659 lines
24 KiB
C
659 lines
24 KiB
C
#ifndef _BGC_VERSOR_H_
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#define _BGC_VERSOR_H_
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#include <stdint.h>
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#include "utilities.h"
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#include "angle.h"
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#include "vector3.h"
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#include "rotation3.h"
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#include "matrix3x3.h"
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#include "quaternion.h"
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#define BGC_SOME_TURN 1
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#define BGC_ZERO_TURN 0
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#define BGC_OPPOSITE -1
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#define BGC_ERROR_PRIMARY_DIRECTION_UNKNOWN -3001
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#define BGC_ERROR_PRIMARY_VECTOR_IS_ZERO -3002
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#define BGC_ERROR_AUXILIARY_DIRECTION_UNKNOWN -3011
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#define BGC_ERROR_AUXILIARY_VECTOR_IS_ZERO -3012
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#define BGC_ERROR_DIRECTIONS_PARALLEL -3021
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#define BGC_ERROR_VECTORS_PARALLEL -3022
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// =================== Types ==================== //
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typedef struct {
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float _s0, _x1, _x2, _x3;
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} BgcVersorFP32;
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typedef struct {
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double _s0, _x1, _x2, _x3;
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} BgcVersorFP64;
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// ================= Constants ================== //
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extern const BgcVersorFP32 BGC_IDLE_VERSOR_FP32;
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extern const BgcVersorFP64 BGC_IDLE_VERSOR_FP64;
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// =================== Reset ==================== //
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inline void bgc_versor_reset_fp32(BgcVersorFP32* versor)
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{
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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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}
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inline void bgc_versor_reset_fp64(BgcVersorFP64* versor)
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{
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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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}
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// ==================== Set ===================== //
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void _bgc_versor_normalize_fp32(const float square_modulus, BgcVersorFP32* twin);
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void _bgc_versor_normalize_fp64(const double square_modulus, BgcVersorFP64* twin);
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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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{
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versor->_s0 = s0;
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versor->_x1 = x1;
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versor->_x2 = x2;
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versor->_x3 = x3;
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const float square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
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if (!bgc_is_sqare_unit_fp32(square_modulus)) {
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_bgc_versor_normalize_fp32(square_modulus, versor);
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}
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}
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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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{
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versor->_s0 = s0;
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versor->_x1 = x1;
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versor->_x2 = x2;
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versor->_x3 = x3;
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const double square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
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if (!bgc_is_sqare_unit_fp64(square_modulus)) {
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_bgc_versor_normalize_fp64(square_modulus, versor);
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}
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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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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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// ================ Set Rotation ================ //
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inline void bgc_versor_set_rotation_fp32(const BgcRotation3FP32* rotation, BgcVersorFP32* result)
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{
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bgc_versor_set_turn_fp32(rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BGC_ANGLE_UNIT_RADIANS, result);
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}
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inline void bgc_versor_set_rotation_fp64(const BgcRotation3FP64* rotation, BgcVersorFP64* result)
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{
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bgc_versor_set_turn_fp64(rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BGC_ANGLE_UNIT_RADIANS, result);
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}
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// ========= Make Direction Difference ========== //
