1319 lines
52 KiB
C
1319 lines
52 KiB
C
#ifndef _BGC_QUATERNION_H_INCLUDED_
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#define _BGC_QUATERNION_H_INCLUDED_
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#include <math.h>
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#include "./utilities.h"
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#include "./types.h"
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#include "./angle.h"
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#include "./matrix3x3.h"
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// ==================== Reset =================== //
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inline void bgc_fp32_quaternion_reset(BGC_FP32_Quaternion* const quaternion)
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{
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quaternion->s = 0.0f;
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quaternion->x = 0.0f;
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quaternion->y = 0.0f;
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quaternion->z = 0.0f;
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}
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inline void bgc_fp64_quaternion_reset(BGC_FP64_Quaternion* const quaternion)
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{
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quaternion->s = 0.0;
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quaternion->x = 0.0;
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quaternion->y = 0.0;
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quaternion->z = 0.0;
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}
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// ============= Get Square Modulus ============= //
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inline float bgc_fp32_quaternion_get_square_magnitude(const BGC_FP32_Quaternion* const quaternion)
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{
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return (quaternion->s * quaternion->s + quaternion->x * quaternion->x) + (quaternion->y * quaternion->y + quaternion->z * quaternion->z);
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}
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inline double bgc_fp64_quaternion_get_square_magnitude(const BGC_FP64_Quaternion* const quaternion)
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{
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return (quaternion->s * quaternion->s + quaternion->x * quaternion->x) + (quaternion->y * quaternion->y + quaternion->z * quaternion->z);
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}
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// ================ Get Modulus ================= //
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inline float bgc_fp32_quaternion_get_magnitude(const BGC_FP32_Quaternion* const quaternion)
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{
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return sqrtf(bgc_fp32_quaternion_get_square_magnitude(quaternion));
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}
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inline double bgc_fp64_quaternion_get_magnitude(const BGC_FP64_Quaternion* const quaternion)
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{
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return sqrt(bgc_fp64_quaternion_get_square_magnitude(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* const quaternion)
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{
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return bgc_fp32_quaternion_get_square_magnitude(quaternion) <= BGC_FP32_SQUARE_EPSILON;
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}
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inline int bgc_fp64_quaternion_is_zero(const BGC_FP64_Quaternion* const quaternion)
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{
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return bgc_fp64_quaternion_get_square_magnitude(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* const quaternion)
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{
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return bgc_fp32_is_square_unit(bgc_fp32_quaternion_get_square_magnitude(quaternion));
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}
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inline int bgc_fp64_quaternion_is_unit(const BGC_FP64_Quaternion* const quaternion)
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{
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return bgc_fp64_is_square_unit(bgc_fp64_quaternion_get_square_magnitude(quaternion));
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}
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// ================== Is Pure =================== //
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inline int bgc_fp32_quaternion_is_pure(const BGC_FP32_Quaternion* const quaternion)
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{
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return bgc_fp32_is_zero(quaternion->s);
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}
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inline int bgc_fp64_quaternion_is_pure(const BGC_FP64_Quaternion* const quaternion)
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{
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return bgc_fp64_is_zero(quaternion->s);
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}
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// ================== Is Real =================== //
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inline int bgc_fp32_quaternion_is_real(const BGC_FP32_Quaternion* const quaternion)
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{
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return quaternion->x * quaternion->x + quaternion->y * quaternion->y + quaternion->z * quaternion->z <= BGC_FP32_SQUARE_EPSILON;
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}
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inline int bgc_fp64_quaternion_is_real(const BGC_FP64_Quaternion* const quaternion)
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{
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return quaternion->x * quaternion->x + quaternion->y * quaternion->y + quaternion->z * quaternion->z <= BGC_FP64_SQUARE_EPSILON;
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}
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// ==================== Copy ==================== //
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inline void bgc_fp32_quaternion_copy(BGC_FP32_Quaternion* const destination, const BGC_FP32_Quaternion* const source)
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{
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destination->s = source->s;
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destination->x = source->x;
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destination->y = source->y;
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destination->z = source->z;
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}
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inline void bgc_fp64_quaternion_copy(BGC_FP64_Quaternion* const destination, const BGC_FP64_Quaternion* const source)
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{
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destination->s = source->s;
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destination->x = source->x;
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destination->y = source->y;
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destination->z = source->z;
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}
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// ==================== Swap ==================== //
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inline void bgc_fp32_quaternion_swap(BGC_FP32_Quaternion* const quarternion1, BGC_FP32_Quaternion* const quarternion2)
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{
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const float s = quarternion2->s;
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const float x = quarternion2->x;
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const float y = quarternion2->y;
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const float z = quarternion2->z;
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quarternion2->s = quarternion1->s;
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quarternion2->x = quarternion1->x;
