier;
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axis->x3 = turn->_versor.x3 * multiplier;
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return 2.0f * atan2f(vector_modulus, turn->_versor.s0);
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}
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double bgc_fp64_turn3_get_rotation(BGC_FP64_Vector3* axis, const BGC_FP64_Turn3* turn, const int angle_unit)
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{
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const double square_vector_modulus = turn->_versor.x1 * turn->_versor.x1 + turn->_versor.x2 * turn->_versor.x2 + turn->_versor.x3 * turn->_versor.x3;
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if (square_vector_modulus <= BGC_FP64_SQUARE_EPSILON) {
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bgc_fp64_vector3_reset(axis);
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return 0.0;
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}
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const double vector_modulus = sqrt(square_vector_modulus);
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const double multiplier = 1.0 / vector_modulus;
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axis->x1 = turn->_versor.x1 * multiplier;
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axis->x2 = turn->_versor.x2 * multiplier;
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axis->x3 = turn->_versor.x3 * multiplier;
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return 2.0 * atan2(vector_modulus, turn->_versor.s0);
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}
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// ================ Set Rotation ================ //
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void bgc_fp32_turn3_set_rotation(BGC_FP32_Turn3* turn, const float x1, const float x2, const float x3, const float angle, const int angle_unit)
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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_FP32_SQUARE_EPSILON) {
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bgc_fp32_turn3_reset(turn);
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return;
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}
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const float half_angle = bgc_fp32_angle_to_radians(0.5f * angle, angle_unit);
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const float sine = sinf(half_angle);
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if (bgc_fp32_is_zero(sine)) {
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bgc_fp32_turn3_reset(turn);
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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_fp32_quaternion_make(&turn->_versor, cosf(half_angle), x1 * multiplier, x2 * multiplier, x3 * multiplier);
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const float square_modulus = bgc_fp32_quaternion_get_square_modulus(&turn->_versor);
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if (!bgc_fp32_is_square_unit(square_modulus)) {
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_bgc_fp32_turn3_normalize(turn, square_modulus);
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}
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}
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void bgc_fp64_turn3_set_rotation(BGC_FP64_Turn3* turn, const double x1, const double x2, const double x3, const double angle, const int angle_unit)
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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_FP64_SQUARE_EPSILON) {
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bgc_fp64_turn3_reset(turn);
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return;
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}
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const double half_angle = bgc_fp64_angle_to_radians(0.5 * angle, angle_unit);
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const double sine = sin(half_angle);
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if (bgc_fp64_is_zero(sine)) {
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bgc_fp64_turn3_reset(turn);
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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_fp64_quaternion_make(&turn->_versor, cos(half_angle), x1 * multiplier, x2 * multiplier, x3 * multiplier);
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const double square_modulus = bgc_fp64_quaternion_get_square_modulus(&turn->_versor);
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if (!bgc_fp64_is_square_unit(square_modulus)) {
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_bgc_fp64_turn3_normalize(turn, square_modulus);
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}
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}
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// ========= Find Direction Difference ========== //
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int bgc_fp32_turn3_find_direction_difference(BGC_FP32_Turn3* turn, const BGC_FP32_Vector3* first, const BGC_FP32_Vector3* second)
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{
