864 lines
32 KiB
C
864 lines
32 KiB
C
#ifndef _BGC_QUATERNION_H_
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#define _BGC_QUATERNION_H_
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#include <math.h>
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#include "utilities.h"
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#include "angle.h"
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#include "matrix3x3.h"
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typedef struct {
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float s0, x1, x2, x3;
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} BGC_FP32_Quaternion;
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typedef struct {
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double s0, x1, x2, x3;
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} BGC_FP64_Quaternion;
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// ==================== Reset =================== //
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inline void bgc_fp32_quaternion_reset(BGC_FP32_Quaternion* quaternion)
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{
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quaternion->s0 = 0.0f;
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quaternion->x1 = 0.0f;
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quaternion->x2 = 0.0f;
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quaternion->x3 = 0.0f;
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}
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inline void bgc_fp64_quaternion_reset(BGC_FP64_Quaternion* quaternion)
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{
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quaternion->s0 = 0.0;
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quaternion->x1 = 0.0;
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quaternion->x2 = 0.0;
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quaternion->x3 = 0.0;
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}
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// ================= Make Unit ================== //
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inline void bgc_fp32_quaternion_make_unit(BGC_FP32_Quaternion* quaternion)
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{
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quaternion->s0 = 1.0f;
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quaternion->x1 = 0.0f;
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quaternion->x2 = 0.0f;
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quaternion->x3 = 0.0f;
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}
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inline void bgc_fp64_quaternion_make_unit(BGC_FP64_Quaternion* quaternion)
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{
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quaternion->s0 = 1.0;
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quaternion->x1 = 0.0;
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quaternion->x2 = 0.0;
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quaternion->x3 = 0.0;
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}
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// ==================== Set ===================== //
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inline void bgc_fp32_quaternion_make(BGC_FP32_Quaternion* quaternion, const float s0, const float x1, const float x2, const float x3)
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{
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quaternion->s0 = s0;
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quaternion->x1 = x1;
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quaternion->x2 = x2;
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quaternion->x3 = x3;
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}
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inline void bgc_fp64_quaternion_make(BGC_FP64_Quaternion* quaternion, const double s0, const double x1, const double x2, const double x3)
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{
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quaternion->s0 = s0;
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quaternion->x1 = x1;
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quaternion->x2 = x2;
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quaternion->x3 = x3;
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}
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// ============= Get Square Modulus ============= //
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inline float bgc_fp32_quaternion_get_square_modulus(const BGC_FP32_Quaternion* quaternion)
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{
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return (quaternion->s0 * quaternion->s0 + quaternion->x1 * quaternion->x1) + (quaternion->x2 * quaternion->x2 + quaternion->x3 * quaternion->x3);
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}
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inline double bgc_fp64_quaternion_get_square_modulus(const BGC_FP64_Quaternion* quaternion)
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{
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return (quaternion->s0 * quaternion->s0 + quaternion->x1 * quaternion->x1) + (quaternion->x2 * quaternion->x2 + quaternion->x3 * quaternion->x3);
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}
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// ================ Get Modulus ================= //
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inline float bgc_fp32_quaternion_get_modulus(const BGC_FP32_Quaternion* quaternion)
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{
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return sqrtf(bgc_fp32_quaternion_get_square_modulus(quaternion));
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}
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inline double bgc_fp64_quaternion_get_modulus(const BGC_FP64_Quaternion* quaternion)