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quarternion2->y = quarternion1->y;
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quarternion2->z = quarternion1->z;
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quarternion1->s = s;
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quarternion1->x = x;
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quarternion1->y = y;
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quarternion1->z = z;
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}
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inline void bgc_fp64_quaternion_swap(BGC_FP64_Quaternion* const quarternion1, BGC_FP64_Quaternion* const quarternion2)
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{
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const double s = quarternion2->s;
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const double x = quarternion2->x;
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const double y = quarternion2->y;
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const double z = quarternion2->z;
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quarternion2->s = quarternion1->s;
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quarternion2->x = quarternion1->x;
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quarternion2->y = quarternion1->y;
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quarternion2->z = quarternion1->z;
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quarternion1->s = s;
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quarternion1->x = x;
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quarternion1->y = y;
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quarternion1->z = z;
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}
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// ================== Convert =================== //
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inline void bgc_fp32_quaternion_convert_to_fp64(BGC_FP64_Quaternion* const destination, const BGC_FP32_Quaternion* const source)
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{
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destination->s = source->s;
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destination->x = source->x;
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destination->y = source->y;
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destination->z = source->z;
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}
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inline void bgc_fp64_quaternion_convert_to_fp32(BGC_FP32_Quaternion* const destination, const BGC_FP64_Quaternion* const source)
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{
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destination->s = (float)source->s;
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destination->x = (float)source->x;
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destination->y = (float)source->y;
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destination->z = (float)source->z;
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}
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// ==================== Add ===================== //
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inline void bgc_fp32_quaternion_add(BGC_FP32_Quaternion* const sum, const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2)
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{
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sum->s = quaternion1->s + quaternion2->s;
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sum->x = quaternion1->x + quaternion2->x;
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sum->y = quaternion1->y + quaternion2->y;
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sum->z = quaternion1->z + quaternion2->z;
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}
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inline void bgc_fp64_quaternion_add(BGC_FP64_Quaternion* const sum, const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2)
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{
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sum->s = quaternion1->s + quaternion2->s;
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sum->x = quaternion1->x + quaternion2->x;
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sum->y = quaternion1->y + quaternion2->y;
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sum->z = quaternion1->z + quaternion2->z;
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}
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// ================= Add Scaled ================= //
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inline void bgc_fp32_quaternion_add_scaled(BGC_FP32_Quaternion* const sum, const BGC_FP32_Quaternion* const basic_quaternion, const BGC_FP32_Quaternion* const scalable_quaternion, const float scale)
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{
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sum->s = basic_quaternion->s + scalable_quaternion->s * scale;
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sum->x = basic_quaternion->x + scalable_quaternion->x * scale;
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sum->y = basic_quaternion->y + scalable_quaternion->y * scale;
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sum->z = basic_quaternion->z + scalable_quaternion->z * scale;
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}
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inline void bgc_fp64_quaternion_add_scaled(BGC_FP64_Quaternion* const sum, const BGC_FP64_Quaternion* const basic_quaternion, const BGC_FP64_Quaternion* const scalable_quaternion, const double scale)
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{
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sum->s = basic_quaternion->s + scalable_quaternion->s * scale;
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sum->x = basic_quaternion->x + scalable_quaternion->x * scale;
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sum->y = basic_quaternion->y + scalable_quaternion->y * scale;
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sum->z = basic_quaternion->z + scalable_quaternion->z * scale;
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}
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// ================== Subtract ================== //
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inline void bgc_fp32_quaternion_subtract(BGC_FP32_Quaternion* const difference, const BGC_FP32_Quaternion* const minuend, const BGC_FP32_Quaternion* const subtrahend)
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{
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difference->s = minuend->s - subtrahend->s;
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difference->x = minuend->x - subtrahend->x;
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difference->y = minuend->y - subtrahend->y;
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difference->z = minuend->z - subtrahend->z;
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}
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inline void bgc_fp64_quaternion_subtract(BGC_FP64_Quaternion* const difference, const BGC_FP64_Quaternion* const minuend, const BGC_FP64_Quaternion* const subtrahend)
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{
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difference->s = minuend->s - subtrahend->s;
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difference->x = minuend->x - subtrahend->x;
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difference->y = minuend->y - subtrahend->y;
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difference->z = minuend->z - subtrahend->z;
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}
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// ============== Subtract Scaled =============== //
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inline void bgc_fp32_quaternion_subtract_scaled(BGC_FP32_Quaternion* const difference, const BGC_FP32_Quaternion* const basic_quaternion, const BGC_FP32_Quaternion* const scalable_quaternion, const float scale)
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{
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difference->s = basic_quaternion->s - scalable_quaternion->s * scale;
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difference->x = basic_quaternion->x - scalable_quaternion->x * scale;
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difference->y = basic_quaternion->y - scalable_quaternion->y * scale;
