711 lines
23 KiB
C
711 lines
23 KiB
C
#ifndef _GEOMETRY_VERSOR_H_
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#define _GEOMETRY_VERSOR_H_
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#include <stdint.h>
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#include "basis.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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// =================== Types ==================== //
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typedef struct {
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const float s0, x1, x2, x3;
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} BgFP32Versor;
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typedef struct {
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const double s0, x1, x2, x3;
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} BgFP64Versor;
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// ================= Dark Twins ================= //
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typedef struct {
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float s0, x1, x2, x3;
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} __BgFP32DarkTwinVersor;
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typedef struct {
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double s0, x1, x2, x3;
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} __BgFP64DarkTwinVersor;
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// ================= Constants ================== //
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extern const BgFP32Versor BG_FP32_IDLE_VERSOR;
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extern const BgFP64Versor BG_FP64_IDLE_VERSOR;
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// =================== Reset ==================== //
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static inline void bg_fp32_versor_reset(BgFP32Versor* versor)
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{
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__BgFP32DarkTwinVersor* twin = (__BgFP32DarkTwinVersor*)versor;
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twin->s0 = 1.0f;
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twin->x1 = 0.0f;
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twin->x2 = 0.0f;
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twin->x3 = 0.0f;
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}
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static inline void bg_fp64_versor_reset(BgFP64Versor* versor)
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{
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__BgFP64DarkTwinVersor* twin = (__BgFP64DarkTwinVersor*)versor;
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twin->s0 = 1.0;
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twin->x1 = 0.0;
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twin->x2 = 0.0;
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twin->x3 = 0.0;
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}
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// ==================== Set ===================== //
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static inline void bg_fp32_versor_set_values(const float s0, const float x1, const float x2, const float x3, BgFP32Versor* versor)
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{
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__BgFP32DarkTwinVersor* twin = (__BgFP32DarkTwinVersor*)versor;
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twin->s0 = s0;
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twin->x1 = x1;
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twin->x2 = x2;
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twin->x3 = x3;
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const float square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
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if (1.0f - BG_FP32_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0f + BG_FP32_TWO_EPSYLON) {
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return;
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}
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if (square_modulus <= BG_FP32_SQUARE_EPSYLON) {
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twin->s0 = 1.0f;
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twin->x1 = 0.0f;
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twin->x2 = 0.0f;
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twin->x3 = 0.0f;
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return;
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}
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const float multiplier = sqrtf(1.0f / square_modulus);
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twin->s0 *= multiplier;
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twin->x1 *= multiplier;
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twin->x2 *= multiplier;
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twin->x3 *= multiplier;
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}
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static inline void bg_fp64_versor_set_values(const double s0, const double x1, const double x2, const double x3, BgFP64Versor* versor)
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{
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__BgFP64DarkTwinVersor* twin = (__BgFP64DarkTwinVersor*)versor;
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twin->s0 = s0;
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twin->x1 = x1;
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twin->x2 = x2;
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twin->x3 = x3;
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const double square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