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{
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return sqrt(bgc_fp64_quaternion_get_square_modulus(quaternion));
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}
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// ================== Is Zero =================== //
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inline int bgc_fp32_quaternion_is_zero(const BGC_FP32_Quaternion* quaternion)
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{
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return bgc_fp32_quaternion_get_square_modulus(quaternion) <= BGC_FP32_SQUARE_EPSILON;
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}
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inline int bgc_fp64_quaternion_is_zero(const BGC_FP64_Quaternion* quaternion)
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{
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return bgc_fp64_quaternion_get_square_modulus(quaternion) <= BGC_FP64_SQUARE_EPSILON;
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}
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// ================== Is Unit =================== //
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inline int bgc_fp32_quaternion_is_unit(const BGC_FP32_Quaternion* quaternion)
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{
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return bgc_fp32_is_square_unit(bgc_fp32_quaternion_get_square_modulus(quaternion));
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}
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inline int bgc_fp64_quaternion_is_unit(const BGC_FP64_Quaternion* quaternion)
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{
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return bgc_fp64_is_square_unit(bgc_fp64_quaternion_get_square_modulus(quaternion));
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}
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// ==================== Copy ==================== //
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inline void bgc_fp32_quaternion_copy(BGC_FP32_Quaternion* destination, const BGC_FP32_Quaternion* 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_quaternion_copy(BGC_FP64_Quaternion* destination, const BGC_FP64_Quaternion* 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_quaternion_swap(BGC_FP32_Quaternion* quarternion1, BGC_FP32_Quaternion* quarternion2)
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{
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const float s0 = quarternion2->s0;
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const float x1 = quarternion2->x1;
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const float x2 = quarternion2->x2;
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const float x3 = quarternion2->x3;
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quarternion2->s0 = quarternion1->s0;
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quarternion2->x1 = quarternion1->x1;
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quarternion2->x2 = quarternion1->x2;
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quarternion2->x3 = quarternion1->x3;
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quarternion1->s0 = s0;
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quarternion1->x1 = x1;
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quarternion1->x2 = x2;
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quarternion1->x3 = x3;
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}
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inline void bgc_fp64_quaternion_swap(BGC_FP64_Quaternion* quarternion1, BGC_FP64_Quaternion* quarternion2)
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{
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const double s0 = quarternion2->s0;
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const double x1 = quarternion2->x1;
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const double x2 = quarternion2->x2;
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const double x3 = quarternion2->x3;
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quarternion2->s0 = quarternion1->s0;
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quarternion2->x1 = quarternion1->x1;
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quarternion2->x2 = quarternion1->x2;
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quarternion2->x3 = quarternion1->x3;
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quarternion1->s0 = s0;
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quarternion1->x1 = x1;
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quarternion1->x2 = x2;
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quarternion1->x3 = x3;
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}
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// ================== Convert =================== //
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inline void bgc_fp32_quaternion_convert_to_fp64(BGC_FP64_Quaternion* destination, const BGC_FP32_Quaternion* 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_quaternion_convert_to_fp32(BGC_FP32_Quaternion* destination, const BGC_FP64_Quaternion* source)
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{
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destination->s0 = (float)source->s0;
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destination->x1 = (float)source->x1;
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destination->x2 = (float)source->x2;
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destination->x3 = (float)source->x3;
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}
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// ==================== Add ===================== //
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inline void bgc_fp32_quaternion_add(BGC_FP32_Quaternion* sum, const BGC_FP32_Quaternion* quaternion1, const BGC_FP32_Quaternion* quaternion2)
