755 lines
26 KiB
C
755 lines
26 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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// =================== Types ==================== //
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typedef struct {
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const float s0, x1, x2, x3;
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} bgc_versor_fp32_t;
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typedef struct {
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const double s0, x1, x2, x3;
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} bgc_versor_fp64_t;
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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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} _bgc_dark_twin_versor_fp32_t;
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typedef struct {
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double s0, x1, x2, x3;
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} _bgc_dark_twin_versor_fp64_t;
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// ================= Constants ================== //
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extern const bgc_versor_fp32_t BGC_IDLE_VERSOR_FP32;
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extern const bgc_versor_fp64_t BGC_IDLE_VERSOR_FP64;
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// =================== Reset ==================== //
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inline void bgc_versor_reset_fp32(bgc_versor_fp32_t* versor)
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{
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_bgc_dark_twin_versor_fp32_t* twin = (_bgc_dark_twin_versor_fp32_t*)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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inline void bgc_versor_reset_fp64(bgc_versor_fp64_t* versor)
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{
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_bgc_dark_twin_versor_fp64_t* twin = (_bgc_dark_twin_versor_fp64_t*)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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inline void bgc_versor_set_values_fp32(const float s0, const float x1, const float x2, const float x3, bgc_versor_fp32_t* versor)
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{
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_bgc_dark_twin_versor_fp32_t* twin = (_bgc_dark_twin_versor_fp32_t*)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 - BGC_TWO_EPSYLON_FP32 <= square_modulus && square_modulus <= 1.0f + BGC_TWO_EPSYLON_FP32) {
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return;
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}
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if (square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
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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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inline void bgc_versor_set_values_fp64(const double s0, const double x1, const double x2, const double x3, bgc_versor_fp64_t* versor)
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{
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_bgc_dark_twin_versor_fp64_t* twin = (_bgc_dark_twin_versor_fp64_t*)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 - BGC_TWO_EPSYLON_FP64 <= square_modulus && square_modulus <= 1.0 + BGC_TWO_EPSYLON_FP64) {
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return;
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}
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if (square_modulus <= BGC_SQUARE_EPSYLON_FP64) {
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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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inline void bgc_versor_copy_fp32(const bgc_versor_fp32_t* from, bgc_versor_fp32_t* to)
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{
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_bgc_dark_twin_versor_fp32_t* twin = (_bgc_dark_twin_versor_fp32_t*)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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inline void bgc_versor_copy_fp64(const bgc_versor_fp64_t* from, bgc_versor_fp64_t* to)
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{
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_bgc_dark_twin_versor_fp64_t* twin = (_bgc_dark_twin_versor_fp64_t*)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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inline void bgc_versor_swap_fp32(bgc_versor_fp32_t* versor1, bgc_versor_fp32_t* 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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_bgc_dark_twin_versor_fp32_t* twin1 = (_bgc_dark_twin_versor_fp32_t*)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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_bgc_dark_twin_versor_fp32_t* twin2 = (_bgc_dark_twin_versor_fp32_t*)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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inline void bgc_versor_swap_fp64(bgc_versor_fp64_t* versor1, bgc_versor_fp64_t* 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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_bgc_dark_twin_versor_fp64_t* twin1 = (_bgc_dark_twin_versor_fp64_t*)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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_bgc_dark_twin_versor_fp64_t* twin2 = (_bgc_dark_twin_versor_fp64_t*)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 bgc_versor_set_crude_turn_fp32(const float x1, const float x2, const float x3, const float angle, const bgc_angle_unit_t unit, bgc_versor_fp32_t* result);