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if (1.0 - BG_FP64_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0 + BG_FP64_TWO_EPSYLON) {
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return;
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}
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if (square_modulus <= BG_FP64_SQUARE_EPSYLON) {
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twin->s0 = 1.0;
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twin->x1 = 0.0;
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twin->x2 = 0.0;
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twin->x3 = 0.0;
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return;
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}
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const double multiplier = sqrt(1.0 / square_modulus);
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twin->s0 *= multiplier;
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twin->x1 *= multiplier;
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twin->x2 *= multiplier;
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twin->x3 *= multiplier;
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}
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// ==================== Copy ==================== //
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static inline void bg_fp32_versor_copy(const BgFP32Versor* from, BgFP32Versor* to)
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{
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__BgFP32DarkTwinVersor* twin = (__BgFP32DarkTwinVersor*)to;
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twin->s0 = from->s0;
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twin->x1 = from->x1;
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twin->x2 = from->x2;
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twin->x3 = from->x3;
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}
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static inline void bg_fp64_versor_copy(const BgFP64Versor* from, BgFP64Versor* to)
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{
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__BgFP64DarkTwinVersor* twin = (__BgFP64DarkTwinVersor*)to;
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twin->s0 = from->s0;
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twin->x1 = from->x1;
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twin->x2 = from->x2;
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twin->x3 = from->x3;
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}
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// ==================== Swap ==================== //
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static inline void bg_fp32_versor_swap(BgFP32Versor* versor1, BgFP32Versor* 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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__BgFP32DarkTwinVersor* twin1 = (__BgFP32DarkTwinVersor*)versor1;
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twin1->s0 = versor2->s0;
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twin1->x1 = versor2->x1;
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twin1->x2 = versor2->x2;
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twin1->x3 = versor2->x3;
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__BgFP32DarkTwinVersor* twin2 = (__BgFP32DarkTwinVersor*)versor2;
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twin2->s0 = s0;
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twin2->x1 = x1;
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twin2->x2 = x2;
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twin2->x3 = x3;
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}
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static inline void bg_fp64_versor_swap(BgFP64Versor* versor1, BgFP64Versor* 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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__BgFP64DarkTwinVersor* twin1 = (__BgFP64DarkTwinVersor*)versor1;
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twin1->s0 = versor2->s0;
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twin1->x1 = versor2->x1;
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twin1->x2 = versor2->x2;
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twin1->x3 = versor2->x3;
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__BgFP64DarkTwinVersor* twin2 = (__BgFP64DarkTwinVersor*)versor2;
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twin2->s0 = s0;
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twin2->x1 = x1;
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twin2->x2 = x2;
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twin2->x3 = x3;
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}
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// =============== Set Crude Turn =============== //
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void bg_fp32_versor_set_crude_turn(const float x1, const float x2, const float x3, const float angle, const angle_unit_t unit, BgFP32Versor* result);
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void bg_fp64_versor_set_crude_turn(const double x1, const double x2, const double x3, const double angle, const angle_unit_t unit, BgFP64Versor* result);
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// ================== Set Turn ================== //
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static inline void bg_fp32_versor_set_turn(const BgFP32Vector3* axis, const float angle, const angle_unit_t unit, BgFP32Versor* result)
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{
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bg_fp32_versor_set_crude_turn(axis->x1, axis->x2, axis->x3, angle, unit, result);
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}