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{
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sum->s0 = quaternion1->s0 + quaternion2->s0;
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sum->x1 = quaternion1->x1 + quaternion2->x1;
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sum->x2 = quaternion1->x2 + quaternion2->x2;
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sum->x3 = quaternion1->x3 + quaternion2->x3;
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}
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inline void bgc_fp64_quaternion_add(BGC_FP64_Quaternion* sum, const BGC_FP64_Quaternion* quaternion1, const BGC_FP64_Quaternion* quaternion2)
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{
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sum->s0 = quaternion1->s0 + quaternion2->s0;
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sum->x1 = quaternion1->x1 + quaternion2->x1;
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sum->x2 = quaternion1->x2 + quaternion2->x2;
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sum->x3 = quaternion1->x3 + quaternion2->x3;
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}
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// ================= Add Scaled ================= //
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inline void bgc_fp32_quaternion_add_scaled(BGC_FP32_Quaternion* sum, const BGC_FP32_Quaternion* basic_quaternion, const BGC_FP32_Quaternion* scalable_quaternion, const float scale)
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{
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sum->s0 = basic_quaternion->s0 + scalable_quaternion->s0 * scale;
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sum->x1 = basic_quaternion->x1 + scalable_quaternion->x1 * scale;
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sum->x2 = basic_quaternion->x2 + scalable_quaternion->x2 * scale;
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sum->x3 = basic_quaternion->x3 + scalable_quaternion->x3 * scale;
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}
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inline void bgc_fp64_quaternion_add_scaled(BGC_FP64_Quaternion* sum, const BGC_FP64_Quaternion* basic_quaternion, const BGC_FP64_Quaternion* scalable_quaternion, const double scale)
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{
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sum->s0 = basic_quaternion->s0 + scalable_quaternion->s0 * scale;
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sum->x1 = basic_quaternion->x1 + scalable_quaternion->x1 * scale;
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sum->x2 = basic_quaternion->x2 + scalable_quaternion->x2 * scale;
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sum->x3 = basic_quaternion->x3 + scalable_quaternion->x3 * scale;
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}
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// ================== Subtract ================== //
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inline void bgc_fp32_quaternion_subtract(BGC_FP32_Quaternion* difference, const BGC_FP32_Quaternion* minuend, const BGC_FP32_Quaternion* subtrahend)
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{
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difference->s0 = minuend->s0 - subtrahend->s0;
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difference->x1 = minuend->x1 - subtrahend->x1;
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difference->x2 = minuend->x2 - subtrahend->x2;
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difference->x3 = minuend->x3 - subtrahend->x3;
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}
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inline void bgc_fp64_quaternion_subtract(BGC_FP64_Quaternion* difference, const BGC_FP64_Quaternion* minuend, const BGC_FP64_Quaternion* subtrahend)
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{
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difference->s0 = minuend->s0 - subtrahend->s0;
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difference->x1 = minuend->x1 - subtrahend->x1;
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difference->x2 = minuend->x2 - subtrahend->x2;
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difference->x3 = minuend->x3 - subtrahend->x3;
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}
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// ================== Multiply ================== //
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inline void bgc_fp32_quaternion_get_product(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* left, const BGC_FP32_Quaternion* right)
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{
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const float s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
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const float x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
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const float x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
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const float x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);
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product->s0 = s0;
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product->x1 = x1;
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product->x2 = x2;
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product->x3 = x3;
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}
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inline void bgc_fp64_quaternion_get_product(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* left, const BGC_FP64_Quaternion* right)
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{
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const double s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
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const double x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