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difference->z = basic_quaternion->z - scalable_quaternion->z * scale;
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}
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inline void bgc_fp64_quaternion_subtract_scaled(BGC_FP64_Quaternion* const difference, const BGC_FP64_Quaternion* const basic_quaternion, const BGC_FP64_Quaternion* const scalable_quaternion, const double scale)
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{
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difference->s = basic_quaternion->s - scalable_quaternion->s * scale;
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difference->x = basic_quaternion->x - scalable_quaternion->x * scale;
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difference->y = basic_quaternion->y - scalable_quaternion->y * scale;
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difference->z = basic_quaternion->z - scalable_quaternion->z * scale;
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}
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// ============= Multiply By Number ============= //
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inline void bgc_fp32_quaternion_multiply_by_real_number(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const multiplicand, const float multiplier)
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{
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product->s = multiplicand->s * multiplier;
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product->x = multiplicand->x * multiplier;
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product->y = multiplicand->y * multiplier;
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product->z = multiplicand->z * multiplier;
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}
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inline void bgc_fp64_quaternion_multiply_by_real_number(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const multiplicand, const double multiplier)
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{
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product->s = multiplicand->s * multiplier;
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product->x = multiplicand->x * multiplier;
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product->y = multiplicand->y * multiplier;
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product->z = multiplicand->z * multiplier;
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}
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// ========== Multiply By Dual Number =========== //
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inline void bgc_fp32_quaternion_multiply_by_dual_number(BGC_FP32_DualQuaternion* const product, const BGC_FP32_Quaternion* const multiplicand, const BGC_FP32_DualNumber* const multiplier)
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{
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const float real_s = multiplicand->s * multiplier->real_part;
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const float real_x = multiplicand->x * multiplier->real_part;
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const float real_y = multiplicand->y * multiplier->real_part;
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const float real_z = multiplicand->z * multiplier->real_part;
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const float dual_s = multiplicand->s * multiplier->dual_part;
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const float dual_x = multiplicand->x * multiplier->dual_part;
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const float dual_y = multiplicand->y * multiplier->dual_part;
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const float dual_z = multiplicand->z * multiplier->dual_part;
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product->real_part.s = real_s;
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product->real_part.x = real_x;
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product->real_part.y = real_y;
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product->real_part.z = real_z;
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product->dual_part.s = dual_s;
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product->dual_part.x = dual_x;
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product->dual_part.y = dual_y;
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product->dual_part.z = dual_z;
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}
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inline void bgc_fp64_quaternion_multiply_by_dual_number(BGC_FP64_DualQuaternion* const product, const BGC_FP64_Quaternion* const multiplicand, const BGC_FP64_DualNumber* const multiplier)
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{
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const double real_s = multiplicand->s * multiplier->real_part;
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const double real_x = multiplicand->x * multiplier->real_part;
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const double real_y = multiplicand->y * multiplier->real_part;
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const double real_z = multiplicand->z * multiplier->real_part;
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const double dual_s = multiplicand->s * multiplier->dual_part;
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const double dual_x = multiplicand->x * multiplier->dual_part;
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const double dual_y = multiplicand->y * multiplier->dual_part;
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const double dual_z = multiplicand->z * multiplier->dual_part;
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product->real_part.s = real_s;
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product->real_part.x = real_x;
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product->real_part.y = real_y;
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product->real_part.z = real_z;
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product->dual_part.s = dual_s;
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product->dual_part.x = dual_x;
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product->dual_part.y = dual_y;
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product->dual_part.z = dual_z;
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}
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// =========== Multiply By Quaternion =========== //
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inline void bgc_fp32_quaternion_multiply_by_quaternion(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_Quaternion* const right)
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{
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const float s = (left->s * right->s - left->x * right->x) - (left->y * right->y + left->z * right->z);
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const float x = (left->x * right->s + left->s * right->x) - (left->z * right->y - left->y * right->z);
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const float y = (left->y * right->s + left->s * right->y) - (left->x * right->z - left->z * right->x);
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const float z = (left->z * right->s + left->s * right->z) - (left->y * right->x - left->x * right->y);
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product->s = s;
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product->x = x;
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product->y = y;
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product->z = z;
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}
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inline void bgc_fp64_quaternion_multiply_by_quaternion(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_Quaternion* const right)
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{
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const double s = (left->s * right->s - left->x * right->x) - (left->y * right->y + left->z * right->z);
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const double x = (left->x * right->s + left->s * right->x) - (left->z * right->y - left->y * right->z);
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const double y = (left->y * right->s + left->s * right->y) - (left->x * right->z - left->z * right->x);
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const double z = (left->z * right->s + left->s * right->z) - (left->y * right->x - left->x * right->y);
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product->s = s;
