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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} BGC_FP32_Versor;
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typedef struct {
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double _s0, _x1, _x2, _x3;
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} BGC_FP64_Versor;
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// ================= Constants ================== //
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extern const BGC_FP32_Versor BGC_FP32_IDLE_VERSOR;
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extern const BGC_FP64_Versor BGC_FP64_IDLE_VERSOR;
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// =================== Reset ==================== //
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inline void bgc_fp32_versor_reset(BGC_FP32_Versor* 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_fp64_versor_reset(BGC_FP64_Versor* 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_fp32_versor_normalize(BGC_FP32_Versor* twin);
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void _bgc_fp64_versor_normalize(BGC_FP64_Versor* twin);
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inline void bgc_fp32_versor_make(BGC_FP32_Versor* versor, const float s0, const float x1, const float x2, const float x3)
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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_fp32_is_square_unit(square_modulus)) {
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_bgc_fp32_versor_normalize(versor);
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}
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}
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inline void bgc_fp64_versor_make(BGC_FP64_Versor* versor, const double s0, const double x1, const double x2, const double x3)
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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_fp64_is_square_unit(square_modulus)) {
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_bgc_fp64_versor_normalize(versor);
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}
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}
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// ================== Set Turn ================== //
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void bgc_fp32_versor_make_for_turn(BGC_FP32_Versor* versor, const float x1, const float x2, const float x3, const float angle, const int unit);
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void bgc_fp64_versor_make_for_turn(BGC_FP64_Versor* versor, const double x1, const double x2, const double x3, const double angle, const int unit);
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// ================ Set Rotation ================ //
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inline void bgc_fp32_versor_make_for_rotation(BGC_FP32_Versor* versor, const BGC_FP32_Rotation3* rotation)
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{
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bgc_fp32_versor_make_for_turn(versor, rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BGC_ANGLE_UNIT_RADIANS);
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}
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inline void bgc_fp64_versor_make_for_rotation(BGC_FP64_Versor* versor, const BGC_FP64_Rotation3* rotation)
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{
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bgc_fp64_versor_make_for_turn(versor, rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BGC_ANGLE_UNIT_RADIANS);
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}
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// ========= Make Direction Difference ========== //
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int bgc_fp32_versor_make_direction_difference(BGC_FP32_Versor* difference, const BGC_FP32_Vector3* start, const BGC_FP32_Vector3* end);
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int bgc_fp64_versor_make_direction_difference(BGC_FP64_Versor* difference, const BGC_FP64_Vector3* start, const BGC_FP64_Vector3* end);
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// =============== Set Directions =============== //
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int bgc_fp32_versor_make_basis_difference(
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BGC_FP32_Versor* versor,
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const BGC_FP32_Vector3* initial_primary_direction,
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const BGC_FP32_Vector3* initial_auxiliary_direction,
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const BGC_FP32_Vector3* final_primary_direction,
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const BGC_FP32_Vector3* final_auxiliary_direction
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);
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int bgc_fp64_versor_make_basis_difference(
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BGC_FP64_Versor* versor,
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const BGC_FP64_Vector3* initial_primary_direction,
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const BGC_FP64_Vector3* initial_auxiliary_direction,
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const BGC_FP64_Vector3* final_primary_direction,
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const BGC_FP64_Vector3* final_auxiliary_direction
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);
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// ==================== Copy ==================== //
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inline void bgc_fp32_versor_copy(BGC_FP32_Versor* destination, const BGC_FP32_Versor* source)
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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_fp64_versor_copy(BGC_FP64_Versor* destination, const BGC_FP64_Versor* source)