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void bgc_versor_set_crude_turn_fp64(const double x1, const double x2, const double x3, const double angle, const bgc_angle_unit_t unit, bgc_versor_fp64_t* result);
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// ================== Set Turn ================== //
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inline void bgc_versor_set_turn_fp32(const bgc_vector3_fp32_t* axis, const float angle, const bgc_angle_unit_t unit, bgc_versor_fp32_t* result)
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{
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bgc_versor_set_crude_turn_fp32(axis->x1, axis->x2, axis->x3, angle, unit, result);
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}
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inline void bgc_versor_set_turn_fp64(const bgc_vector3_fp32_t* axis, const double angle, const bgc_angle_unit_t unit, bgc_versor_fp64_t* result)
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{
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bgc_versor_set_crude_turn_fp64(axis->x1, axis->x2, axis->x3, angle, unit, result);
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}
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// ================ Set Rotation ================ //
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inline void bgc_versor_set_rotation_fp32(const bgc_rotation3_fp32_t* rotation, bgc_versor_fp32_t* result)
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{
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bgc_versor_set_crude_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 bgc_rotation3_fp64_t* rotation, bgc_versor_fp64_t* result)
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{
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bgc_versor_set_crude_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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// ================= Comparison ================= //
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inline int bgc_versor_is_idle_fp32(const bgc_versor_fp32_t* versor)
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{
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return 1.0f - BGC_EPSYLON_FP32 <= versor->s0 || versor->s0 <= -(1.0 - BGC_EPSYLON_FP32);
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}
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inline int bgc_versor_is_idle_fp64(const bgc_versor_fp64_t* versor)
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{
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return 1.0 - BGC_EPSYLON_FP64 <= versor->s0 || versor->s0 <= -(1.0 - BGC_EPSYLON_FP64);
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}
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// ============= Copy to twin type ============== //
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inline void bgc_versor_convert_fp64_to_fp32(const bgc_versor_fp64_t* versor, bgc_versor_fp32_t* result)
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{
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bgc_versor_set_values_fp32(
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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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inline void bgc_versor_convert_fp32_to_fp64(const bgc_versor_fp32_t* versor, bgc_versor_fp64_t* result)
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{
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bgc_versor_set_values_fp64(
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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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inline void bgc_versor_shorten_fp32(bgc_versor_fp32_t* 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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_bgc_dark_twin_versor_fp32_t* twin = (_bgc_dark_twin_versor_fp32_t*)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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inline void bgc_versor_shorten_fp64(bgc_versor_fp64_t* 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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_bgc_dark_twin_versor_fp64_t* twin = (_bgc_dark_twin_versor_fp64_t*)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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inline void bgc_versor_set_shortened_fp32(const bgc_versor_fp32_t* versor, bgc_versor_fp32_t* shortened)
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{