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const double x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
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const double x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);
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product->s0 = s0;
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product->x1 = x1;
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product->x2 = x2;
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product->x3 = x3;
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}
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inline void bgc_fp32_quaternion_get_product_by_conjugate(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* left, const BGC_FP32_Quaternion* right)
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{
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const float s0 = (left->s0 * right->s0 + left->x1 * right->x1) + (left->x2 * right->x2 + left->x3 * right->x3);
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const float x1 = (left->x1 * right->s0 + left->x3 * right->x2) - (left->s0 * right->x1 + left->x2 * right->x3);
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const float x2 = (left->x2 * right->s0 + left->x1 * right->x3) - (left->s0 * right->x2 + left->x3 * right->x1);
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const float x3 = (left->x3 * right->s0 + left->x2 * right->x1) - (left->s0 * right->x3 + left->x1 * right->x2);
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product->s0 = s0;
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product->x1 = x1;
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product->x2 = x2;
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product->x3 = x3;
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}
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inline void bgc_fp64_quaternion_get_product_by_conjugate(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* left, const BGC_FP64_Quaternion* right)
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{
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const double s0 = (left->s0 * right->s0 + left->x1 * right->x1) + (left->x2 * right->x2 + left->x3 * right->x3);
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const double x1 = (left->x1 * right->s0 + left->x3 * right->x2) - (left->s0 * right->x1 + left->x2 * right->x3);
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const double x2 = (left->x2 * right->s0 + left->x1 * right->x3) - (left->s0 * right->x2 + left->x3 * right->x1);
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const double x3 = (left->x3 * right->s0 + left->x2 * right->x1) - (left->s0 * right->x3 + left->x1 * right->x2);
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product->s0 = s0;
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product->x1 = x1;
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product->x2 = x2;
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product->x3 = x3;
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}
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inline void bgc_fp32_quaternion_multiply(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* multiplicand, const float multipier)
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{
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product->s0 = multiplicand->s0 * multipier;
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product->x1 = multiplicand->x1 * multipier;
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product->x2 = multiplicand->x2 * multipier;
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product->x3 = multiplicand->x3 * multipier;
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}
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inline void bgc_fp64_quaternion_multiply(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* multiplicand, const double multipier)
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{
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product->s0 = multiplicand->s0 * multipier;
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product->x1 = multiplicand->x1 * multipier;
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product->x2 = multiplicand->x2 * multipier;
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product->x3 = multiplicand->x3 * multipier;
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}
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// =================== Divide =================== //
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inline int bgc_fp32_quaternion_get_ratio(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* divident, const BGC_FP32_Quaternion* divisor)
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{
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const float square_modulus = bgc_fp32_quaternion_get_square_modulus(divisor);
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if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
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return 0;
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}
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const float s0 = (divident->s0 * divisor->s0 + divident->x1 * divisor->x1) + (divident->x2 * divisor->x2 + divident->x3 * divisor->x3);
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const float x1 = (divident->x1 * divisor->s0 + divident->x3 * divisor->x2) - (divident->s0 * divisor->x1 + divident->x2 * divisor->x3);
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const float x2 = (divident->x2 * divisor->s0 + divident->x1 * divisor->x3) - (divident->s0 * divisor->x2 + divident->x3 * divisor->x1);
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const float x3 = (divident->x3 * divisor->s0 + divident->x2 * divisor->x1) - (divident->s0 * divisor->x3 + divident->x1 * divisor->x2);
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const float multiplicand = 1.0f / square_modulus;
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quotient->s0 = s0 * multiplicand;