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int bgc_versor_make_direction_difference_fp32(const BgcVector3FP32* start, const BgcVector3FP32* end, BgcVersorFP32* result);
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int bgc_versor_make_direction_difference_fp64(const BgcVector3FP64* start, const BgcVector3FP64* end, BgcVersorFP64* result);
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// =============== Set Directions =============== //
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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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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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// ==================== Copy ==================== //
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inline void bgc_versor_copy_fp32(const BgcVersorFP32* source, BgcVersorFP32* destination)
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{
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destination->_s0 = source->_s0;
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destination->_x1 = source->_x1;
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destination->_x2 = source->_x2;
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destination->_x3 = source->_x3;
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}
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inline void bgc_versor_copy_fp64(const BgcVersorFP64* source, BgcVersorFP64* destination)
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{
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destination->_s0 = source->_s0;
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destination->_x1 = source->_x1;
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destination->_x2 = source->_x2;
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destination->_x3 = source->_x3;
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}
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// ==================== Swap ==================== //
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inline void bgc_versor_swap_fp32(BgcVersorFP32* versor1, BgcVersorFP32* versor2)
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{
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const float s0 = versor1->_s0;
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const float x1 = versor1->_x1;
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const float x2 = versor1->_x2;
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const float x3 = versor1->_x3;
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versor1->_s0 = versor2->_s0;
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versor1->_x1 = versor2->_x1;
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versor1->_x2 = versor2->_x2;
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versor1->_x3 = versor2->_x3;
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versor2->_s0 = s0;
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versor2->_x1 = x1;
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versor2->_x2 = x2;
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versor2->_x3 = x3;
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}
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inline void bgc_versor_swap_fp64(BgcVersorFP64* versor1, BgcVersorFP64* versor2)
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{
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const double s0 = versor1->_s0;
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const double x1 = versor1->_x1;
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const double x2 = versor1->_x2;
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const double x3 = versor1->_x3;
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versor1->_s0 = versor2->_s0;
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versor1->_x1 = versor2->_x1;
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versor1->_x2 = versor2->_x2;
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versor1->_x3 = versor2->_x3;
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versor2->_s0 = s0;
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versor2->_x1 = x1;
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versor2->_x2 = x2;
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versor2->_x3 = x3;
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}
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// ================= Comparison ================= //
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inline int bgc_versor_is_identity_fp32(const BgcVersorFP32* versor)
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{
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return versor->_x1 * versor->_x1 + versor->_x2 * versor->_x2 + versor->_x3 * versor->_x3 <= BGC_SQUARE_EPSYLON_FP32;
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}
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inline int bgc_versor_is_identity_fp64(const BgcVersorFP64* versor)
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{
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return versor->_x1 * versor->_x1 + versor->_x2 * versor->_x2 + versor->_x3 * versor->_x3 <= BGC_SQUARE_EPSYLON_FP64;
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}
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// ================== Convert =================== //
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inline void bgc_versor_convert_fp64_to_fp32(const BgcVersorFP64* source, BgcVersorFP32* destination)
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{
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bgc_versor_set_values_fp32(
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(float)source->_s0,
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(float)source->_x1,
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(float)source->_x2,
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(float)source->_x3,
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destination
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);
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}
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inline void bgc_versor_convert_fp32_to_fp64(const BgcVersorFP32* source, BgcVersorFP64* destination)
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{