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static inline void bg_fp64_versor_set_turn(const BgFP32Vector3* axis, const double angle, const angle_unit_t unit, BgFP64Versor* result)
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{
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bg_fp64_versor_set_crude_turn(axis->x1, axis->x2, axis->x3, angle, unit, result);
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}
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// ================ Set Rotation ================ //
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static inline void bg_fp32_versor_set_rotation(const BgFP32Rotation3* rotation, BgFP32Versor* result)
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{
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bg_fp32_versor_set_crude_turn(rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BG_ANGLE_UNIT_RADIANS, result);
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}
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static inline void bg_fp64_versor_set_rotation(const BgFP64Rotation3* rotation, BgFP64Versor* result)
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{
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bg_fp64_versor_set_crude_turn(rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BG_ANGLE_UNIT_RADIANS, result);
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}
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// =============== Square modulus =============== //
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static inline float bg_fp32_versor_get_square_modulus(const BgFP32Versor* versor)
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{
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return (versor->s0 * versor->s0 + versor->x1 * versor->x1) + (versor->x2 * versor->x2 + versor->x3 * versor->x3);
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}
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static inline double bg_fp64_versor_get_square_modulus(const BgFP64Versor* versor)
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{
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return (versor->s0 * versor->s0 + versor->x1 * versor->x1) + (versor->x2 * versor->x2 + versor->x3 * versor->x3);
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}
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// =================== Modulus ================== //
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static inline float bg_fp32_versor_get_modulus(const BgFP32Versor* versor)
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{
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return sqrtf(bg_fp32_versor_get_square_modulus(versor));
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}
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static inline double bg_fp64_versor_get_modulus(const BgFP64Versor* versor)
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{
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return sqrt(bg_fp64_versor_get_square_modulus(versor));
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}
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// ================= Comparison ================= //
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static inline int bg_fp32_versor_is_idle(const BgFP32Versor* versor)
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{
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return 1.0f - BG_FP32_EPSYLON <= versor->s0 || versor->s0 <= -(1.0 - BG_FP32_EPSYLON);
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}
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static inline int bg_fp64_versor_is_idle(const BgFP64Versor* versor)
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{
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return 1.0 - BG_FP64_EPSYLON <= versor->s0 || versor->s0 <= -(1.0 - BG_FP64_EPSYLON);
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}
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// ============= Copy to twin type ============== //
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static inline void bg_fp32_versor_set_from_fp64(const BgFP64Versor* versor, BgFP32Versor* result)
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{
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bg_fp32_versor_set_values(
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(float) versor->s0,
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(float) versor->x1,
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(float) versor->x2,
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(float) versor->x3,
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result
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);
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}
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static inline void bg_fp64_versor_set_from_fp32(const BgFP32Versor* versor, BgFP64Versor* result)
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{
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bg_fp64_versor_set_values(
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versor->s0,
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versor->x1,
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versor->x2,
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versor->x3,
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result
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);
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}
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// ================== Shorten =================== //
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static inline void bg_fp32_versor_shorten(BgFP32Versor* versor)
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{
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if (versor->s0 >= 0.0f) {