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quotient->x1 = x1 * multiplicand;
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quotient->x2 = x2 * multiplicand;
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quotient->x3 = x3 * multiplicand;
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return 1;
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}
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inline int bgc_fp64_quaternion_get_ratio(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* divident, const BGC_FP64_Quaternion* divisor)
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{
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const double square_modulus = bgc_fp64_quaternion_get_square_modulus(divisor);
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if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
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return 0;
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}
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const double s0 = (divident->s0 * divisor->s0 + divident->x1 * divisor->x1) + (divident->x2 * divisor->x2 + divident->x3 * divisor->x3);
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const double x1 = (divident->x1 * divisor->s0 + divident->x3 * divisor->x2) - (divident->s0 * divisor->x1 + divident->x2 * divisor->x3);
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const double x2 = (divident->x2 * divisor->s0 + divident->x1 * divisor->x3) - (divident->s0 * divisor->x2 + divident->x3 * divisor->x1);
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const double x3 = (divident->x3 * divisor->s0 + divident->x2 * divisor->x1) - (divident->s0 * divisor->x3 + divident->x1 * divisor->x2);
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const double multiplicand = 1.0 / square_modulus;
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quotient->s0 = s0 * multiplicand;
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quotient->x1 = x1 * multiplicand;
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quotient->x2 = x2 * multiplicand;
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quotient->x3 = x3 * multiplicand;
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return 1;
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}
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inline void bgc_fp32_quaternion_divide(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* dividend, const float divisor)
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{
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bgc_fp32_quaternion_multiply(quotient, dividend, 1.0f / divisor);
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}
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inline void bgc_fp64_quaternion_divide(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* dividend, const double divisor)
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{
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bgc_fp64_quaternion_multiply(quotient, dividend, 1.0 / divisor);
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}
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// ================ Mean of Two ================= //
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inline void bgc_fp32_quaternion_get_mean2(BGC_FP32_Quaternion* mean, const BGC_FP32_Quaternion* quaternion1, const BGC_FP32_Quaternion* quaternion2)
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{
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mean->s0 = (quaternion1->s0 + quaternion2->s0) * 0.5f;
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mean->x1 = (quaternion1->x1 + quaternion2->x1) * 0.5f;
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mean->x2 = (quaternion1->x2 + quaternion2->x2) * 0.5f;
|
|
mean->x3 = (quaternion1->x3 + quaternion2->x3) * 0.5f;
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_get_mean2(BGC_FP64_Quaternion* mean, const BGC_FP64_Quaternion* quaternion1, const BGC_FP64_Quaternion* quaternion2)
|
|
{
|
|
mean->s0 = (quaternion1->s0 + quaternion2->s0) * 0.5f;
|
|
mean->x1 = (quaternion1->x1 + quaternion2->x1) * 0.5f;
|
|
mean->x2 = (quaternion1->x2 + quaternion2->x2) * 0.5f;
|
|
mean->x3 = (quaternion1->x3 + quaternion2->x3) * 0.5f;
|
|
}
|
|
|
|
// =============== Mean of Three ================ //
|
|
|
|
inline void bgc_fp32_quaternion_get_mean3(BGC_FP32_Quaternion* mean, const BGC_FP32_Quaternion* quaternion1, const BGC_FP32_Quaternion* quaternion2, const BGC_FP32_Quaternion* quaternion3)
|
|
{
|
|
mean->s0 = (quaternion1->s0 + quaternion2->s0 + quaternion3->s0) * BGC_FP32_ONE_THIRD;
|
|
mean->x1 = (quaternion1->x1 + quaternion2->x1 + quaternion3->x1) * BGC_FP32_ONE_THIRD;
|
|
mean->x2 = (quaternion1->x2 + quaternion2->x2 + quaternion3->x2) * BGC_FP32_ONE_THIRD;
|
|
mean->x3 = (quaternion1->x3 + quaternion2->x3 + quaternion3->x3) * BGC_FP32_ONE_THIRD;
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_get_mean3(BGC_FP64_Quaternion* mean, const BGC_FP64_Quaternion* quaternion1, const BGC_FP64_Quaternion* quaternion2, const BGC_FP64_Quaternion* quaternion3)
|
|
{
|
|
mean->s0 = (quaternion1->s0 + quaternion2->s0 + quaternion3->s0) * BGC_FP64_ONE_THIRD;
|
|
mean->x1 = (quaternion1->x1 + quaternion2->x1 + quaternion3->x1) * BGC_FP64_ONE_THIRD;
|
|
mean->x2 = (quaternion1->x2 + quaternion2->x2 + quaternion3->x2) * BGC_FP64_ONE_THIRD;
|
|
mean->x3 = (quaternion1->x3 + quaternion2->x3 + quaternion3->x3) * BGC_FP64_ONE_THIRD;
|
|
}
|
|
|
|
// ============ Linear Interpolation ============ //
|
|
|
|
inline void bgc_fp32_quaternion_interpolate(BGC_FP32_Quaternion* interpolation, const BGC_FP32_Quaternion* quaternion1, const BGC_FP32_Quaternion* quaternion2, const float phase)
|
|
{
|
|
const float counter_phase = 1.0f - phase;
|
|
|
|
interpolation->s0 = quaternion1->s0 * counter_phase + quaternion2->s0 * phase;
|
|
interpolation->x1 = quaternion1->x1 * counter_phase + quaternion2->x1 * phase;
|
|
interpolation->x2 = quaternion1->x2 * counter_phase + quaternion2->x2 * phase;
|
|
interpolation->x3 = quaternion1->x3 * counter_phase + quaternion2->x3 * phase;