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const float first_square_modulus = bgc_fp32_vector3_get_square_modulus(first);
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bgc_fp32_turn3_reset(turn);
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if (first_square_modulus <= BGC_FP32_SQUARE_EPSILON) {
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return BGC_ERROR_TURN3_FIRST_VECTOR_ZERO;
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}
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const float second_square_modulus = bgc_fp32_vector3_get_square_modulus(second);
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if (second_square_modulus <= BGC_FP32_SQUARE_EPSILON) {
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return BGC_ERROR_TURN3_SECOND_VECTOR_ZERO;
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}
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BGC_FP32_Vector3 axis;
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bgc_fp32_vector3_get_cross_product(&axis, first, second);
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const float square_product = first_square_modulus * second_square_modulus;
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const float dot_product = bgc_fp32_vector3_get_dot_product(first, second);
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const float axis_square_modulus = bgc_fp32_vector3_get_square_modulus(&axis);
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if (axis_square_modulus <= BGC_FP32_SQUARE_EPSILON * square_product) {
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if (dot_product < 0.0f) {
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return BGC_ERROR_TURN3_VECTORS_OPPOSITE;
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}
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return BGC_SUCCESS;
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}
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const float axis_modulus = sqrtf(axis_square_modulus);
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const float trigonometry_fix = sqrtf(1.0f / square_product);
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const float angle = 0.5f * atan2f(axis_modulus * trigonometry_fix, dot_product * trigonometry_fix);
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const float vector_multiplier = sinf(angle) / axis_modulus;
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bgc_fp32_turn3_set_raw_values(turn, cosf(angle), axis.x1 * vector_multiplier, axis.x2 * vector_multiplier, axis.x3 * vector_multiplier);
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return BGC_SUCCESS;
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}
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int bgc_fp64_turn3_find_direction_difference(BGC_FP64_Turn3* turn, const BGC_FP64_Vector3* first, const BGC_FP64_Vector3* second)
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{
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const double first_square_modulus = bgc_fp64_vector3_get_square_modulus(first);
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bgc_fp64_turn3_reset(turn);
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if (first_square_modulus <= BGC_FP64_SQUARE_EPSILON) {
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return BGC_ERROR_TURN3_FIRST_VECTOR_ZERO;
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}
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const double second_square_modulus = bgc_fp64_vector3_get_square_modulus(second);
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if (second_square_modulus <= BGC_FP64_SQUARE_EPSILON) {
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return BGC_ERROR_TURN3_SECOND_VECTOR_ZERO;
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}
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BGC_FP64_Vector3 axis;
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bgc_fp64_vector3_get_cross_product(&axis, first, second);
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const double square_product = first_square_modulus * second_square_modulus;
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const double dot_product = bgc_fp64_vector3_get_dot_product(first, second);
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const double axis_square_modulus = bgc_fp64_vector3_get_square_modulus(&axis);
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if (axis_square_modulus <= BGC_FP64_SQUARE_EPSILON * square_product) {
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bgc_fp64_turn3_reset(turn);
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if (dot_product < 0.0) {
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return BGC_ERROR_TURN3_VECTORS_OPPOSITE;
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}
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return BGC_SUCCESS;
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}
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const double axis_modulus = sqrt(axis_square_modulus);
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const double trigonometry_fix = sqrt(1.0 / square_product);
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const double angle = 0.5 * atan2(axis_modulus * trigonometry_fix, dot_product * trigonometry_fix);