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product->x = x;
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product->y = y;
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product->z = z;
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}
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// ====== Multiply By Conjugate Quaternion ====== //
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inline void bgc_fp32_quaternion_multiply_by_conjugate(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_Quaternion* const right)
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{
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const float s = (left->s * right->s + left->x * right->x) + (left->y * right->y + left->z * right->z);
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const float x = (left->x * right->s + left->z * right->y) - (left->s * right->x + left->y * right->z);
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const float y = (left->y * right->s + left->x * right->z) - (left->s * right->y + left->z * right->x);
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const float z = (left->z * right->s + left->y * right->x) - (left->s * right->z + left->x * right->y);
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product->s = s;
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product->x = x;
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product->y = y;
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product->z = z;
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}
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inline void bgc_fp64_quaternion_multiply_by_conjugate(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_Quaternion* const right)
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{
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const double s = (left->s * right->s + left->x * right->x) + (left->y * right->y + left->z * right->z);
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const double x = (left->x * right->s + left->z * right->y) - (left->s * right->x + left->y * right->z);
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const double y = (left->y * right->s + left->x * right->z) - (left->s * right->y + left->z * right->x);
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const double z = (left->z * right->s + left->y * right->x) - (left->s * right->z + left->x * right->y);
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product->s = s;
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product->x = x;
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product->y = y;
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product->z = z;
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}
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// ====== Multiply Conjugate By Quaternion ====== //
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inline void bgc_fp32_conjugate_quaternion_multiply_by_quaternion(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_Quaternion* const right)
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{
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const float s = (left->s * right->s + left->x * right->x) + (left->y * right->y + left->z * right->z);
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const float x = (left->s * right->x - left->x * right->s) + (left->z * right->y - left->y * right->z);
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const float y = (left->s * right->y - left->y * right->s) + (left->x * right->z - left->z * right->x);
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const float z = (left->s * right->z - left->z * right->s) + (left->y * right->x - left->x * right->y);
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product->s = s;
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product->x = x;
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product->y = y;
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product->z = z;
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}
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inline void bgc_fp64_conjugate_quaternion_multiply_by_quaternion(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_Quaternion* const right)
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{
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const double s = (left->s * right->s + left->x * right->x) + (left->y * right->y + left->z * right->z);
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const double x = (left->s * right->x - left->x * right->s) + (left->z * right->y - left->y * right->z);
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const double y = (left->s * right->y - left->y * right->s) + (left->x * right->z - left->z * right->x);
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const double z = (left->s * right->z - left->z * right->s) + (left->y * right->x - left->x * right->y);
|
|
|
|
product->s = s;
|
|
product->x = x;
|
|
product->y = y;
|
|
product->z = z;
|
|
}
|
|
|
|
// ====== Multiply Conjugate By Conjugate ======= //
|
|
|
|
inline void bgc_fp32_conjugate_quaternion_multiply_by_conjugate(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_Quaternion* const right)
|
|
{
|
|
const float s = (left->s * right->s - left->x * right->x) - (left->y * right->y + left->z * right->z);
|
|
const float x = (left->y * right->z - left->z * right->y) - (left->x * right->s + left->s * right->x);
|
|
const float y = (left->z * right->x - left->x * right->z) - (left->y * right->s + left->s * right->y);
|
|
const float z = (left->x * right->y - left->y * right->x) - (left->z * right->s + left->s * right->z);
|
|
|
|
product->s = s;
|
|
product->x = x;
|
|
product->y = y;
|
|
product->z = z;
|
|
}
|
|
|
|
inline void bgc_fp64_conjugate_quaternion_multiply_by_conjugate(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_Quaternion* const right)
|
|
{
|
|
const double s = (left->s * right->s - left->x * right->x) - (left->y * right->y + left->z * right->z);
|
|
const double x = (left->y * right->z - left->z * right->y) - (left->x * right->s + left->s * right->x);
|
|
const double y = (left->z * right->x - left->x * right->z) - (left->y * right->s + left->s * right->y);
|
|
const double z = (left->x * right->y - left->y * right->x) - (left->z * right->s + left->s * right->z);
|
|
|
|
product->s = s;
|
|
product->x = x;
|
|
product->y = y;
|
|
product->z = z;
|
|
}
|
|
|
|
// ======== Multiply By Dual Quaternion ========= //
|
|
|
|
inline void bgc_fp32_quaternion_multiply_by_dual_quaternion(BGC_FP32_DualQuaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_DualQuaternion* const right)
|
|
{
|
|
bgc_fp32_quaternion_multiply_by_quaternion(&product->real_part, left, &right->real_part);
|
|
bgc_fp32_quaternion_multiply_by_quaternion(&product->dual_part, left, &right->dual_part);
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_multiply_by_dual_quaternion(BGC_FP64_DualQuaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_DualQuaternion* const right)
|
|
{
|
|
bgc_fp64_quaternion_multiply_by_quaternion(&product->real_part, left, &right->real_part);
|
|
bgc_fp64_quaternion_multiply_by_quaternion(&product->dual_part, left, &right->dual_part);
|
|
}
|
|
|
|
// ============== Divide By Number ============== //
|
|
|
|
inline int bgc_fp32_quaternion_divide_by_real_number(BGC_FP32_Quaternion* const quotient, const BGC_FP32_Quaternion* const dividend, const float divisor)
|
|
{
|
|
if (bgc_fp32_is_zero(divisor) || isnan(divisor)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
bgc_fp32_quaternion_multiply_by_real_number(quotient, dividend, 1.0f / divisor);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_divide_by_real_number(BGC_FP64_Quaternion* const quotient, const BGC_FP64_Quaternion* const dividend, const double divisor)
|
|
{
|
|
if (bgc_fp64_is_zero(divisor) || isnan(divisor)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
bgc_fp64_quaternion_multiply_by_real_number(quotient, dividend, 1.0 / divisor);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
// ============ Divide By Quaternion ============ //
|
|
|
|
inline int bgc_fp32_quaternion_divide_by_quaternion(BGC_FP32_Quaternion* const quotient, const BGC_FP32_Quaternion* const divident, const BGC_FP32_Quaternion* const divisor)
|
|
{
|
|
const float square_modulus = bgc_fp32_quaternion_get_square_magnitude(divisor);
|
|
|
|
if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
bgc_fp32_quaternion_multiply_by_conjugate(quotient, divident, divisor);
|
|
bgc_fp32_quaternion_multiply_by_real_number(quotient, quotient, 1.0f / square_modulus);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_divide_by_quaternion(BGC_FP64_Quaternion* const quotient, const BGC_FP64_Quaternion* const divident, const BGC_FP64_Quaternion* const divisor)