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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_fp32_versor_swap(BGC_FP32_Versor* versor1, BGC_FP32_Versor* 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_fp64_versor_swap(BGC_FP64_Versor* versor1, BGC_FP64_Versor* 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_fp32_versor_is_idle(const BGC_FP32_Versor* versor)
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{
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return versor->_x1 * versor->_x1 + versor->_x2 * versor->_x2 + versor->_x3 * versor->_x3 <= BGC_FP32_SQUARE_EPSILON;
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}
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inline int bgc_fp64_versor_is_idle(const BGC_FP64_Versor* versor)
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{
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return versor->_x1 * versor->_x1 + versor->_x2 * versor->_x2 + versor->_x3 * versor->_x3 <= BGC_FP64_SQUARE_EPSILON;
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}
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// ================== Convert =================== //
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inline void bgc_fp32_versor_convert_to_fp64(BGC_FP64_Versor* destination, const BGC_FP32_Versor* source)
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{
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bgc_fp64_versor_make(
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destination,
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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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);
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}
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inline void bgc_fp64_versor_convert_to_fp32(BGC_FP32_Versor* destination, const BGC_FP64_Versor* source)
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{
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bgc_fp32_versor_make(
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destination,
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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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);
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}
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// ================== Shorten =================== //
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inline void bgc_fp32_versor_shorten(BGC_FP32_Versor* 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_fp64_versor_shorten(BGC_FP64_Versor* 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_fp32_versor_get_shortened(BGC_FP32_Versor* shortened, const BGC_FP32_Versor* versor)
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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_fp64_versor_get_shortened(BGC_FP64_Versor* shortened, const BGC_FP64_Versor* versor)
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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_fp32_versor_alternate(BGC_FP32_Versor* 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_fp64_versor_alternate(BGC_FP64_Versor* 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_fp32_versor_get_alternative(BGC_FP32_Versor* alternative, const BGC_FP32_Versor* versor)
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{
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alternative->_s0 = -versor->_s0;
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alternative->_x1 = -versor->_x1;
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alternative->_x2 = -versor->_x2;
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alternative->_x3 = -versor->_x3;
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}
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inline void bgc_fp64_versor_get_alternative(BGC_FP64_Versor* alternative, const BGC_FP64_Versor* versor)
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{
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alternative->_s0 = -versor->_s0;
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alternative->_x1 = -versor->_x1;
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alternative->_x2 = -versor->_x2;
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alternative->_x3 = -versor->_x3;
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}
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// =================== Invert =================== //
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inline void bgc_fp32_versor_revert(BGC_FP32_Versor* 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_fp64_versor_revert(BGC_FP64_Versor* 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_fp32_versor_get_reverse(BGC_FP32_Versor* inverse, const BGC_FP32_Versor* versor)
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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_fp64_versor_get_reverse(BGC_FP64_Versor* inverse, const BGC_FP64_Versor* versor)
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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_fp32_versor_get_exponation(BGC_FP32_Versor* power, const BGC_FP32_Versor* base, const float exponent);
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void bgc_fp64_versor_get_exponation(BGC_FP64_Versor* power, const BGC_FP64_Versor* base, const double exponent);
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// ================ Combination ================= //
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inline void bgc_fp32_versor_combine(BGC_FP32_Versor* combination, const BGC_FP32_Versor* first, const BGC_FP32_Versor* second)
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{
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bgc_fp32_versor_make(
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combination,
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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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);
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}
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inline void bgc_fp64_versor_combine(BGC_FP64_Versor* combination, const BGC_FP64_Versor* first, const BGC_FP64_Versor* second)
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{
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bgc_fp64_versor_make(