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bgc_versor_set_values_fp64(
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source->_s0,
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source->_x1,
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source->_x2,
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source->_x3,
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destination
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);
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}
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// ================== Shorten =================== //
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inline void bgc_versor_shorten_fp32(BgcVersorFP32* versor)
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{
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if (versor->_s0 < 0.0f) {
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versor->_s0 = -versor->_s0;
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versor->_x1 = -versor->_x1;
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versor->_x2 = -versor->_x2;
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versor->_x3 = -versor->_x3;
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}
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}
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inline void bgc_versor_shorten_fp64(BgcVersorFP64* versor)
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{
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if (versor->_s0 < 0.0) {
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versor->_s0 = -versor->_s0;
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versor->_x1 = -versor->_x1;
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versor->_x2 = -versor->_x2;
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versor->_x3 = -versor->_x3;
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}
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}
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inline void bgc_versor_get_shortened_fp32(const BgcVersorFP32* versor, BgcVersorFP32* shortened)
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{
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if (versor->_s0 >= 0.0f) {
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shortened->_s0 = versor->_s0;
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shortened->_x1 = versor->_x1;
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shortened->_x2 = versor->_x2;
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shortened->_x3 = versor->_x3;
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return;
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}
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shortened->_s0 = -versor->_s0;
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shortened->_x1 = -versor->_x1;
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shortened->_x2 = -versor->_x2;
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shortened->_x3 = -versor->_x3;
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}
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inline void bgc_versor_get_shortened_fp64(const BgcVersorFP64* versor, BgcVersorFP64* shortened)
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{
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if (versor->_s0 >= 0.0) {
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shortened->_s0 = versor->_s0;
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shortened->_x1 = versor->_x1;
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shortened->_x2 = versor->_x2;
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shortened->_x3 = versor->_x3;
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return;
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}
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shortened->_s0 = -versor->_s0;
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shortened->_x1 = -versor->_x1;
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shortened->_x2 = -versor->_x2;
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shortened->_x3 = -versor->_x3;
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}
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// ================== Negative ================== //
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inline void bgc_versor_make_opposite_fp32(BgcVersorFP32* versor)
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{
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versor->_s0 = -versor->_s0;
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versor->_x1 = -versor->_x1;
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versor->_x2 = -versor->_x2;
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versor->_x3 = -versor->_x3;
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}
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inline void bgc_versor_make_opposite_fp64(BgcVersorFP64* versor)
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{
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versor->_s0 = -versor->_s0;
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versor->_x1 = -versor->_x1;
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versor->_x2 = -versor->_x2;
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versor->_x3 = -versor->_x3;
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}
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inline void bgc_versor_get_opposite_fp32(const BgcVersorFP32* versor, BgcVersorFP32* opposite)
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{
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opposite->_s0 = -versor->_s0;
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opposite->_x1 = -versor->_x1;
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opposite->_x2 = -versor->_x2;
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opposite->_x3 = -versor->_x3;
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}
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inline void bgc_versor_get_opposite_fp64(const BgcVersorFP64* versor, BgcVersorFP64* opposite)
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{
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opposite->_s0 = -versor->_s0;
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opposite->_x1 = -versor->_x1;
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opposite->_x2 = -versor->_x2;