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const double vector_multiplier = sin(angle) / axis_modulus;
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bgc_fp64_turn3_set_raw_values(turn, cos(angle), axis.x1 * vector_multiplier, axis.x2 * vector_multiplier, axis.x3 * vector_multiplier);
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return BGC_SUCCESS;
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}
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// ============ Make Orthogonal Pair ============ //
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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)
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{
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const float main_square_modulus = bgc_fp32_vector3_get_square_modulus(main);
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if (main_square_modulus <= BGC_FP32_SQUARE_EPSILON) {
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return _BGC_ERROR_TURN3_EMPTY_MAIN;
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}
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const float branch_square_modulus = bgc_fp32_vector3_get_square_modulus(branch);
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if (branch_square_modulus <= BGC_FP32_SQUARE_EPSILON) {
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return _BGC_ERROR_TURN3_EMPTY_BRANCH;
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}
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bgc_fp32_vector3_multiply(unit_main, main, sqrtf(1.0f / main_square_modulus));
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bgc_fp32_vector3_add_scaled(unit_branch, branch, unit_main, -bgc_fp32_vector3_get_dot_product(branch, unit_main));
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const float orthogonal_square_modulus = bgc_fp32_vector3_get_square_modulus(unit_branch);
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if (orthogonal_square_modulus <= BGC_FP32_SQUARE_EPSILON) {
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return _BGC_ERROR_TURN3_PAIR_PARALLEL;
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}
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bgc_fp32_vector3_multiply(unit_branch, unit_branch, sqrtf(1.0f / orthogonal_square_modulus));
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return BGC_SUCCESS;
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}
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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)
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{
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const double main_square_modulus = bgc_fp64_vector3_get_square_modulus(main);
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if (main_square_modulus <= BGC_FP64_SQUARE_EPSILON) {
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return _BGC_ERROR_TURN3_EMPTY_MAIN;
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}
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const double branch_square_modulus = bgc_fp64_vector3_get_square_modulus(branch);
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if (branch_square_modulus <= BGC_FP64_SQUARE_EPSILON) {
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return _BGC_ERROR_TURN3_EMPTY_BRANCH;
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}
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bgc_fp64_vector3_multiply(unit_main, main, sqrt(1.0 / main_square_modulus));
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bgc_fp64_vector3_add_scaled(unit_branch, branch, unit_main, -bgc_fp64_vector3_get_dot_product(branch, unit_main));
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const double orthogonal_square_modulus = bgc_fp64_vector3_get_square_modulus(unit_branch);
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if (orthogonal_square_modulus <= BGC_FP64_SQUARE_EPSILON) {
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return _BGC_ERROR_TURN3_PAIR_PARALLEL;
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}
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bgc_fp64_vector3_multiply(unit_branch, unit_branch, sqrt(1.0 / orthogonal_square_modulus));
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return BGC_SUCCESS;
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}
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// ========= Make Direction Difference ========== //
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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)
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{
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BGC_FP32_Vector3 axis;
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bgc_fp32_vector3_get_cross_product(&axis, unit_start, unit_end);
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const float dot_product = bgc_fp32_vector3_get_dot_product(unit_start, unit_end);
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const float axis_square_modulus = bgc_fp32_vector3_get_square_modulus(&axis);
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// unit_start and unit_end are parallel
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if (axis_square_modulus <= BGC_FP32_SQUARE_EPSILON) {