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return;
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}
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__BgFP32DarkTwinVersor* twin = (__BgFP32DarkTwinVersor*)versor;
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twin->s0 = -versor->s0;
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twin->x1 = -versor->x1;
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twin->x2 = -versor->x2;
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twin->x3 = -versor->x3;
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}
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static inline void bg_fp64_versor_shorten(BgFP64Versor* versor)
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{
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if (versor->s0 >= 0.0f) {
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return;
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}
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__BgFP64DarkTwinVersor* twin = (__BgFP64DarkTwinVersor*)versor;
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twin->s0 = -versor->s0;
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twin->x1 = -versor->x1;
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twin->x2 = -versor->x2;
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twin->x3 = -versor->x3;
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}
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// ================== Shorten =================== //
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static inline void bg_fp32_versor_set_shortened(const BgFP32Versor* versor, BgFP32Versor* shortened)
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{
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__BgFP32DarkTwinVersor* twin = (__BgFP32DarkTwinVersor*)shortened;
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if (versor->s0 >= 0.0f) {
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twin->x1 = versor->s0;
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twin->x1 = versor->x1;
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twin->x2 = versor->x2;
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twin->x3 = versor->x3;
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return;
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}
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twin->x1 = -versor->s0;
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twin->x1 = -versor->x1;
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twin->x2 = -versor->x2;
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twin->x3 = -versor->x3;
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}
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static inline void bg_fp64_versor_set_shortened(const BgFP64Versor* versor, BgFP64Versor* shortened)
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{
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__BgFP64DarkTwinVersor* twin = (__BgFP64DarkTwinVersor*)shortened;
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if (versor->s0 >= 0.0) {
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twin->x1 = versor->s0;
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twin->x1 = versor->x1;
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twin->x2 = versor->x2;
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twin->x3 = versor->x3;
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return;
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}
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twin->x1 = -versor->s0;
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twin->x1 = -versor->x1;
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twin->x2 = -versor->x2;
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twin->x3 = -versor->x3;
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}
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// ================= Inversion ================== //
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static inline void bg_fp32_versor_invert(BgFP32Versor* versor)
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{
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__BgFP32DarkTwinVersor* twin = (__BgFP32DarkTwinVersor*)versor;
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twin->x1 = -versor->x1;
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twin->x2 = -versor->x2;
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twin->x3 = -versor->x3;
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}
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static inline void bg_fp64_versor_invert(BgFP64Versor* versor)
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{
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__BgFP64DarkTwinVersor* twin = (__BgFP64DarkTwinVersor*)versor;
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twin->x1 = -versor->x1;
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twin->x2 = -versor->x2;
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twin->x3 = -versor->x3;
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}
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// ================ Set Inverted ================ //
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static inline void bg_fp32_versor_set_inverted(const BgFP32Versor* versor, BgFP32Versor* to)
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{
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__BgFP32DarkTwinVersor* twin = (__BgFP32DarkTwinVersor*)to;
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twin->s0 = versor->s0;
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twin->x1 = -versor->x1;
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twin->x2 = -versor->x2;
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twin->x3 = -versor->x3;
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}