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opposite->_x3 = -versor->_x3;
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}
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// =================== Invert =================== //
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inline void bgc_versor_invert_fp32(BgcVersorFP32* versor)
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{
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versor->_x1 = -versor->_x1;
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versor->_x2 = -versor->_x2;
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versor->_x3 = -versor->_x3;
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}
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inline void bgc_versor_invert_fp64(BgcVersorFP64* versor)
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{
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versor->_x1 = -versor->_x1;
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versor->_x2 = -versor->_x2;
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versor->_x3 = -versor->_x3;
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}
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inline void bgc_versor_get_inverse_fp32(const BgcVersorFP32* versor, BgcVersorFP32* inverse)
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{
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inverse->_s0 = versor->_s0;
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inverse->_x1 = -versor->_x1;
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inverse->_x2 = -versor->_x2;
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inverse->_x3 = -versor->_x3;
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}
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inline void bgc_versor_get_inverse_fp64(const BgcVersorFP64* versor, BgcVersorFP64* inverse)
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{
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inverse->_s0 = versor->_s0;
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inverse->_x1 = -versor->_x1;
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inverse->_x2 = -versor->_x2;
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inverse->_x3 = -versor->_x3;
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}
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// =============== Get Exponation =============== //
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void bgc_versor_get_exponation_fp32(const BgcVersorFP32* base, const float exponent, BgcVersorFP32* power);
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void bgc_versor_get_exponation_fp64(const BgcVersorFP64* base, const double exponent, BgcVersorFP64* power);
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// ================ Combination ================= //
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inline void bgc_versor_combine_fp32(const BgcVersorFP32* second, const BgcVersorFP32* first, BgcVersorFP32* result)
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{
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bgc_versor_set_values_fp32(
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(second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3),
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(second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3),
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(second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1),
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(second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2),
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result
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);
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}
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inline void bgc_versor_combine_fp64(const BgcVersorFP64* second, const BgcVersorFP64* first, BgcVersorFP64* result)
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{
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bgc_versor_set_values_fp64(
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(second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3),
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(second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3),
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(second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1),
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(second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2),
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result
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);
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}
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// ============ Combination of three ============ //
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inline void bgc_versor_combine3_fp32(const BgcVersorFP32* third, const BgcVersorFP32* second, const BgcVersorFP32* first, BgcVersorFP32* result)
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{
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const float s0 = (second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3);
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const float x1 = (second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3);
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const float x2 = (second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1);
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const float x3 = (second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2);
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bgc_versor_set_values_fp32(
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(third->_s0 * s0 - third->_x1 * x1) - (third->_x2 * x2 + third->_x3 * x3),
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(third->_x1 * s0 + third->_s0 * x1) - (third->_x3 * x2 - third->_x2 * x3),
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(third->_x2 * s0 + third->_s0 * x2) - (third->_x1 * x3 - third->_x3 * x1),
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(third->_x3 * s0 + third->_s0 * x3) - (third->_x2 * x1 - third->_x1 * x2),
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result
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);
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}