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combination,
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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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);
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}
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// ============ Combination of three ============ //
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inline void bgc_fp32_versor_combine3(BGC_FP32_Versor* combination, const BGC_FP32_Versor* first, const BGC_FP32_Versor* second, const BGC_FP32_Versor* third)
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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_fp32_versor_make(
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combination,
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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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);
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}
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inline void bgc_fp64_versor_combine3(BGC_FP64_Versor* combination, const BGC_FP64_Versor* first, const BGC_FP64_Versor* second, const BGC_FP64_Versor* third)
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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_fp64_versor_make(
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combination,
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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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);
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}
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// ================= Exclusion ================== //
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inline void bgc_fp32_versor_exclude(BGC_FP32_Versor* difference, const BGC_FP32_Versor* base, const BGC_FP32_Versor* excludant)
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{
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bgc_fp32_versor_make(
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difference,
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(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)
|
|
);
|
|
}
|
|
|
|
inline void bgc_fp64_versor_exclude(BGC_FP64_Versor* difference, const BGC_FP64_Versor* base, const BGC_FP64_Versor* excludant)
|
|
{
|
|
bgc_fp64_versor_make(
|
|
difference,
|
|
(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)
|
|
);
|
|
}
|
|
|
|
// ============ Sphere Interpolation ============ //
|
|
|
|
void bgc_fp32_versor_spherically_interpolate(BGC_FP32_Versor* interpolation, const BGC_FP32_Versor* start, const BGC_FP32_Versor* end, const float phase);
|
|
|
|
void bgc_fp64_versor_spherically_interpolate(BGC_FP64_Versor* interpolation, const BGC_FP64_Versor* start, const BGC_FP64_Versor* end, const double phase);
|
|
|
|
// ================ Get Rotation ================ //
|
|
|
|
void bgc_fp32_versor_get_rotation(BGC_FP32_Rotation3* rotation, const BGC_FP32_Versor* versor);
|
|
|
|
void bgc_fp64_versor_get_rotation(BGC_FP64_Rotation3* rotation, const BGC_FP64_Versor* versor);
|
|
|
|
// ============ Get Rotation Matrix ============= //
|
|
|
|
inline void bgc_fp32_versor_get_rotation_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_Versor* versor)
|
|
{
|
|
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_fp64_versor_get_rotation_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_Versor* versor)
|
|
{
|
|
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_fp32_versor_get_reverse_matrix(BGC_FP32_Matrix3x3* matrix, const BGC_FP32_Versor* versor)
|
|
{
|
|
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_fp64_versor_get_reverse_matrix(BGC_FP64_Matrix3x3* matrix, const BGC_FP64_Versor* versor)
|
|
{
|
|
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_fp32_versor_get_both_matrices(BGC_FP32_Matrix3x3* rotation, BGC_FP32_Matrix3x3* reverse, const BGC_FP32_Versor* versor)
|
|
{
|
|
bgc_fp32_versor_get_reverse_matrix(reverse, versor);
|
|
bgc_fp32_matrix3x3_get_transposed(rotation, reverse);
|
|
}
|
|
|
|
inline void bgc_fp64_versor_get_both_matrices(BGC_FP64_Matrix3x3* rotation, BGC_FP64_Matrix3x3* reverse, const BGC_FP64_Versor* versor)
|
|
{
|
|
bgc_fp64_versor_get_reverse_matrix(reverse, versor);
|
|
bgc_fp64_matrix3x3_get_transposed(rotation, reverse);
|
|
}
|
|
|
|
// ================ Turn Vector ================= //
|
|
|
|
inline void bgc_fp32_versor_turn_vector(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Versor* versor, const BGC_FP32_Vector3* vector)
|
|
{
|
|
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);
|
|
|
|
turned_vector->x1 = x1;
|
|
turned_vector->x2 = x2;
|
|
turned_vector->x3 = x3;
|
|
}
|
|
|
|
inline void bgc_fp64_versor_turn_vector(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Versor* versor, const BGC_FP64_Vector3* vector)
|
|
{
|
|
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);
|
|
|
|
turned_vector->x1 = x1;
|
|
turned_vector->x2 = x2;
|
|
turned_vector->x3 = x3;
|
|
}
|
|
|
|
// ============== Turn Vector Back ============== //
|
|
|
|
inline void bgc_fp32_versor_turn_vector_back(BGC_FP32_Vector3* turned_vector, const BGC_FP32_Versor* versor, const BGC_FP32_Vector3* vector)
|
|
{
|
|
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);
|
|
|
|
turned_vector->x1 = x1;
|
|
turned_vector->x2 = x2;
|
|
turned_vector->x3 = x3;
|
|
}
|
|
|
|
inline void bgc_fp64_versor_turn_vector_back(BGC_FP64_Vector3* turned_vector, const BGC_FP64_Versor* versor, const BGC_FP64_Vector3* vector)
|
|
{
|
|
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);
|
|
|
|
turned_vector->x1 = x1;
|
|
turned_vector->x2 = x2;
|
|
turned_vector->x3 = x3;
|
|
}
|
|
|
|
// ================== Are Close ================= //
|
|
|
|
inline int bgc_fp32_versor_are_close(const BGC_FP32_Versor* versor1, const BGC_FP32_Versor* 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_FP32_SQUARE_EPSILON;
|
|
}
|
|
|
|
inline int bgc_fp64_versor_are_close(const BGC_FP64_Versor* versor1, const BGC_FP64_Versor* 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_FP64_SQUARE_EPSILON;
|
|
}
|
|
|
|
#endif
|