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_interpolate(BGC_FP64_Quaternion* interpolation, const BGC_FP64_Quaternion* quaternion1, const BGC_FP64_Quaternion* quaternion2, const double phase)
|
|
{
|
|
const double counter_phase = 1.0 - phase;
|
|
|
|
interpolation->s0 = quaternion1->s0 * counter_phase + quaternion2->s0 * phase;
|
|
interpolation->x1 = quaternion1->x1 * counter_phase + quaternion2->x1 * phase;
|
|
interpolation->x2 = quaternion1->x2 * counter_phase + quaternion2->x2 * phase;
|
|
interpolation->x3 = quaternion1->x3 * counter_phase + quaternion2->x3 * phase;
|
|
}
|
|
|
|
// ================= Conjugate ================== //
|
|
|
|
inline void bgc_fp32_quaternion_conjugate(BGC_FP32_Quaternion* quaternion)
|
|
{
|
|
quaternion->x1 = -quaternion->x1;
|
|
quaternion->x2 = -quaternion->x2;
|
|
quaternion->x3 = -quaternion->x3;
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_conjugate(BGC_FP64_Quaternion* quaternion)
|
|
{
|
|
quaternion->x1 = -quaternion->x1;
|
|
quaternion->x2 = -quaternion->x2;
|
|
quaternion->x3 = -quaternion->x3;
|
|
}
|
|
|
|
inline void bgc_fp32_quaternion_get_conjugate(BGC_FP32_Quaternion* conjugate, const BGC_FP32_Quaternion* quaternion)
|
|
{
|
|
conjugate->s0 = quaternion->s0;
|
|
conjugate->x1 = -quaternion->x1;
|
|
conjugate->x2 = -quaternion->x2;
|
|
conjugate->x3 = -quaternion->x3;
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_get_conjugate(BGC_FP64_Quaternion* conjugate, const BGC_FP64_Quaternion* quaternion)
|
|
{
|
|
conjugate->s0 = quaternion->s0;
|
|
conjugate->x1 = -quaternion->x1;
|
|
conjugate->x2 = -quaternion->x2;
|
|
conjugate->x3 = -quaternion->x3;
|
|
}
|
|
|
|
// ================== Negative ================== //
|
|
|
|
inline void bgc_fp32_quaternion_revert(BGC_FP32_Quaternion* quaternion)
|
|
{
|
|
quaternion->s0 = -quaternion->s0;
|
|
quaternion->x1 = -quaternion->x1;
|
|
quaternion->x2 = -quaternion->x2;
|
|
quaternion->x3 = -quaternion->x3;
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_revert(BGC_FP64_Quaternion* quaternion)
|
|
{
|
|
quaternion->s0 = -quaternion->s0;
|
|
quaternion->x1 = -quaternion->x1;
|
|
quaternion->x2 = -quaternion->x2;
|
|
quaternion->x3 = -quaternion->x3;
|
|
}
|
|
|
|
inline void bgc_fp32_quaternion_get_reverse(BGC_FP32_Quaternion* reverse, const BGC_FP32_Quaternion* quaternion)
|
|
{
|
|
reverse->s0 = -quaternion->s0;
|
|
reverse->x1 = -quaternion->x1;
|
|
reverse->x2 = -quaternion->x2;
|
|
reverse->x3 = -quaternion->x3;
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_get_reverse(BGC_FP64_Quaternion* reverse, const BGC_FP64_Quaternion* quaternion)
|
|
{
|
|
reverse->s0 = -quaternion->s0;
|
|
reverse->x1 = -quaternion->x1;
|
|
reverse->x2 = -quaternion->x2;
|
|
reverse->x3 = -quaternion->x3;
|
|
}
|
|
|
|
// =================== Invert =================== //
|
|
|
|
inline int bgc_fp32_quaternion_get_inverse(BGC_FP32_Quaternion* inverse, const BGC_FP32_Quaternion* quaternion)
|
|
{
|
|
const float square_modulus = bgc_fp32_quaternion_get_square_modulus(quaternion);
|
|
|
|
if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return 0;
|
|
}
|
|
|
|
const float multiplicand = 1.0f / square_modulus;
|
|
|
|
inverse->s0 = quaternion->s0 * multiplicand;
|
|
inverse->x1 = -quaternion->x1 * multiplicand;
|
|
inverse->x2 = -quaternion->x2 * multiplicand;
|
|
inverse->x3 = -quaternion->x3 * multiplicand;
|
|
|
|
return 1;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_get_inverse(BGC_FP64_Quaternion* inverse, const BGC_FP64_Quaternion* quaternion)
|
|
{
|
|
const double square_modulus = bgc_fp64_quaternion_get_square_modulus(quaternion);
|
|
|
|
if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return 0;
|
|
}
|
|
|
|
const double multiplicand = 1.0 / square_modulus;
|
|
|
|
inverse->s0 = quaternion->s0 * multiplicand;
|
|
inverse->x1 = -quaternion->x1 * multiplicand;
|
|
inverse->x2 = -quaternion->x2 * multiplicand;
|
|
inverse->x3 = -quaternion->x3 * multiplicand;
|
|
|
|
return 1;
|
|
}
|
|
|
|
inline int bgc_fp32_quaternion_invert(BGC_FP32_Quaternion* quaternion)
|
|
{
|
|
return bgc_fp32_quaternion_get_inverse(quaternion, quaternion);
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_invert(BGC_FP64_Quaternion* quaternion)
|
|
{
|
|
return bgc_fp64_quaternion_get_inverse(quaternion, quaternion);
|
|
}
|
|
|
|
// ================= Normalize ================== //
|
|
|
|
inline int bgc_fp32_quaternion_normalize(BGC_FP32_Quaternion* quaternion)
|
|
{
|
|
const float square_modulus = bgc_fp32_quaternion_get_square_modulus(quaternion);
|
|
|
|
if (bgc_fp32_is_square_unit(square_modulus)) {
|
|
return 1;
|
|
}
|
|
|
|
if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return 0;
|
|
}
|
|
|
|
const float multiplier = sqrtf(1.0f / square_modulus);
|
|
|
|
quaternion->s0 *= multiplier;
|
|
quaternion->x1 *= multiplier;
|
|
quaternion->x2 *= multiplier;
|
|
quaternion->x3 *= multiplier;
|
|
|
|
return 1;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_normalize(BGC_FP64_Quaternion* quaternion)
|
|
{
|
|
const double square_modulus = bgc_fp64_quaternion_get_square_modulus(quaternion);
|
|
|
|
if (bgc_fp64_is_square_unit(square_modulus)) {
|
|
return 1;
|
|
}
|
|
|
|
if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return 0;
|
|
}
|
|
|
|
const double multiplier = sqrt(1.0 / square_modulus);
|
|
|
|
quaternion->s0 *= multiplier;
|
|
quaternion->x1 *= multiplier;
|
|
quaternion->x2 *= multiplier;
|
|
quaternion->x3 *= multiplier;
|
|
|
|
return 1;
|
|
}
|
|
|
|
inline int bgc_fp32_quaternion_get_normalized(BGC_FP32_Quaternion* normalized, const BGC_FP32_Quaternion* quaternion)
|
|
{
|
|
const float square_modulus = bgc_fp32_quaternion_get_square_modulus(quaternion);
|
|
|
|
if (bgc_fp32_is_square_unit(square_modulus)) {
|
|
bgc_fp32_quaternion_copy(normalized, quaternion);
|
|
return 1;
|
|
}
|
|
|
|
if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
bgc_fp32_quaternion_reset(normalized);
|
|
return 0;
|
|
}
|
|
|
|
bgc_fp32_quaternion_multiply(normalized, quaternion, sqrtf(1.0f / square_modulus));
|
|