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_bgc_dark_twin_versor_fp32_t* twin = (_bgc_dark_twin_versor_fp32_t*)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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inline void bgc_versor_set_shortened_fp64(const bgc_versor_fp64_t* versor, bgc_versor_fp64_t* shortened)
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{
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_bgc_dark_twin_versor_fp64_t* twin = (_bgc_dark_twin_versor_fp64_t*)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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inline void bgc_versor_invert_fp32(bgc_versor_fp32_t* versor)
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{
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_bgc_dark_twin_versor_fp32_t* twin = (_bgc_dark_twin_versor_fp32_t*)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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inline void bgc_versor_invert_fp64(bgc_versor_fp64_t* versor)
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{
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_bgc_dark_twin_versor_fp64_t* twin = (_bgc_dark_twin_versor_fp64_t*)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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inline void bgc_versor_set_inverted_fp32(const bgc_versor_fp32_t* versor, bgc_versor_fp32_t* to)
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{
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_bgc_dark_twin_versor_fp32_t* twin = (_bgc_dark_twin_versor_fp32_t*)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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inline void bgc_versor_set_inverted_fp64(const bgc_versor_fp64_t* versor, bgc_versor_fp64_t* to)
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{
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_bgc_dark_twin_versor_fp64_t* twin = (_bgc_dark_twin_versor_fp64_t*)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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inline void bgc_versor_set_inverted_fp64_to_fp32(const bgc_versor_fp64_t* versor, bgc_versor_fp32_t* to)
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{
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bgc_versor_set_values_fp32(
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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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inline void bgc_versor_set_inverted_fp32_to_fp64(const bgc_versor_fp32_t* versor, bgc_versor_fp64_t* to)
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{
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bgc_versor_set_values_fp64(
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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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inline void bgc_versor_combine_fp32(const bgc_versor_fp32_t* second, const bgc_versor_fp32_t* first, bgc_versor_fp32_t* 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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_bgc_dark_twin_versor_fp32_t* twin = (_bgc_dark_twin_versor_fp32_t*)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 - BGC_TWO_EPSYLON_FP32 <= square_modulus && square_modulus <= 1.0f + BGC_TWO_EPSYLON_FP32) {
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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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inline void bgc_versor_combine_fp64(const bgc_versor_fp64_t* second, const bgc_versor_fp64_t* first, bgc_versor_fp64_t* 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);
|
|
|
|
_bgc_dark_twin_versor_fp64_t* twin = (_bgc_dark_twin_versor_fp64_t*)result;
|
|
|
|
twin->s0 = s0;
|
|
twin->x1 = x1;
|
|
twin->x2 = x2;
|
|
twin->x3 = x3;
|
|
|
|
if (1.0 - BGC_TWO_EPSYLON_FP64 <= square_modulus && square_modulus <= 1.0 + BGC_TWO_EPSYLON_FP64) {
|
|
return;
|
|
}
|
|
|
|
const double multiplier = sqrt(1.0 / square_modulus);
|
|
|
|
twin->s0 *= multiplier;
|
|
twin->x1 *= multiplier;
|
|
twin->x2 *= multiplier;
|
|
twin->x3 *= multiplier;
|
|
}
|
|
|
|
// ============ Combination of three ============ //
|
|
|
|
inline void bgc_versor_combine3_fp32(const bgc_versor_fp32_t* third, const bgc_versor_fp32_t* second, const bgc_versor_fp32_t* first, bgc_versor_fp32_t* result)
|
|
{
|
|
const float s0a = (second->s0 * first->s0 - second->x1 * first->x1) - (second->x2 * first->x2 + second->x3 * first->x3);
|
|
const float x1a = (second->x1 * first->s0 + second->s0 * first->x1) - (second->x3 * first->x2 - second->x2 * first->x3);
|
|
const float x2a = (second->x2 * first->s0 + second->s0 * first->x2) - (second->x1 * first->x3 - second->x3 * first->x1);
|
|
const float x3a = (second->x3 * first->s0 + second->s0 * first->x3) - (second->x2 * first->x1 - second->x1 * first->x2);
|
|
|
|
const float s0b = (third->s0 * s0a - third->x1 * x1a) - (third->x2 * x2a + third->x3 * x3a);
|
|
const float x1b = (third->x1 * s0a + third->s0 * x1a) - (third->x3 * x2a - third->x2 * x3a);
|
|
const float x2b = (third->x2 * s0a + third->s0 * x2a) - (third->x1 * x3a - third->x3 * x1a);
|
|
const float x3b = (third->x3 * s0a + third->s0 * x3a) - (third->x2 * x1a - third->x1 * x2a);
|
|
|
|