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inline void bgc_versor_combine3_fp64(const BgcVersorFP64* third, const BgcVersorFP64* second, const BgcVersorFP64* first, BgcVersorFP64* result)
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{
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const double s0 = (second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3);
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const double x1 = (second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3);
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const double x2 = (second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1);
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const double x3 = (second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2);
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bgc_versor_set_values_fp64(
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(third->_s0 * s0 - third->_x1 * x1) - (third->_x2 * x2 + third->_x3 * x3),
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(third->_x1 * s0 + third->_s0 * x1) - (third->_x3 * x2 - third->_x2 * x3),
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(third->_x2 * s0 + third->_s0 * x2) - (third->_x1 * x3 - third->_x3 * x1),
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(third->_x3 * s0 + third->_s0 * x3) - (third->_x2 * x1 - third->_x1 * x2),
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result
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);
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}
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// ================= Exclusion ================== //
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inline void bgc_versor_exclude_fp32(const BgcVersorFP32* base, const BgcVersorFP32* excludant, BgcVersorFP32* difference)
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{
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bgc_versor_set_values_fp32(
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(base->_s0 * excludant->_s0 + base->_x1 * excludant->_x1) + (base->_x2 * excludant->_x2 + base->_x3 * excludant->_x3),
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(base->_x1 * excludant->_s0 + base->_x3 * excludant->_x2) - (base->_s0 * excludant->_x1 + base->_x2 * excludant->_x3),
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(base->_x2 * excludant->_s0 + base->_x1 * excludant->_x3) - (base->_s0 * excludant->_x2 + base->_x3 * excludant->_x1),
|
|
(base->_x3 * excludant->_s0 + base->_x2 * excludant->_x1) - (base->_s0 * excludant->_x3 + base->_x1 * excludant->_x2),
|
|
difference
|
|
);
|
|
}
|
|
|
|
inline void bgc_versor_exclude_fp64(const BgcVersorFP64* base, const BgcVersorFP64* excludant, BgcVersorFP64* difference)
|
|
{
|
|
bgc_versor_set_values_fp64(
|
|
(base->_s0 * excludant->_s0 + base->_x1 * excludant->_x1) + (base->_x2 * excludant->_x2 + base->_x3 * excludant->_x3),
|
|
(base->_x1 * excludant->_s0 + base->_x3 * excludant->_x2) - (base->_s0 * excludant->_x1 + base->_x2 * excludant->_x3),
|
|
(base->_x2 * excludant->_s0 + base->_x1 * excludant->_x3) - (base->_s0 * excludant->_x2 + base->_x3 * excludant->_x1),
|
|
(base->_x3 * excludant->_s0 + base->_x2 * excludant->_x1) - (base->_s0 * excludant->_x3 + base->_x1 * excludant->_x2),
|
|
difference
|
|
);
|
|
}
|
|
|
|
// ============ Sphere Interpolation ============ //
|
|
|
|
void bgc_versor_spherically_interpolate_fp32(const BgcVersorFP32* start, const BgcVersorFP32* end, const float phase, BgcVersorFP32* result);
|
|
|
|
void bgc_versor_spherically_interpolate_fp64(const BgcVersorFP64* start, const BgcVersorFP64* end, const double phase, BgcVersorFP64* result);
|
|
|
|
// ================ Get Rotation ================ //
|
|
|
|
void bgc_versor_get_rotation_fp32(const BgcVersorFP32* versor, BgcRotation3FP32* result);
|
|
|
|
void bgc_versor_get_rotation_fp64(const BgcVersorFP64* versor, BgcRotation3FP64* result);
|
|
|
|
// ============ Get Rotation Matrix ============= //
|
|
|
|
inline void bgc_versor_get_rotation_matrix_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* matrix)
|
|
{
|
|
const float s0s0 = versor->_s0 * versor->_s0;
|
|
const float x1x1 = versor->_x1 * versor->_x1;
|
|
const float x2x2 = versor->_x2 * versor->_x2;
|
|
const float x3x3 = versor->_x3 * versor->_x3;
|
|
|
|
const float s0x1 = versor->_s0 * versor->_x1;
|
|
const float s0x2 = versor->_s0 * versor->_x2;
|
|
const float s0x3 = versor->_s0 * versor->_x3;
|
|
const float x1x2 = versor->_x1 * versor->_x2;
|
|
const float x1x3 = versor->_x1 * versor->_x3;
|
|
const float x2x3 = versor->_x2 * versor->_x3;
|
|
|
|
matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
|
|
matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
|
|
matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
|
|
|
|
matrix->r1c2 = 2.0f * (x1x2 - s0x3);
|
|
matrix->r2c3 = 2.0f * (x2x3 - s0x1);
|
|
matrix->r3c1 = 2.0f * (x1x3 - s0x2);
|
|
|
|
matrix->r2c1 = 2.0f * (x1x2 + s0x3);
|
|
matrix->r3c2 = 2.0f * (x2x3 + s0x1);
|
|
matrix->r1c3 = 2.0f * (x1x3 + s0x2);
|
|
}
|
|
|
|
inline void bgc_versor_get_rotation_matrix_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* matrix)
|
|
{
|
|
const double s0s0 = versor->_s0 * versor->_s0;
|
|
const double x1x1 = versor->_x1 * versor->_x1;
|
|
const double x2x2 = versor->_x2 * versor->_x2;
|
|
const double x3x3 = versor->_x3 * versor->_x3;
|
|
|
|
const double s0x1 = versor->_s0 * versor->_x1;
|
|
const double s0x2 = versor->_s0 * versor->_x2;
|
|
const double s0x3 = versor->_s0 * versor->_x3;
|
|
const double x1x2 = versor->_x1 * versor->_x2;
|
|
const double x1x3 = versor->_x1 * versor->_x3;
|
|
const double x2x3 = versor->_x2 * versor->_x3;
|
|
|
|
matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
|
|
matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
|
|
matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
|
|
|
|
matrix->r1c2 = 2.0 * (x1x2 - s0x3);
|
|
matrix->r2c3 = 2.0 * (x2x3 - s0x1);
|
|
matrix->r3c1 = 2.0 * (x1x3 - s0x2);
|
|
|
|
matrix->r2c1 = 2.0 * (x1x2 + s0x3);
|
|
matrix->r3c2 = 2.0 * (x2x3 + s0x1);
|
|
matrix->r1c3 = 2.0 * (x1x3 + s0x2);
|
|
}
|
|
|
|
// ============= Get Reverse Matrix ============= //
|
|
|
|
inline void bgc_versor_get_reverse_matrix_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* matrix)
|
|
{
|
|
const float s0s0 = versor->_s0 * versor->_s0;
|
|
const float x1x1 = versor->_x1 * versor->_x1;
|
|
const float x2x2 = versor->_x2 * versor->_x2;