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// unit_start and unit_end are co-directional, angle = 180 degrees
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if (dot_product >= 0.0f) {
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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;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
// =============== Get Exponation =============== //
|
|
|
|
void bgc_fp32_turn3_get_exponation(BGC_FP32_Turn3* power, const BGC_FP32_Turn3* base, const float exponent)
|
|
{
|
|
const float square_vector = base->_versor.x1 * base->_versor.x1 + base->_versor.x2 * base->_versor.x2 + base->_versor.x3 * base->_versor.x3;
|
|
|
|
if (square_vector <= BGC_FP32_SQUARE_EPSILON || square_vector != square_vector) {
|
|
bgc_fp32_turn3_reset(power);
|
|
return;
|
|
}
|
|
|
|
const float vector_modulus = sqrtf(square_vector);
|
|
|
|
const float angle = atan2f(vector_modulus, base->_versor.s0) * exponent;
|
|
|
|
const float multiplier = sinf(angle) / vector_modulus;
|
|
|
|
bgc_fp32_turn3_set_raw_values(power, cosf(angle), base->_versor.x1 * multiplier, base->_versor.x2 * multiplier, base->_versor.x3 * multiplier);
|
|
}
|
|
|
|
void bgc_fp64_turn3_get_exponation(BGC_FP64_Turn3* power, const BGC_FP64_Turn3* base, const double exponent)
|
|
{
|
|
const double square_vector = base->_versor.x1 * base->_versor.x1 + base->_versor.x2 * base->_versor.x2 + base->_versor.x3 * base->_versor.x3;
|
|
|
|
if (square_vector <= BGC_FP64_SQUARE_EPSILON || square_vector != square_vector) {
|
|
bgc_fp64_turn3_reset(power);
|
|
return;
|
|
}
|
|
|
|
const double vector_modulus = sqrt(square_vector);
|
|
|
|
const double angle = atan2(vector_modulus, base->_versor.s0) * exponent;
|
|
|
|
const double multiplier = sin(angle) / vector_modulus;
|
|
|
|
bgc_fp64_turn3_set_raw_values(power, cos(angle), base->_versor.x1 * multiplier, base->_versor.x2 * multiplier, base->_versor.x3 * multiplier);
|
|
}
|
|
|
|
// ============ Sphere Interpolation ============ //
|
|
|
|
void bgc_fp32_turn3_spherically_interpolate(BGC_FP32_Turn3* interpolation, const BGC_FP32_Turn3* start, const BGC_FP32_Turn3* end, const float phase)
|
|
{
|
|
const float delta_s0 = (end->_versor.s0 * start->_versor.s0 + end->_versor.x1 * start->_versor.x1) + (end->_versor.x2 * start->_versor.x2 + end->_versor.x3 * start->_versor.x3);
|
|
const float delta_x1 = (end->_versor.x1 * start->_versor.s0 + end->_versor.x3 * start->_versor.x2) - (end->_versor.s0 * start->_versor.x1 + end->_versor.x2 * start->_versor.x3);
|
|
const float delta_x2 = (end->_versor.x2 * start->_versor.s0 + end->_versor.x1 * start->_versor.x3) - (end->_versor.s0 * start->_versor.x2 + end->_versor.x3 * start->_versor.x1);
|
|
const float delta_x3 = (end->_versor.x3 * start->_versor.s0 + end->_versor.x2 * start->_versor.x1) - (end->_versor.s0 * start->_versor.x3 + end->_versor.x1 * start->_versor.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_FP32_SQUARE_EPSILON || isnan(square_vector)) {
|
|
bgc_fp32_turn3_copy(interpolation, end);
|
|
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_fp32_turn3_set_raw_values(
|
|
interpolation,
|
|
(turn_s0 * start->_versor.s0 - turn_x1 * start->_versor.x1) - (turn_x2 * start->_versor.x2 + turn_x3 * start->_versor.x3),
|
|
(turn_x1 * start->_versor.s0 + turn_s0 * start->_versor.x1) - (turn_x3 * start->_versor.x2 - turn_x2 * start->_versor.x3),
|
|
(turn_x2 * start->_versor.s0 + turn_s0 * start->_versor.x2) - (turn_x1 * start->_versor.x3 - turn_x3 * start->_versor.x1),
|
|
(turn_x3 * start->_versor.s0 + turn_s0 * start->_versor.x3) - (turn_x2 * start->_versor.x1 - turn_x1 * start->_versor.x2)
|
|
);
|
|
}
|
|
|
|
void bgc_fp64_turn3_spherically_interpolate(BGC_FP64_Turn3* interpolation, const BGC_FP64_Turn3* start, const BGC_FP64_Turn3* end, const double phase)
|
|
{
|
|
const double delta_s0 = (end->_versor.s0 * start->_versor.s0 + end->_versor.x1 * start->_versor.x1) + (end->_versor.x2 * start->_versor.x2 + end->_versor.x3 * start->_versor.x3);
|
|
const double delta_x1 = (end->_versor.x1 * start->_versor.s0 + end->_versor.x3 * start->_versor.x2) - (end->_versor.s0 * start->_versor.x1 + end->_versor.x2 * start->_versor.x3);
|
|
const double delta_x2 = (end->_versor.x2 * start->_versor.s0 + end->_versor.x1 * start->_versor.x3) - (end->_versor.s0 * start->_versor.x2 + end->_versor.x3 * start->_versor.x1);
|
|
const double delta_x3 = (end->_versor.x3 * start->_versor.s0 + end->_versor.x2 * start->_versor.x1) - (end->_versor.s0 * start->_versor.x3 + end->_versor.x1 * start->_versor.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_FP64_SQUARE_EPSILON || isnan(square_vector)) {
|
|
bgc_fp64_turn3_copy(interpolation, end);
|
|
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_fp64_turn3_set_raw_values(
|
|
interpolation,
|
|
(turn_s0 * start->_versor.s0 - turn_x1 * start->_versor.x1) - (turn_x2 * start->_versor.x2 + turn_x3 * start->_versor.x3),
|
|
(turn_x1 * start->_versor.s0 + turn_s0 * start->_versor.x1) - (turn_x3 * start->_versor.x2 - turn_x2 * start->_versor.x3),
|
|
(turn_x2 * start->_versor.s0 + turn_s0 * start->_versor.x2) - (turn_x1 * start->_versor.x3 - turn_x3 * start->_versor.x1),
|
|
(turn_x3 * start->_versor.s0 + turn_s0 * start->_versor.x3) - (turn_x2 * start->_versor.x1 - turn_x1 * start->_versor.x2)
|
|
);
|
|
}
|