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static inline void bg_fp64_versor_set_inverted(const BgFP64Versor* versor, BgFP64Versor* to)
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{
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__BgFP64DarkTwinVersor* twin = (__BgFP64DarkTwinVersor*)to;
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twin->s0 = versor->s0;
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twin->x1 = -versor->x1;
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twin->x2 = -versor->x2;
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twin->x3 = -versor->x3;
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}
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// ================ Set Inverted ================ //
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static inline void bg_fp32_versor_set_inverted_fp64(const BgFP64Versor* versor, BgFP32Versor* to)
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{
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bg_fp32_versor_set_values(
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(float) versor->s0,
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(float) -versor->x1,
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(float) -versor->x2,
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(float) -versor->x3,
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to
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);
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}
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static inline void bg_fp64_versor_set_inverted_fp32(const BgFP32Versor* versor, BgFP64Versor* to)
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{
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bg_fp64_versor_set_values(
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versor->s0,
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-versor->x1,
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-versor->x2,
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-versor->x3,
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to
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);
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}
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// ================ Combination ================= //
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static inline void bg_fp32_versor_combine(const BgFP32Versor* second, const BgFP32Versor* first, BgFP32Versor* 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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const float square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
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__BgFP32DarkTwinVersor* twin = (__BgFP32DarkTwinVersor*)result;
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twin->s0 = s0;
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twin->x1 = x1;
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twin->x2 = x2;
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twin->x3 = x3;
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if (1.0f - BG_FP32_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0f + BG_FP32_TWO_EPSYLON) {
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return;
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}
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const float multiplier = sqrtf(1.0f / square_modulus);
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twin->s0 *= multiplier;
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twin->x1 *= multiplier;
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twin->x2 *= multiplier;
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twin->x3 *= multiplier;
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}
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static inline void bg_fp64_versor_combine(const BgFP64Versor* second, const BgFP64Versor* first, BgFP64Versor* 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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const double square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
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__BgFP64DarkTwinVersor* twin = (__BgFP64DarkTwinVersor*)result;
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|
|
|
twin->s0 = s0;
|
|
twin->x1 = x1;
|
|
twin->x2 = x2;
|
|
twin->x3 = x3;
|
|
|
|
if (1.0 - BG_FP64_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0 + BG_FP64_TWO_EPSYLON) {
|
|
return;
|
|
}
|
|
|
|
const double multiplier = sqrt(1.0 / square_modulus);
|
|
|
|
twin->s0 *= multiplier;
|
|
twin->x1 *= multiplier;
|
|
twin->x2 *= multiplier;
|
|
twin->x3 *= multiplier;
|
|
}
|
|
|
|
// ================= Exclusion ================== //
|
|
|
|
static inline void bg_fp32_versor_exclude(const BgFP32Versor* basic, const BgFP32Versor* exclusion, BgFP32Versor* result)
|
|
{
|
|
const float s0 = (basic->s0 * exclusion->s0 + basic->x1 * exclusion->x1) + (basic->x2 * exclusion->x2 + basic->x3 * exclusion->x3);
|
|
const float x1 = (basic->x1 * exclusion->s0 - basic->s0 * exclusion->x1) + (basic->x3 * exclusion->x2 - basic->x2 * exclusion->x3);
|
|
const float x2 = (basic->x2 * exclusion->s0 - basic->s0 * exclusion->x2) + (basic->x1 * exclusion->x3 - basic->x3 * exclusion->x1);
|
|
const float x3 = (basic->x3 * exclusion->s0 - basic->s0 * exclusion->x3) + (basic->x2 * exclusion->x1 - basic->x1 * exclusion->x2);
|
|
|
|
const float square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
|
|
|
|
__BgFP32DarkTwinVersor* twin = (__BgFP32DarkTwinVersor*)result;
|
|
|
|
twin->s0 = s0;
|
|
twin->x1 = x1;
|
|
twin->x2 = x2;
|
|
twin->x3 = x3;
|
|
|
|
if (1.0f - BG_FP32_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0f + BG_FP32_TWO_EPSYLON) {
|
|
return;
|
|
}
|
|
|
|
const float multiplier = sqrtf(1.0f / square_modulus);
|
|
|
|
twin->s0 *= multiplier;
|
|
twin->x1 *= multiplier;
|
|