const float square_modulus = (s0b * s0b + x1b * x1b) + (x2b * x2b + x3b * x3b);
|
|
|
|
_bgc_dark_twin_versor_fp32_t* twin = (_bgc_dark_twin_versor_fp32_t*)result;
|
|
|
|
twin->s0 = s0b;
|
|
twin->x1 = x1b;
|
|
twin->x2 = x2b;
|
|
twin->x3 = x3b;
|
|
|
|
if (1.0f - BGC_TWO_EPSYLON_FP32 <= square_modulus && square_modulus <= 1.0f + BGC_TWO_EPSYLON_FP32) {
|
|
return;
|
|
}
|
|
|
|
const float multiplier = sqrtf(1.0f / square_modulus);
|
|
|
|
twin->s0 *= multiplier;
|
|
twin->x1 *= multiplier;
|
|
twin->x2 *= multiplier;
|
|
twin->x3 *= multiplier;
|
|
}
|
|
|
|
inline void bgc_versor_combine3_fp64(const bgc_versor_fp64_t* third, const bgc_versor_fp64_t* second, const bgc_versor_fp64_t* first, bgc_versor_fp64_t* result)
|
|
{
|
|
const double s0a = (second->s0 * first->s0 - second->x1 * first->x1) - (second->x2 * first->x2 + second->x3 * first->x3);
|
|
const double x1a = (second->x1 * first->s0 + second->s0 * first->x1) - (second->x3 * first->x2 - second->x2 * first->x3);
|
|
const double x2a = (second->x2 * first->s0 + second->s0 * first->x2) - (second->x1 * first->x3 - second->x3 * first->x1);
|
|
const double x3a = (second->x3 * first->s0 + second->s0 * first->x3) - (second->x2 * first->x1 - second->x1 * first->x2);
|
|
|
|
const double s0b = (third->s0 * s0a - third->x1 * x1a) - (third->x2 * x2a + third->x3 * x3a);
|
|
const double x1b = (third->x1 * s0a + third->s0 * x1a) - (third->x3 * x2a - third->x2 * x3a);
|
|
const double x2b = (third->x2 * s0a + third->s0 * x2a) - (third->x1 * x3a - third->x3 * x1a);
|
|
const double x3b = (third->x3 * s0a + third->s0 * x3a) - (third->x2 * x1a - third->x1 * x2a);
|
|
|
|
const double square_modulus = (s0b * s0b + x1b * x1b) + (x2b * x2b + x3b * x3b);
|
|
|
|
_bgc_dark_twin_versor_fp64_t* twin = (_bgc_dark_twin_versor_fp64_t*)result;
|
|
|
|
twin->s0 = s0b;
|
|
twin->x1 = x1b;
|
|
twin->x2 = x2b;
|
|
twin->x3 = x3b;
|
|
|
|
if (1.0 - BGC_TWO_EPSYLON_FP64 <= square_modulus && square_modulus <= 1.0 + BGC_TWO_EPSYLON_FP64) {
|
|
return;
|
|
}
|
|
|
|
const double multiplier = sqrt(1.0 / square_modulus);
|
|
|
|
twin->s0 *= multiplier;
|
|
twin->x1 *= multiplier;
|
|
twin->x2 *= multiplier;
|
|
twin->x3 *= multiplier;
|
|
}
|
|
|
|
// ================= Exclusion ================== //
|
|
|
|
inline void bgc_versor_exclude_fp32(const bgc_versor_fp32_t* basic, const bgc_versor_fp32_t* exclusion, bgc_versor_fp32_t* 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);
|
|
|
|
_bgc_dark_twin_versor_fp32_t* twin = (_bgc_dark_twin_versor_fp32_t*)result;
|
|
|
|
twin->s0 = s0;
|
|
twin->x1 = x1;
|
|
twin->x2 = x2;
|
|
twin->x3 = x3;
|
|
|
|
if (1.0f - BGC_TWO_EPSYLON_FP32 <= square_modulus && square_modulus <= 1.0f + BGC_TWO_EPSYLON_FP32) {
|
|
return;
|
|
}
|
|
|
|
const float multiplier = sqrtf(1.0f / square_modulus);
|
|
|
|
twin->s0 *= multiplier;
|
|
twin->x1 *= multiplier;
|
|
twin->x2 *= multiplier;
|
|
twin->x3 *= multiplier;
|
|
}
|
|
|
|
inline void bgc_versor_exclude_fp64(const bgc_versor_fp64_t* basic, const bgc_versor_fp64_t* exclusion, bgc_versor_fp64_t* 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);
|
|
|
|
_bgc_dark_twin_versor_fp64_t* twin = (_bgc_dark_twin_versor_fp64_t*)result;
|
|
|
|
twin->s0 = s0;
|
|
twin->x1 = x1;
|
|
twin->x2 = x2;
|
|
twin->x3 = x3;
|
|
|
|
if (1.0 - BGC_TWO_EPSYLON_FP64 <= square_modulus && square_modulus <= 1.0 + BGC_TWO_EPSYLON_FP64) {
|
|
return;
|
|
}
|
|
|
|
const double multiplier = sqrt(1.0 / square_modulus);
|
|
|
|
twin->s0 *= multiplier;
|
|
twin->x1 *= multiplier;
|
|
twin->x2 *= multiplier;
|
|
twin->x3 *= multiplier;
|
|
}
|
|
|
|
// ================= Rotation3 ================== //
|
|
|
|
void bgc_versor_get_rotation_fp32(const bgc_versor_fp32_t* versor, bgc_rotation3_fp32_t* result);
|
|
|
|
void bgc_versor_get_rotation_fp64(const bgc_versor_fp64_t* versor, bgc_rotation3_fp64_t* result);
|
|
|
|
// =========== Make Rotation Matrix3x3 ========== //
|
|
|
|
inline void bgc_versor_make_rotation_matrix_fp32(const bgc_versor_fp32_t* versor, bgc_matrix3x3_fp32_t* 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;
|
|
}
|
|
|
|
inline void bgc_versor_make_rotation_matrix_fp64(const bgc_versor_fp64_t* versor, bgc_matrix3x3_fp64_t* 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 =========== //
|
|
|
|
inline void bgc_versor_make_reverse_matrix_fp32(const bgc_versor_fp32_t* versor, bgc_matrix3x3_fp32_t* 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;
|
|
}
|
|
|
|
inline void bgc_versor_make_reverse_matrix_fp64(const bgc_versor_fp64_t* versor, bgc_matrix3x3_fp64_t* 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 ================= //
|
|
|
|
inline void bgc_versor_turn_vector_fp32(const bgc_versor_fp32_t* versor, const bgc_vector3_fp32_t* vector, bgc_vector3_fp32_t* 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 bgc_versor_fp64_t* versor, const bgc_vector3_fp64_t* vector, bgc_vector3_fp64_t* 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 bgc_versor_fp32_t* versor, const bgc_vector3_fp32_t* vector, bgc_vector3_fp32_t* 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 bgc_versor_fp64_t* versor, const bgc_vector3_fp64_t* vector, bgc_vector3_fp64_t* 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
|