return 1;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_get_normalized(BGC_FP64_Quaternion* normalized, const BGC_FP64_Quaternion* quaternion)
|
|
{
|
|
const double square_modulus = bgc_fp64_quaternion_get_square_modulus(quaternion);
|
|
|
|
if (bgc_fp64_is_square_unit(square_modulus)) {
|
|
bgc_fp64_quaternion_copy(normalized, quaternion);
|
|
return 1;
|
|
}
|
|
|
|
if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
bgc_fp64_quaternion_reset(normalized);
|
|
return 0;
|
|
}
|
|
|
|
bgc_fp64_quaternion_multiply(normalized, quaternion, sqrt(1.0 / square_modulus));
|
|
return 1;
|
|
}
|
|
|
|
// =============== Get Exponation =============== //
|
|
|
|
int bgc_fp32_quaternion_get_exponation(BGC_FP32_Quaternion* power, const BGC_FP32_Quaternion* base, const float exponent);
|
|
|
|
int bgc_fp64_quaternion_get_exponation(BGC_FP64_Quaternion* power, const BGC_FP64_Quaternion* base, const double exponent);
|
|
|
|
// ============ Get Rotation Matrix ============= //
|
|
|
|
inline int bgc_fp32_quaternion_get_rotation_matrix(BGC_FP32_Matrix3x3* rotation, const BGC_FP32_Quaternion* quaternion)
|
|
{
|
|
const float s0s0 = quaternion->s0 * quaternion->s0;
|
|
const float x1x1 = quaternion->x1 * quaternion->x1;
|
|
const float x2x2 = quaternion->x2 * quaternion->x2;
|
|
const float x3x3 = quaternion->x3 * quaternion->x3;
|
|
|
|
const float square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);
|
|
|
|
if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus))
|
|
{
|
|
bgc_fp32_matrix3x3_make_identity(rotation);
|
|
return 0;
|
|
}
|
|
|
|
const float corrector1 = 1.0f / square_modulus;
|
|
|
|
const float s0x1 = quaternion->s0 * quaternion->x1;
|
|
const float s0x2 = quaternion->s0 * quaternion->x2;
|
|
const float s0x3 = quaternion->s0 * quaternion->x3;
|
|
const float x1x2 = quaternion->x1 * quaternion->x2;
|
|
const float x1x3 = quaternion->x1 * quaternion->x3;
|
|
const float x2x3 = quaternion->x2 * quaternion->x3;
|
|
|
|
const float corrector2 = 2.0f * corrector1;
|
|
|
|
rotation->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
|
|
rotation->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
|
|
rotation->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
|
|
|
|
rotation->r1c2 = corrector2 * (x1x2 - s0x3);
|
|
rotation->r2c3 = corrector2 * (x2x3 - s0x1);
|
|
rotation->r3c1 = corrector2 * (x1x3 - s0x2);
|
|
|
|
rotation->r2c1 = corrector2 * (x1x2 + s0x3);
|
|
rotation->r3c2 = corrector2 * (x2x3 + s0x1);
|
|
rotation->r1c3 = corrector2 * (x1x3 + s0x2);
|
|
|
|
return 1;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_get_rotation_matrix(BGC_FP64_Matrix3x3* rotation, const BGC_FP64_Quaternion* quaternion)
|
|
{
|
|
const double s0s0 = quaternion->s0 * quaternion->s0;
|
|
const double x1x1 = quaternion->x1 * quaternion->x1;
|
|
const double x2x2 = quaternion->x2 * quaternion->x2;
|
|
const double x3x3 = quaternion->x3 * quaternion->x3;
|
|
|
|
const double square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);
|
|
|
|
if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus))
|
|
{
|
|
bgc_fp64_matrix3x3_make_identity(rotation);
|
|
return 0;
|
|
}
|
|
|
|
const double corrector1 = 1.0f / square_modulus;
|
|
|
|
const double s0x1 = quaternion->s0 * quaternion->x1;
|
|
const double s0x2 = quaternion->s0 * quaternion->x2;
|
|
const double s0x3 = quaternion->s0 * quaternion->x3;
|
|
const double x1x2 = quaternion->x1 * quaternion->x2;
|
|
const double x1x3 = quaternion->x1 * quaternion->x3;
|
|
const double x2x3 = quaternion->x2 * quaternion->x3;
|
|
|
|
const double corrector2 = 2.0f * corrector1;
|
|
|
|
rotation->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
|
|
rotation->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
|
|
rotation->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
|
|
|
|
rotation->r1c2 = corrector2 * (x1x2 - s0x3);
|
|
rotation->r2c3 = corrector2 * (x2x3 - s0x1);
|
|
rotation->r3c1 = corrector2 * (x1x3 - s0x2);
|
|
|
|
rotation->r2c1 = corrector2 * (x1x2 + s0x3);
|
|
rotation->r3c2 = corrector2 * (x2x3 + s0x1);
|
|
rotation->r1c3 = corrector2 * (x1x3 + s0x2);
|
|
|
|
return 1;
|
|
}
|
|
|
|
// ============= Get Reverse Matrix ============= //
|
|
|
|
inline int bgc_fp32_quaternion_get_reverse_matrix(BGC_FP32_Matrix3x3* reverse, const BGC_FP32_Quaternion* quaternion)
|
|
{
|
|
const float s0s0 = quaternion->s0 * quaternion->s0;
|
|
const float x1x1 = quaternion->x1 * quaternion->x1;
|
|
const float x2x2 = quaternion->x2 * quaternion->x2;
|
|
const float x3x3 = quaternion->x3 * quaternion->x3;
|
|
|
|
const float square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);
|
|
|
|
if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus))
|
|
{
|
|
bgc_fp32_matrix3x3_make_identity(reverse);
|
|
return 0;
|
|
}
|
|
|
|
const float corrector1 = 1.0f / square_modulus;
|
|
|
|
const float s0x1 = quaternion->s0 * quaternion->x1;
|
|
const float s0x2 = quaternion->s0 * quaternion->x2;
|
|
const float s0x3 = quaternion->s0 * quaternion->x3;
|
|
const float x1x2 = quaternion->x1 * quaternion->x2;
|
|
const float x1x3 = quaternion->x1 * quaternion->x3;
|
|
const float x2x3 = quaternion->x2 * quaternion->x3;
|
|
|
|
const float corrector2 = 2.0f * corrector1;
|
|
|
|
reverse->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
|
|
reverse->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
|
|
reverse->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
|
|
|
|
reverse->r1c2 = corrector2 * (x1x2 + s0x3);
|
|
reverse->r2c3 = corrector2 * (x2x3 + s0x1);
|
|
reverse->r3c1 = corrector2 * (x1x3 + s0x2);
|
|
|
|
reverse->r2c1 = corrector2 * (x1x2 - s0x3);
|
|
reverse->r3c2 = corrector2 * (x2x3 - s0x1);
|
|
reverse->r1c3 = corrector2 * (x1x3 - s0x2);
|
|
|
|
return 1;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_get_reverse_matrix(BGC_FP64_Matrix3x3* reverse, const BGC_FP64_Quaternion* quaternion)
|
|
{
|
|
const double s0s0 = quaternion->s0 * quaternion->s0;
|
|
const double x1x1 = quaternion->x1 * quaternion->x1;
|
|
const double x2x2 = quaternion->x2 * quaternion->x2;
|
|
const double x3x3 = quaternion->x3 * quaternion->x3;
|
|
|
|
const double square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);