|
|
const float x3x3 = versor->_x3 * versor->_x3;
|
|
|
|
const float s0x1 = versor->_s0 * versor->_x1;
|
|
const float s0x2 = versor->_s0 * versor->_x2;
|
|
const float s0x3 = versor->_s0 * versor->_x3;
|
|
const float x1x2 = versor->_x1 * versor->_x2;
|
|
const float x1x3 = versor->_x1 * versor->_x3;
|
|
const float x2x3 = versor->_x2 * versor->_x3;
|
|
|
|
matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
|
|
matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
|
|
matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
|
|
|
|
matrix->r1c2 = 2.0f * (x1x2 + s0x3);
|
|
matrix->r2c3 = 2.0f * (x2x3 + s0x1);
|
|
matrix->r3c1 = 2.0f * (x1x3 + s0x2);
|
|
|
|
matrix->r2c1 = 2.0f * (x1x2 - s0x3);
|
|
matrix->r3c2 = 2.0f * (x2x3 - s0x1);
|
|
matrix->r1c3 = 2.0f * (x1x3 - s0x2);
|
|
}
|
|
|
|
inline void bgc_versor_get_reverse_matrix_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* matrix)
|
|
{
|
|
const double s0s0 = versor->_s0 * versor->_s0;
|
|
const double x1x1 = versor->_x1 * versor->_x1;
|
|
const double x2x2 = versor->_x2 * versor->_x2;
|
|
const double x3x3 = versor->_x3 * versor->_x3;
|
|
|
|
const double s0x1 = versor->_s0 * versor->_x1;
|
|
const double s0x2 = versor->_s0 * versor->_x2;
|
|
const double s0x3 = versor->_s0 * versor->_x3;
|
|
const double x1x2 = versor->_x1 * versor->_x2;
|
|
const double x1x3 = versor->_x1 * versor->_x3;
|
|
const double x2x3 = versor->_x2 * versor->_x3;
|
|
|
|
matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
|
|
matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
|
|
matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
|
|
|
|
matrix->r1c2 = 2.0 * (x1x2 + s0x3);
|
|
matrix->r2c3 = 2.0 * (x2x3 + s0x1);
|
|
matrix->r3c1 = 2.0 * (x1x3 + s0x2);
|
|
|
|
matrix->r2c1 = 2.0 * (x1x2 - s0x3);
|
|
matrix->r3c2 = 2.0 * (x2x3 - s0x1);
|
|
matrix->r1c3 = 2.0 * (x1x3 - s0x2);
|
|
}
|
|
|
|
// ============= Get Both Matrixes ============== //
|
|
|
|
inline void bgc_versor_get_both_matrices_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* rotation, BgcMatrix3x3FP32* reverse)
|
|
{
|
|
bgc_versor_get_reverse_matrix_fp32(versor, reverse);
|
|
bgc_matrix3x3_transpose_fp32(reverse, rotation);
|
|
}
|
|
|
|
inline void bgc_versor_get_both_matrices_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* rotation, BgcMatrix3x3FP64* reverse)
|
|
{
|
|
bgc_versor_get_reverse_matrix_fp64(versor, reverse);
|
|
bgc_matrix3x3_transpose_fp64(reverse, rotation);
|
|
}
|
|
|
|
// ================ Turn Vector ================= //
|
|
|
|
inline void bgc_versor_turn_vector_fp32(const BgcVersorFP32* versor, const BgcVector3FP32* vector, BgcVector3FP32* result)
|
|
{
|
|
const float tx1 = 2.0f * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
|
|
const float tx2 = 2.0f * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
|
|
const float tx3 = 2.0f * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);
|
|
|
|
const float x1 = (vector->x1 + tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
|
|
const float x2 = (vector->x2 + tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
|
|
const float x3 = (vector->x3 + tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);
|
|
|
|
result->x1 = x1;
|
|
result->x2 = x2;
|
|
result->x3 = x3;
|
|
}
|
|
|
|
inline void bgc_versor_turn_vector_fp64(const BgcVersorFP64* versor, const BgcVector3FP64* vector, BgcVector3FP64* result)
|
|
{
|
|
const double tx1 = 2.0 * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
|
|
const double tx2 = 2.0 * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
|
|
const double tx3 = 2.0 * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);
|
|
|
|
const double x1 = (vector->x1 + tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
|
|
const double x2 = (vector->x2 + tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
|
|
const double x3 = (vector->x3 + tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);
|
|
|
|
result->x1 = x1;
|
|
result->x2 = x2;
|
|
result->x3 = x3;
|
|
}
|
|
|
|
// ============== Turn Vector Back ============== //
|
|
|
|
inline void bgc_versor_turn_vector_back_fp32(const BgcVersorFP32* versor, const BgcVector3FP32* vector, BgcVector3FP32* result)
|
|
{
|
|
const float tx1 = 2.0f * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
|
|
const float tx2 = 2.0f * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
|
|
const float tx3 = 2.0f * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);
|
|
|
|
const float x1 = (vector->x1 - tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
|
|
const float x2 = (vector->x2 - tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
|
|
const float x3 = (vector->x3 - tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);
|
|
|
|
result->x1 = x1;
|
|
result->x2 = x2;
|
|
result->x3 = x3;
|
|
}
|
|
|
|
inline void bgc_versor_turn_vector_back_fp64(const BgcVersorFP64* versor, const BgcVector3FP64* vector, BgcVector3FP64* result)
|
|
{
|
|
const double tx1 = 2.0 * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
|
|
const double tx2 = 2.0 * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
|
|
const double tx3 = 2.0 * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);
|
|
|
|
const double x1 = (vector->x1 - tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
|
|
const double x2 = (vector->x2 - tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
|
|
const double x3 = (vector->x3 - tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);
|
|
|
|
result->x1 = x1;
|
|
result->x2 = x2;
|
|
result->x3 = x3;
|
|
}
|
|
|
|
// ================== Are Close ================= //
|
|
|
|
inline int bgc_versor_are_close_fp32(const BgcVersorFP32* versor1, const BgcVersorFP32* versor2)
|
|
{
|
|
const float ds0 = versor1->_s0 - versor2->_s0;
|
|
const float dx1 = versor1->_x1 - versor2->_x1;
|
|
const float dx2 = versor1->_x2 - versor2->_x2;
|
|
const float dx3 = versor1->_x3 - versor2->_x3;
|
|
|
|
return (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3) <= BGC_SQUARE_EPSYLON_FP32;
|
|
}
|
|
|
|
inline int bgc_versor_are_close_fp64(const BgcVersorFP64* versor1, const BgcVersorFP64* versor2)
|
|
{
|
|
const double ds0 = versor1->_s0 - versor2->_s0;
|
|
const double dx1 = versor1->_x1 - versor2->_x1;
|
|
const double dx2 = versor1->_x2 - versor2->_x2;
|
|
const double dx3 = versor1->_x3 - versor2->_x3;
|
|
|
|
return (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3) <= BGC_SQUARE_EPSYLON_FP64;
|
|
}
|
|
|
|
#endif
|