|
|
{
|
|
const double square_modulus = bgc_fp64_quaternion_get_square_magnitude(divisor);
|
|
|
|
if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
bgc_fp64_quaternion_multiply_by_conjugate(quotient, divident, divisor);
|
|
bgc_fp64_quaternion_multiply_by_real_number(quotient, quotient, 1.0 / square_modulus);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
// ======= Divide By Conjugate Quaternion ======= //
|
|
|
|
inline int bgc_fp32_quaternion_divide_by_conjugate(BGC_FP32_Quaternion* const quotient, const BGC_FP32_Quaternion* const divident, const BGC_FP32_Quaternion* const divisor_to_conjugate)
|
|
{
|
|
const float square_modulus = bgc_fp32_quaternion_get_square_magnitude(divisor_to_conjugate);
|
|
|
|
if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
bgc_fp32_quaternion_multiply_by_quaternion(quotient, divisor_to_conjugate, divisor_to_conjugate);
|
|
bgc_fp32_quaternion_multiply_by_real_number(quotient, quotient, 1.0f / square_modulus);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_divide_by_conjugate(BGC_FP64_Quaternion* const quotient, const BGC_FP64_Quaternion* const divident, const BGC_FP64_Quaternion* const divisor_to_conjugate)
|
|
{
|
|
const double square_modulus = bgc_fp64_quaternion_get_square_magnitude(divisor_to_conjugate);
|
|
|
|
if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
bgc_fp64_quaternion_multiply_by_quaternion(quotient, divisor_to_conjugate, divisor_to_conjugate);
|
|
bgc_fp64_quaternion_multiply_by_real_number(quotient, quotient, 1.0 / square_modulus);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
// ================ Mean of Two ================= //
|
|
|
|
inline void bgc_fp32_quaternion_get_mean2(BGC_FP32_Quaternion* const mean, const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2)
|
|
{
|
|
mean->s = (quaternion1->s + quaternion2->s) * 0.5f;
|
|
mean->x = (quaternion1->x + quaternion2->x) * 0.5f;
|
|
mean->y = (quaternion1->y + quaternion2->y) * 0.5f;
|
|
mean->z = (quaternion1->z + quaternion2->z) * 0.5f;
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_get_mean2(BGC_FP64_Quaternion* const mean, const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2)
|
|
{
|
|
mean->s = (quaternion1->s + quaternion2->s) * 0.5f;
|
|
mean->x = (quaternion1->x + quaternion2->x) * 0.5f;
|
|
mean->y = (quaternion1->y + quaternion2->y) * 0.5f;
|
|
mean->z = (quaternion1->z + quaternion2->z) * 0.5f;
|
|
}
|
|
|
|
// =============== Mean of Three ================ //
|
|
|
|
inline void bgc_fp32_quaternion_get_mean3(BGC_FP32_Quaternion* const mean, const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2, const BGC_FP32_Quaternion* const quaternion3)
|
|
{
|
|
mean->s = (quaternion1->s + quaternion2->s + quaternion3->s) * BGC_FP32_ONE_THIRD;
|
|
mean->x = (quaternion1->x + quaternion2->x + quaternion3->x) * BGC_FP32_ONE_THIRD;
|
|
mean->y = (quaternion1->y + quaternion2->y + quaternion3->y) * BGC_FP32_ONE_THIRD;
|
|
mean->z = (quaternion1->z + quaternion2->z + quaternion3->z) * BGC_FP32_ONE_THIRD;
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_get_mean3(BGC_FP64_Quaternion* const mean, const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2, const BGC_FP64_Quaternion* const quaternion3)
|
|
{
|
|
mean->s = (quaternion1->s + quaternion2->s + quaternion3->s) * BGC_FP64_ONE_THIRD;
|
|
mean->x = (quaternion1->x + quaternion2->x + quaternion3->x) * BGC_FP64_ONE_THIRD;
|
|
mean->y = (quaternion1->y + quaternion2->y + quaternion3->y) * BGC_FP64_ONE_THIRD;
|
|
mean->z = (quaternion1->z + quaternion2->z + quaternion3->z) * BGC_FP64_ONE_THIRD;
|
|
}
|
|
|
|
// ============ Linear Interpolation ============ //
|
|
|
|
inline void bgc_fp32_quaternion_interpolate(BGC_FP32_Quaternion* const interpolation, const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2, const float phase)
|
|
{
|
|
const float counter_phase = 1.0f - phase;
|
|
|
|
interpolation->s = quaternion1->s * counter_phase + quaternion2->s * phase;
|
|
interpolation->x = quaternion1->x * counter_phase + quaternion2->x * phase;
|
|
interpolation->y = quaternion1->y * counter_phase + quaternion2->y * phase;
|
|
interpolation->z = quaternion1->z * counter_phase + quaternion2->z * phase;
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_interpolate(BGC_FP64_Quaternion* const interpolation, const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2, const double phase)
|
|
{
|
|
const double counter_phase = 1.0 - phase;
|
|
|
|
interpolation->s = quaternion1->s * counter_phase + quaternion2->s * phase;
|
|
interpolation->x = quaternion1->x * counter_phase + quaternion2->x * phase;
|
|
interpolation->y = quaternion1->y * counter_phase + quaternion2->y * phase;
|
|
interpolation->z = quaternion1->z * counter_phase + quaternion2->z * phase;
|
|
}
|
|
|
|
// ============== Get Dot Product =============== //
|
|
|
|
inline float bgc_fp32_quaternion_get_dot_product(const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2)
|
|
{
|
|
return (quaternion1->s * quaternion2->s + quaternion1->x * quaternion2->x) + (quaternion1->y * quaternion2->y + quaternion1->z * quaternion2->z);
|
|
}
|
|
|
|
inline double bgc_fp64_quaternion_get_dot_product(const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2)
|
|
{
|
|
return (quaternion1->s * quaternion2->s + quaternion1->x * quaternion2->x) + (quaternion1->y * quaternion2->y + quaternion1->z * quaternion2->z);
|
|
}
|
|
|
|
// ================= Conjugate ================== //
|
|
|
|
inline void bgc_fp32_quaternion_conjugate(BGC_FP32_Quaternion* const quaternion)
|
|
{
|
|
quaternion->x = -quaternion->x;
|
|
quaternion->y = -quaternion->y;
|
|
quaternion->z = -quaternion->z;
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_conjugate(BGC_FP64_Quaternion* const quaternion)
|
|
{
|
|
quaternion->x = -quaternion->x;
|
|
quaternion->y = -quaternion->y;
|
|
quaternion->z = -quaternion->z;
|
|
}
|
|
|
|
inline void bgc_fp32_quaternion_get_conjugate(BGC_FP32_Quaternion* const conjugate, const BGC_FP32_Quaternion* const quaternion)
|
|
{
|
|
conjugate->s = quaternion->s;
|
|
conjugate->x = -quaternion->x;
|
|
conjugate->y = -quaternion->y;
|
|
conjugate->z = -quaternion->z;
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_get_conjugate(BGC_FP64_Quaternion* const conjugate, const BGC_FP64_Quaternion* const quaternion)
|
|
{
|
|
conjugate->s = quaternion->s;
|
|
conjugate->x = -quaternion->x;
|
|
conjugate->y = -quaternion->y;
|
|
conjugate->z = -quaternion->z;
|
|
}
|
|
|
|
// ================== Negative ================== //
|
|
|
|
inline void bgc_fp32_quaternion_revert(BGC_FP32_Quaternion* const quaternion)
|
|
{
|
|
quaternion->s = -quaternion->s;
|
|
quaternion->x = -quaternion->x;
|
|
quaternion->y = -quaternion->y;
|
|
quaternion->z = -quaternion->z;
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_revert(BGC_FP64_Quaternion* const quaternion)
|
|
{
|
|
quaternion->s = -quaternion->s;
|
|
quaternion->x = -quaternion->x;
|
|
quaternion->y = -quaternion->y;
|
|
quaternion->z = -quaternion->z;
|
|
}
|
|
|
|
inline void bgc_fp32_quaternion_get_reverse(BGC_FP32_Quaternion* const reverse, const BGC_FP32_Quaternion* const quaternion)
|
|
{
|
|
reverse->s = -quaternion->s;
|
|
reverse->x = -quaternion->x;
|
|
reverse->y = -quaternion->y;
|
|
reverse->z = -quaternion->z;
|
|
}
|
|
|
|
inline void bgc_fp64_quaternion_get_reverse(BGC_FP64_Quaternion* const reverse, const BGC_FP64_Quaternion* const quaternion)
|
|
{
|
|
reverse->s = -quaternion->s;
|
|
reverse->x = -quaternion->x;
|
|
reverse->y = -quaternion->y;
|
|
reverse->z = -quaternion->z;
|
|
}
|
|
|
|
// =================== Invert =================== //
|
|
|
|
inline int bgc_fp32_quaternion_get_inverse(BGC_FP32_Quaternion* const inverse, const BGC_FP32_Quaternion* const quaternion)
|
|
{
|
|
const float square_modulus = bgc_fp32_quaternion_get_square_magnitude(quaternion);
|
|
|
|
if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const float multiplicand = 1.0f / square_modulus;
|
|
|
|
inverse->s = quaternion->s * multiplicand;
|
|
inverse->x = -quaternion->x * multiplicand;
|
|
inverse->y = -quaternion->y * multiplicand;
|
|
inverse->z = -quaternion->z * multiplicand;
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_get_inverse(BGC_FP64_Quaternion* const inverse, const BGC_FP64_Quaternion* const quaternion)
|
|
{
|
|
const double square_modulus = bgc_fp64_quaternion_get_square_magnitude(quaternion);
|
|
|
|
if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const double multiplicand = 1.0 / square_modulus;
|
|
|
|
inverse->s = quaternion->s * multiplicand;
|
|
inverse->x = -quaternion->x * multiplicand;
|
|
inverse->y = -quaternion->y * multiplicand;
|
|
inverse->z = -quaternion->z * multiplicand;