|
|
|
|
if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus))
|
|
{
|
|
bgc_fp64_matrix3x3_make_identity(reverse);
|
|
return 0;
|
|
}
|
|
|
|
const double corrector1 = 1.0f / square_modulus;
|
|
|
|
const double s0x1 = quaternion->s0 * quaternion->x1;
|
|
const double s0x2 = quaternion->s0 * quaternion->x2;
|
|
const double s0x3 = quaternion->s0 * quaternion->x3;
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const double x1x2 = quaternion->x1 * quaternion->x2;
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const double x1x3 = quaternion->x1 * quaternion->x3;
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const double x2x3 = quaternion->x2 * quaternion->x3;
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const double corrector2 = 2.0f * corrector1;
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reverse->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
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reverse->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
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reverse->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
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reverse->r1c2 = corrector2 * (x1x2 + s0x3);
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reverse->r2c3 = corrector2 * (x2x3 + s0x1);
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reverse->r3c1 = corrector2 * (x1x3 + s0x2);
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reverse->r2c1 = corrector2 * (x1x2 - s0x3);
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reverse->r3c2 = corrector2 * (x2x3 - s0x1);
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reverse->r1c3 = corrector2 * (x1x3 - s0x2);
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return 1;
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}
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// ============= Get Both Matrixes ============== //
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inline int bgc_fp32_quaternion_get_both_matrices(BGC_FP32_Matrix3x3* rotation, BGC_FP32_Matrix3x3* reverse, const BGC_FP32_Quaternion* quaternion)
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{
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if (bgc_fp32_quaternion_get_reverse_matrix(reverse, quaternion)) {
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bgc_fp32_matrix3x3_get_transposed(rotation, reverse);
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return 1;
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}
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return 0;
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}
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inline int bgc_fp64_quaternion_get_both_matrices(BGC_FP64_Matrix3x3* rotation, BGC_FP64_Matrix3x3* reverse, const BGC_FP64_Quaternion* quaternion)
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{
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if (bgc_fp64_quaternion_get_reverse_matrix(reverse, quaternion)) {
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bgc_fp64_matrix3x3_get_transposed(rotation, reverse);
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return 1;
|
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}
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|
|
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return 0;
|
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}
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|
|
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// ================== Are Close ================= //
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|
|
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inline int bgc_fp32_quaternion_are_close(const BGC_FP32_Quaternion* quaternion1, const BGC_FP32_Quaternion* quaternion2)
|
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{
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const float ds0 = quaternion1->s0 - quaternion2->s0;
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const float dx1 = quaternion1->x1 - quaternion2->x1;
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const float dx2 = quaternion1->x2 - quaternion2->x2;
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const float dx3 = quaternion1->x3 - quaternion2->x3;
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|
|
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const float square_modulus1 = bgc_fp32_quaternion_get_square_modulus(quaternion1);
|
|
const float square_modulus2 = bgc_fp32_quaternion_get_square_modulus(quaternion2);
|
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const float square_distance = (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3);
|
|
|
|
if (square_modulus1 <= BGC_FP32_EPSILON_EFFECTIVENESS_LIMIT || square_modulus2 <= BGC_FP32_EPSILON_EFFECTIVENESS_LIMIT) {
|
|
return square_distance <= BGC_FP32_SQUARE_EPSILON;
|
|
}
|
|
|
|
return square_distance <= BGC_FP32_SQUARE_EPSILON * square_modulus1 && square_distance <= BGC_FP32_SQUARE_EPSILON * square_modulus2;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_are_close(const BGC_FP64_Quaternion* quaternion1, const BGC_FP64_Quaternion* quaternion2)
|
|
{
|
|
const double ds0 = quaternion1->s0 - quaternion2->s0;
|
|
const double dx1 = quaternion1->x1 - quaternion2->x1;
|
|
const double dx2 = quaternion1->x2 - quaternion2->x2;
|
|
const double dx3 = quaternion1->x3 - quaternion2->x3;
|
|
|
|
const double square_modulus1 = bgc_fp64_quaternion_get_square_modulus(quaternion1);
|
|
const double square_modulus2 = bgc_fp64_quaternion_get_square_modulus(quaternion2);
|
|
const double square_distance = (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3);
|
|
|
|
if (square_modulus1 <= BGC_FP64_EPSILON_EFFECTIVENESS_LIMIT || square_modulus2 <= BGC_FP64_EPSILON_EFFECTIVENESS_LIMIT) {
|
|
return square_distance <= BGC_FP64_SQUARE_EPSILON;
|
|
}
|
|
|
|
return square_distance <= BGC_FP64_SQUARE_EPSILON * square_modulus1 && square_distance <= BGC_FP64_SQUARE_EPSILON * square_modulus2;
|
|
}
|
|
|
|
#endif
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