twin->x2 *= multiplier;
|
|
twin->x3 *= multiplier;
|
|
}
|
|
|
|
static inline void bg_fp64_versor_exclude(const BgFP64Versor* basic, const BgFP64Versor* exclusion, BgFP64Versor* result)
|
|
{
|
|
const double s0 = (basic->s0 * exclusion->s0 + basic->x1 * exclusion->x1) + (basic->x2 * exclusion->x2 + basic->x3 * exclusion->x3);
|
|
const double x1 = (basic->x1 * exclusion->s0 - basic->s0 * exclusion->x1) + (basic->x3 * exclusion->x2 - basic->x2 * exclusion->x3);
|
|
const double x2 = (basic->x2 * exclusion->s0 - basic->s0 * exclusion->x2) + (basic->x1 * exclusion->x3 - basic->x3 * exclusion->x1);
|
|
const double x3 = (basic->x3 * exclusion->s0 - basic->s0 * exclusion->x3) + (basic->x2 * exclusion->x1 - basic->x1 * exclusion->x2);
|
|
|
|
const double square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);
|
|
|
|
__BgFP64DarkTwinVersor* twin = (__BgFP64DarkTwinVersor*)result;
|
|
|
|
twin->s0 = s0;
|
|
twin->x1 = x1;
|
|
twin->x2 = x2;
|
|
twin->x3 = x3;
|
|
|
|
if (1.0 - BG_FP64_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0 + BG_FP64_TWO_EPSYLON) {
|
|
return;
|
|
}
|
|
|
|
const double multiplier = sqrt(1.0 / square_modulus);
|
|
|
|
twin->s0 *= multiplier;
|
|
twin->x1 *= multiplier;
|
|
twin->x2 *= multiplier;
|
|
twin->x3 *= multiplier;
|
|
}
|
|
|
|
// ================= Rotation3 ================== //
|
|
|
|
void bg_fp32_versor_get_rotation(const BgFP32Versor* versor, BgFP32Rotation3* result);
|
|
|
|
void bg_fp64_versor_get_rotation(const BgFP64Versor* versor, BgFP64Rotation3* result);
|
|
|
|
// =========== Make Rotation Matrix3x3 ========== //
|
|
|
|
static inline void bg_fp32_versor_make_rotation_matrix(const BgFP32Versor* versor, BgFP32Matrix3x3* 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 = 2.0f * versor->s0 * versor->x1;
|
|
const float s0x2 = 2.0f * versor->s0 * versor->x2;
|
|
const float s0x3 = 2.0f * versor->s0 * versor->x3;
|
|
|
|
const float x1x2 = 2.0f * versor->x1 * versor->x2;
|
|
const float x1x3 = 2.0f * versor->x1 * versor->x3;
|
|
const float x2x3 = 2.0f * versor->x2 * versor->x3;
|
|
|
|
matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
|
|
matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
|
|
matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
|
|
|
|
matrix->r1c2 = x1x2 - s0x3;
|
|
matrix->r2c3 = x2x3 - s0x1;
|
|
matrix->r3c1 = x1x3 - s0x2;
|
|
|
|
matrix->r2c1 = x1x2 + s0x3;
|
|
matrix->r3c2 = x2x3 + s0x1;
|
|
matrix->r1c3 = x1x3 + s0x2;
|
|
}
|
|
|
|
static inline void bg_fp64_versor_make_rotation_matrix(const BgFP64Versor* versor, BgFP64Matrix3x3* 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 = 2.0 * versor->s0 * versor->x1;
|
|
const double s0x2 = 2.0 * versor->s0 * versor->x2;
|
|
const double s0x3 = 2.0 * versor->s0 * versor->x3;
|
|
|
|
const double x1x2 = 2.0 * versor->x1 * versor->x2;
|
|
const double x1x3 = 2.0 * versor->x1 * versor->x3;
|
|
const double x2x3 = 2.0 * versor->x2 * versor->x3;
|
|
|
|
matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
|
|
matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
|
|
matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
|
|
|
|
matrix->r1c2 = x1x2 - s0x3;
|
|
matrix->r2c3 = x2x3 - s0x1;
|
|
matrix->r3c1 = x1x3 - s0x2;
|
|
|
|
matrix->r2c1 = x1x2 + s0x3;
|
|
matrix->r3c2 = x2x3 + s0x1;
|
|
matrix->r1c3 = x1x3 + s0x2;
|
|
}
|
|
|
|
// =========== Make Reverse Matrix3x3 =========== //
|
|
|
|
static inline void bg_fp32_versor_make_reverse_matrix(const BgFP32Versor* versor, BgFP32Matrix3x3* 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 = 2.0f * versor->s0 * versor->x1;
|
|
const float s0x2 = 2.0f * versor->s0 * versor->x2;
|
|
const float s0x3 = 2.0f * versor->s0 * versor->x3;
|
|
|
|
const float x1x2 = 2.0f * versor->x1 * versor->x2;
|
|
const float x1x3 = 2.0f * versor->x1 * versor->x3;
|
|
const float x2x3 = 2.0f * versor->x2 * versor->x3;
|
|
|
|
matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
|
|
matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
|
|
matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
|
|
|
|
matrix->r1c2 = x1x2 + s0x3;
|
|
matrix->r2c3 = x2x3 + s0x1;
|
|
matrix->r3c1 = x1x3 + s0x2;
|
|
|
|
matrix->r2c1 = x1x2 - s0x3;
|
|
matrix->r3c2 = x2x3 - s0x1;
|
|
matrix->r1c3 = x1x3 - s0x2;
|
|
}
|
|
|
|
static inline void bg_fp64_versor_make_reverse_matrix(const BgFP64Versor* versor, BgFP64Matrix3x3* 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 = 2.0 * versor->s0 * versor->x1;
|
|
const double s0x2 = 2.0 * versor->s0 * versor->x2;
|
|
const double s0x3 = 2.0 * versor->s0 * versor->x3;
|
|
|
|
const double x1x2 = 2.0 * versor->x1 * versor->x2;
|
|
const double x1x3 = 2.0 * versor->x1 * versor->x3;
|
|
const double x2x3 = 2.0 * versor->x2 * versor->x3;
|
|
|
|
matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
|
|
matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
|
|
matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);
|
|
|
|
matrix->r1c2 = x1x2 + s0x3;
|
|
matrix->r2c3 = x2x3 + s0x1;
|
|
matrix->r3c1 = x1x3 + s0x2;
|
|
|
|
matrix->r2c1 = x1x2 - s0x3;
|
|
matrix->r3c2 = x2x3 - s0x1;
|
|
matrix->r1c3 = x1x3 - s0x2;
|
|
}
|
|
|
|
// ================ Turn Vector ================= //
|
|
|
|
static inline void bg_fp32_versor_turn(const BgFP32Versor* versor, const BgFP32Vector3* vector, BgFP32Vector3* 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;
|
|
}
|
|
|
|
static inline void bg_fp64_versor_turn(const BgFP64Versor* versor, const BgFP64Vector3* vector, BgFP64Vector3* 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 ============== //
|
|
|
|
static inline void bg_fp32_versor_turn_back(const BgFP32Versor* versor, const BgFP32Vector3* vector, BgFP32Vector3* 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;
|
|
}
|
|
|
|
static inline void bg_fp64_versor_turn_back(const BgFP64Versor* versor, const BgFP64Vector3* vector, BgFP64Vector3* 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;
|
|
}
|
|
|
|
#endif
|