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp32_quaternion_invert(BGC_FP32_Quaternion* const quaternion)
|
|
{
|
|
return bgc_fp32_quaternion_get_inverse(quaternion, quaternion);
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_invert(BGC_FP64_Quaternion* const quaternion)
|
|
{
|
|
return bgc_fp64_quaternion_get_inverse(quaternion, quaternion);
|
|
}
|
|
|
|
// ================= Normalize ================== //
|
|
|
|
inline int bgc_fp32_quaternion_normalize(BGC_FP32_Quaternion* const quaternion)
|
|
{
|
|
const float square_modulus = bgc_fp32_quaternion_get_square_magnitude(quaternion);
|
|
|
|
if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
if (bgc_fp32_is_square_unit(square_modulus)) {
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
const float multiplier = sqrtf(1.0f / square_modulus);
|
|
|
|
quaternion->s *= multiplier;
|
|
quaternion->x *= multiplier;
|
|
quaternion->y *= multiplier;
|
|
quaternion->z *= multiplier;
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_normalize(BGC_FP64_Quaternion* const quaternion)
|
|
{
|
|
const double square_modulus = bgc_fp64_quaternion_get_square_magnitude(quaternion);
|
|
|
|
if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
if (bgc_fp64_is_square_unit(square_modulus)) {
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
const double multiplier = sqrt(1.0 / square_modulus);
|
|
|
|
quaternion->s *= multiplier;
|
|
quaternion->x *= multiplier;
|
|
quaternion->y *= multiplier;
|
|
quaternion->z *= multiplier;
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp32_quaternion_get_normalized(BGC_FP32_Quaternion* const normalized, const BGC_FP32_Quaternion* const quaternion)
|
|
{
|
|
const float square_modulus = bgc_fp32_quaternion_get_square_magnitude(quaternion);
|
|
|
|
if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
bgc_fp32_quaternion_reset(normalized);
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
if (bgc_fp32_is_square_unit(square_modulus)) {
|
|
bgc_fp32_quaternion_copy(normalized, quaternion);
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
bgc_fp32_quaternion_multiply_by_real_number(normalized, quaternion, sqrtf(1.0f / square_modulus));
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_get_normalized(BGC_FP64_Quaternion* const normalized, const BGC_FP64_Quaternion* const quaternion)
|
|
{
|
|
const double square_modulus = bgc_fp64_quaternion_get_square_magnitude(quaternion);
|
|
|
|
if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
bgc_fp64_quaternion_reset(normalized);
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
if (bgc_fp64_is_square_unit(square_modulus)) {
|
|
bgc_fp64_quaternion_copy(normalized, quaternion);
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
bgc_fp64_quaternion_multiply_by_real_number(normalized, quaternion, sqrt(1.0 / square_modulus));
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
// =============== Get Exponation =============== //
|
|
|
|
int bgc_fp32_quaternion_get_power(BGC_FP32_Quaternion* const power, const BGC_FP32_Quaternion* const base, const float exponent);
|
|
|
|
int bgc_fp64_quaternion_get_power(BGC_FP64_Quaternion* const power, const BGC_FP64_Quaternion* const base, const double exponent);
|
|
|
|
// ============== Raw Turn Vector3 ============== //
|
|
|
|
// An internal function
|
|
inline void _bgc_fp32_versor_turn_vector(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Vector3* const original_vector)
|
|
{
|
|
const float tx = 2.0f * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
|
|
const float ty = 2.0f * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
|
|
const float tz = 2.0f * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);
|
|
|
|
const float x = (original_vector->x + tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
|
|
const float y = (original_vector->y + ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
|
|
const float z = (original_vector->z + tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);
|
|
|
|
turned_vector->x = x;
|
|
turned_vector->y = y;
|
|
turned_vector->z = z;
|
|
}
|
|
|
|
// An internal function
|
|
inline void _bgc_fp64_versor_turn_vector(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Vector3* const original_vector)
|
|
{
|
|
const double tx = 2.0f * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
|
|
const double ty = 2.0f * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
|
|
const double tz = 2.0f * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);
|
|
|
|
const double x = (original_vector->x + tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
|
|
const double y = (original_vector->y + ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
|
|
const double z = (original_vector->z + tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);
|
|
|
|
turned_vector->x = x;
|
|
turned_vector->y = y;
|
|
turned_vector->z = z;
|
|
}
|
|
|
|
// ========= Raw Turn Vector3 Backwards ========= //
|
|
|
|
// An internal function
|
|
inline void _bgc_fp32_versor_turn_vector_back(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Vector3* const original_vector)
|
|
{
|
|
const float tx = 2.0f * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
|
|
const float ty = 2.0f * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
|
|
const float tz = 2.0f * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);
|
|
|
|
const float x = (original_vector->x + tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
|
|
const float y = (original_vector->y + ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
|
|
const float z = (original_vector->z + tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);
|
|
|
|
turned_vector->x = x;
|
|
turned_vector->y = y;
|
|
turned_vector->z = z;
|
|
}
|
|
|
|
// An internal function
|
|
inline void _bgc_fp64_versor_turn_vector_back(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Vector3* const original_vector)
|
|
{
|
|
const double tx = 2.0f * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
|
|
const double ty = 2.0f * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
|
|
const double tz = 2.0f * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);
|
|
|
|
const double x = (original_vector->x + tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
|
|
const double y = (original_vector->y + ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
|
|
const double z = (original_vector->z + tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);
|
|
|
|
turned_vector->x = x;
|
|
turned_vector->y = y;
|
|
turned_vector->z = z;
|
|
}
|
|
|
|
// ================ Turn Vector3 ================ //
|
|
|
|
inline int bgc_fp32_quaternion_turn_vector(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Vector3* const original_vector)
|
|
{
|
|
const float square_modulus = bgc_fp32_quaternion_get_square_magnitude(quaternion);
|
|
|
|
if (square_modulus < BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const float multiplier = 2.0f / square_modulus;
|
|
|
|
const float tx = multiplier * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
|
|
const float ty = multiplier * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
|
|
const float tz = multiplier * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);
|
|
|
|
const float x = (original_vector->x + tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
|
|
const float y = (original_vector->y + ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
|
|
const float z = (original_vector->z + tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);
|
|
|
|
turned_vector->x = x;
|
|
turned_vector->y = y;
|
|
turned_vector->z = z;
|
|
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_turn_vector(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Vector3* const original_vector)
|
|
{
|
|
const double square_modulus = bgc_fp64_quaternion_get_square_magnitude(quaternion);
|
|
|
|
if (square_modulus < BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const double multiplier = 2.0 / square_modulus;
|
|
|
|
const double tx = multiplier * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
|
|
const double ty = multiplier * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
|
|
const double tz = multiplier * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);
|
|
|
|
const double x = (original_vector->x + tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
|
|
const double y = (original_vector->y + ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
|
|
const double z = (original_vector->z + tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);
|
|
|
|
turned_vector->x = x;
|
|
turned_vector->y = y;
|
|
turned_vector->z = z;
|
|
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
// =========== Turn Vector3 Backwards =========== //
|
|
|
|
inline int bgc_fp32_quaternion_turn_vector_back(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Vector3* const original_vector)
|
|
{
|
|
const float square_modulus = bgc_fp32_quaternion_get_square_magnitude(quaternion);
|
|
|
|
if (square_modulus < BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const float multiplier = 2.0f / square_modulus;
|
|
|
|
const float tx = multiplier * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
|
|
const float ty = multiplier * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
|
|
const float tz = multiplier * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);
|
|
|
|
const float x = (original_vector->x - tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
|
|
const float y = (original_vector->y - ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
|
|
const float z = (original_vector->z - tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);
|
|
|
|
turned_vector->x = x;
|
|
turned_vector->y = y;
|
|
turned_vector->z = z;
|
|
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_turn_vector_back(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Vector3* const original_vector)
|
|
{
|
|
const double square_modulus = bgc_fp64_quaternion_get_square_magnitude(quaternion);
|
|
|
|
if (square_modulus < BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const double multiplier = 2.0 / square_modulus;
|
|
|
|
const double tx = multiplier * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
|
|
const double ty = multiplier * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
|
|
const double tz = multiplier * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);
|
|
|
|
const double x = (original_vector->x - tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
|
|
const double y = (original_vector->y - ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
|
|
const double z = (original_vector->z - tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);
|
|
|
|
turned_vector->x = x;
|
|
turned_vector->y = y;
|
|
turned_vector->z = z;
|
|
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
// ========= Get Versor Rotation Matrix ========= //
|
|
|
|
inline void _bgc_fp32_versor_get_rotation_matrix(BGC_FP32_Matrix3x3* const matrix, const BGC_FP32_Quaternion* const versor)
|
|
{
|
|
const float ss = versor->s * versor->s;
|
|
const float xx = versor->x * versor->x;
|
|
const float yy = versor->y * versor->y;
|
|
const float zz = versor->z * versor->z;
|
|
|
|
const float sx = versor->s * versor->x;
|
|
const float sy = versor->s * versor->y;
|
|
const float sz = versor->s * versor->z;
|
|
|
|
const float xy = versor->x * versor->y;
|
|
const float xz = versor->x * versor->z;
|
|
|
|
const float yz = versor->y * versor->z;
|
|
|
|
matrix->r1c1 = ((ss + xx) - (yy + zz));
|
|
matrix->r2c2 = ((ss + yy) - (xx + zz));
|
|
matrix->r3c3 = ((ss + zz) - (xx + yy));
|
|
|
|
matrix->r1c2 = 2.0f * (xy - sz);
|
|
matrix->r2c3 = 2.0f * (yz - sx);
|
|
matrix->r3c1 = 2.0f * (xz - sy);
|
|
|
|
matrix->r2c1 = 2.0f * (xy + sz);
|
|
matrix->r3c2 = 2.0f * (yz + sx);
|
|
matrix->r1c3 = 2.0f * (xz + sy);
|
|
}
|
|
|
|
inline void _bgc_fp64_versor_get_rotation_matrix(BGC_FP64_Matrix3x3* const matrix, const BGC_FP64_Quaternion* const versor)
|
|
{
|
|
const double ss = versor->s * versor->s;
|
|
const double xx = versor->x * versor->x;
|
|
const double yy = versor->y * versor->y;
|
|
const double zz = versor->z * versor->z;
|
|
|
|
const double sx = versor->s * versor->x;
|
|
const double sy = versor->s * versor->y;
|
|
const double sz = versor->s * versor->z;
|
|
|
|
const double xy = versor->x * versor->y;
|
|
const double xz = versor->x * versor->z;
|
|
|
|
const double yz = versor->y * versor->z;
|
|
|
|
matrix->r1c1 = ((ss + xx) - (yy + zz));
|
|
matrix->r2c2 = ((ss + yy) - (xx + zz));
|
|
matrix->r3c3 = ((ss + zz) - (xx + yy));
|
|
|
|
matrix->r1c2 = 2.0 * (xy - sz);
|
|
matrix->r2c3 = 2.0 * (yz - sx);
|
|
matrix->r3c1 = 2.0 * (xz - sy);
|
|
|
|
matrix->r2c1 = 2.0 * (xy + sz);
|
|
matrix->r3c2 = 2.0 * (yz + sx);
|
|
matrix->r1c3 = 2.0 * (xz + sy);
|
|
}
|
|
|
|
// ========= Get Versor Reverse Matrix ========== //
|
|
|
|
inline void _bgc_fp32_versor_get_reverse_matrix(BGC_FP32_Matrix3x3* const matrix, const BGC_FP32_Quaternion* const versor)
|
|
{
|
|
const float ss = versor->s * versor->s;
|
|
const float xx = versor->x * versor->x;
|
|
const float yy = versor->y * versor->y;
|
|
const float zz = versor->z * versor->z;
|
|
|
|
const float sx = versor->s * versor->x;
|
|
const float sy = versor->s * versor->y;
|
|
const float sz = versor->s * versor->z;
|
|
|
|
const float xy = versor->x * versor->y;
|
|
const float xz = versor->x * versor->z;
|
|
|
|
const float yz = versor->y * versor->z;
|
|
|
|
matrix->r1c1 = ((ss + xx) - (yy + zz));
|
|
matrix->r2c2 = ((ss + yy) - (xx + zz));
|
|
matrix->r3c3 = ((ss + zz) - (xx + yy));
|
|
|
|
matrix->r1c2 = 2.0f * (xy + sz);
|
|
matrix->r2c3 = 2.0f * (yz + sx);
|
|
matrix->r3c1 = 2.0f * (xz + sy);
|
|
|
|
matrix->r2c1 = 2.0f * (xy - sz);
|
|
matrix->r3c2 = 2.0f * (yz - sx);
|
|
matrix->r1c3 = 2.0f * (xz - sy);
|
|
}
|
|
|
|
inline void _bgc_fp64_versor_get_reverse_matrix(BGC_FP64_Matrix3x3* const matrix, const BGC_FP64_Quaternion* const versor)
|
|
{
|
|
const double ss = versor->s * versor->s;
|
|
const double xx = versor->x * versor->x;
|
|
const double yy = versor->y * versor->y;
|
|
const double zz = versor->z * versor->z;
|
|
|
|
const double sx = versor->s * versor->x;
|
|
const double sy = versor->s * versor->y;
|
|
const double sz = versor->s * versor->z;
|
|
|
|
const double xy = versor->x * versor->y;
|
|
const double xz = versor->x * versor->z;
|
|
|
|
const double yz = versor->y * versor->z;
|
|
|
|
matrix->r1c1 = ((ss + xx) - (yy + zz));
|
|
matrix->r2c2 = ((ss + yy) - (xx + zz));
|
|
matrix->r3c3 = ((ss + zz) - (xx + yy));
|
|
|
|
matrix->r1c2 = 2.0 * (xy + sz);
|
|
matrix->r2c3 = 2.0 * (yz + sx);
|
|
matrix->r3c1 = 2.0 * (xz + sy);
|
|
|
|
matrix->r2c1 = 2.0 * (xy - sz);
|
|
matrix->r3c2 = 2.0 * (yz - sx);
|
|
matrix->r1c3 = 2.0 * (xz - sy);
|
|
}
|
|
|
|
// ============ Get Rotation Matrix ============= //
|
|
|
|
inline int bgc_fp32_quaternion_get_rotation_matrix(BGC_FP32_Matrix3x3* const rotation, const BGC_FP32_Quaternion* const quaternion)
|
|
{
|
|
const float ss = quaternion->s * quaternion->s;
|
|
const float xx = quaternion->x * quaternion->x;
|
|
const float yy = quaternion->y * quaternion->y;
|
|
const float zz = quaternion->z * quaternion->z;
|
|
|
|
const float square_modulus = (ss + xx) + (yy + zz);
|
|
|
|
if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus))
|
|
{
|
|
bgc_fp32_matrix3x3_make_identity(rotation);
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const float corrector1 = 1.0f / square_modulus;
|
|
|
|
const float sx = quaternion->s * quaternion->x;
|
|
const float sy = quaternion->s * quaternion->y;
|
|
const float sz = quaternion->s * quaternion->z;
|
|
const float xy = quaternion->x * quaternion->y;
|
|
const float xz = quaternion->x * quaternion->z;
|
|
const float yz = quaternion->y * quaternion->z;
|
|
|
|
const float corrector2 = 2.0f * corrector1;
|
|
|
|
rotation->r1c1 = corrector1 * ((ss + xx) - (yy + zz));
|
|
rotation->r2c2 = corrector1 * ((ss + yy) - (xx + zz));
|
|
rotation->r3c3 = corrector1 * ((ss + zz) - (xx + yy));
|
|
|
|
rotation->r1c2 = corrector2 * (xy - sz);
|
|
rotation->r2c3 = corrector2 * (yz - sx);
|
|
rotation->r3c1 = corrector2 * (xz - sy);
|
|
|
|
rotation->r2c1 = corrector2 * (xy + sz);
|
|
rotation->r3c2 = corrector2 * (yz + sx);
|
|
rotation->r1c3 = corrector2 * (xz + sy);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_get_rotation_matrix(BGC_FP64_Matrix3x3* const rotation, const BGC_FP64_Quaternion* const quaternion)
|
|
{
|
|
const double ss = quaternion->s * quaternion->s;
|
|
const double xx = quaternion->x * quaternion->x;
|
|
const double yy = quaternion->y * quaternion->y;
|
|
const double zz = quaternion->z * quaternion->z;
|
|
|
|
const double square_modulus = (ss + xx) + (yy + zz);
|
|
|
|
if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus))
|
|
{
|
|
bgc_fp64_matrix3x3_make_identity(rotation);
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const double corrector1 = 1.0f / square_modulus;
|
|
|
|
const double sx = quaternion->s * quaternion->x;
|
|
const double sy = quaternion->s * quaternion->y;
|
|
const double sz = quaternion->s * quaternion->z;
|
|
const double xy = quaternion->x * quaternion->y;
|
|
const double xz = quaternion->x * quaternion->z;
|
|
const double yz = quaternion->y * quaternion->z;
|
|
|
|
const double corrector2 = 2.0f * corrector1;
|
|
|
|
rotation->r1c1 = corrector1 * ((ss + xx) - (yy + zz));
|
|
rotation->r2c2 = corrector1 * ((ss + yy) - (xx + zz));
|
|
rotation->r3c3 = corrector1 * ((ss + zz) - (xx + yy));
|
|
|
|
rotation->r1c2 = corrector2 * (xy - sz);
|
|
rotation->r2c3 = corrector2 * (yz - sx);
|
|
rotation->r3c1 = corrector2 * (xz - sy);
|
|
|
|
rotation->r2c1 = corrector2 * (xy + sz);
|
|
rotation->r3c2 = corrector2 * (yz + sx);
|
|
rotation->r1c3 = corrector2 * (xz + sy);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
// ============= Get Reverse Matrix ============= //
|
|
|
|
inline int bgc_fp32_quaternion_get_reverse_matrix(BGC_FP32_Matrix3x3* const reverse, const BGC_FP32_Quaternion* const quaternion)
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{
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const float ss = quaternion->s * quaternion->s;
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const float xx = quaternion->x * quaternion->x;
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const float yy = quaternion->y * quaternion->y;
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const float zz = quaternion->z * quaternion->z;
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const float square_modulus = (ss + xx) + (yy + zz);
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if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus))
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{
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bgc_fp32_matrix3x3_make_identity(reverse);
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return BGC_FAILURE;
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}
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const float corrector1 = 1.0f / square_modulus;
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const float sx = quaternion->s * quaternion->x;
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const float sy = quaternion->s * quaternion->y;
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const float sz = quaternion->s * quaternion->z;
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const float xy = quaternion->x * quaternion->y;
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const float xz = quaternion->x * quaternion->z;
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const float yz = quaternion->y * quaternion->z;
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const float corrector2 = 2.0f * corrector1;
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reverse->r1c1 = corrector1 * ((ss + xx) - (yy + zz));
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reverse->r2c2 = corrector1 * ((ss + yy) - (xx + zz));
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reverse->r3c3 = corrector1 * ((ss + zz) - (xx + yy));
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reverse->r1c2 = corrector2 * (xy + sz);
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reverse->r2c3 = corrector2 * (yz + sx);
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reverse->r3c1 = corrector2 * (xz + sy);
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reverse->r2c1 = corrector2 * (xy - sz);
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reverse->r3c2 = corrector2 * (yz - sx);
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reverse->r1c3 = corrector2 * (xz - sy);
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return BGC_SUCCESS;
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}
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inline int bgc_fp64_quaternion_get_reverse_matrix(BGC_FP64_Matrix3x3* const reverse, const BGC_FP64_Quaternion* const quaternion)
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{
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const double ss = quaternion->s * quaternion->s;
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const double xx = quaternion->x * quaternion->x;
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const double yy = quaternion->y * quaternion->y;
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const double zz = quaternion->z * quaternion->z;
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const double square_modulus = (ss + xx) + (yy + zz);
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if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus))
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{
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bgc_fp64_matrix3x3_make_identity(reverse);
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return BGC_FAILURE;
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}
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const double corrector1 = 1.0f / square_modulus;
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|
|
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const double sx = quaternion->s * quaternion->x;
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const double sy = quaternion->s * quaternion->y;
|
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const double sz = quaternion->s * quaternion->z;
|
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const double xy = quaternion->x * quaternion->y;
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const double xz = quaternion->x * quaternion->z;
|
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const double yz = quaternion->y * quaternion->z;
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|
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const double corrector2 = 2.0f * corrector1;
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|
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reverse->r1c1 = corrector1 * ((ss + xx) - (yy + zz));
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reverse->r2c2 = corrector1 * ((ss + yy) - (xx + zz));
|
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reverse->r3c3 = corrector1 * ((ss + zz) - (xx + yy));
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|
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reverse->r1c2 = corrector2 * (xy + sz);
|
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reverse->r2c3 = corrector2 * (yz + sx);
|
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reverse->r3c1 = corrector2 * (xz + sy);
|
|
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reverse->r2c1 = corrector2 * (xy - sz);
|
|
reverse->r3c2 = corrector2 * (yz - sx);
|
|
reverse->r1c3 = corrector2 * (xz - sy);
|
|
|
|
return BGC_SUCCESS;
|
|
}
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|
|
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// ============= Get Both Matrixes ============== //
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|
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|
inline int bgc_fp32_quaternion_get_both_matrices(BGC_FP32_Matrix3x3* const rotation, BGC_FP32_Matrix3x3* const reverse, const BGC_FP32_Quaternion* const quaternion)
|
|
{
|
|
if (bgc_fp32_quaternion_get_reverse_matrix(reverse, quaternion) != BGC_SUCCESS) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
bgc_fp32_matrix3x3_get_transposed(rotation, reverse);
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_quaternion_get_both_matrices(BGC_FP64_Matrix3x3* const rotation, BGC_FP64_Matrix3x3* const reverse, const BGC_FP64_Quaternion* const quaternion)
|
|
{
|
|
if (bgc_fp64_quaternion_get_reverse_matrix(reverse, quaternion) != BGC_SUCCESS) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
bgc_fp64_matrix3x3_get_transposed(rotation, reverse);
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
// ================== Are Close ================= //
|
|
|
|
inline int bgc_fp32_quaternion_are_close(const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2)
|
|
{
|
|
const float ds = quaternion1->s - quaternion2->s;
|
|
const float dx = quaternion1->x - quaternion2->x;
|
|
const float dy = quaternion1->y - quaternion2->y;
|
|
const float dz = quaternion1->z - quaternion2->z;
|
|
|
|
const float square_modulus1 = bgc_fp32_quaternion_get_square_magnitude(quaternion1);
|
|
const float square_modulus2 = bgc_fp32_quaternion_get_square_magnitude(quaternion2);
|
|
const float square_distance = (ds * ds + dx * dx) + (dy * dy + dz * dz);
|
|
|
|
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* const quaternion1, const BGC_FP64_Quaternion* const quaternion2)
|
|
{
|
|
const double ds = quaternion1->s - quaternion2->s;
|
|
const double dx = quaternion1->x - quaternion2->x;
|
|
const double dy = quaternion1->y - quaternion2->y;
|
|
const double dz = quaternion1->z - quaternion2->z;
|
|
|
|
const double square_modulus1 = bgc_fp64_quaternion_get_square_magnitude(quaternion1);
|
|
const double square_modulus2 = bgc_fp64_quaternion_get_square_magnitude(quaternion2);
|
|
const double square_distance = (ds * ds + dx * dx) + (dy * dy + dz * dz);
|
|
|
|
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
|