538 lines
18 KiB
C
538 lines
18 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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} BgcQuaternionFP32;
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typedef struct {
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double s0, x1, x2, x3;
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} BgcQuaternionFP64;
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// ==================== Reset =================== //
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inline void bgc_quaternion_reset_fp32(BgcQuaternionFP32 * 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_quaternion_reset_fp64(BgcQuaternionFP64 * 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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// ================== Set Unit ================== //
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inline void bgc_quaternion_set_to_identity_fp32(BgcQuaternionFP32 * 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_quaternion_set_to_identity_fp64(BgcQuaternionFP64 * 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_quaternion_set_values_fp32(const float s0, const float x1, const float x2, const float x3, BgcQuaternionFP32 * quaternion)
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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_quaternion_set_values_fp64(const double s0, const double x1, const double x2, const double x3, BgcQuaternionFP64 * quaternion)
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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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// ==================== Copy ==================== //
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inline void bgc_quaternion_copy_fp32(const BgcQuaternionFP32* from, BgcQuaternionFP32* to)
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{
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to->s0 = from->s0;
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to->x1 = from->x1;
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to->x2 = from->x2;
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to->x3 = from->x3;
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}
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inline void bgc_quaternion_copy_fp64(const BgcQuaternionFP64* from, BgcQuaternionFP64* to)
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{
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to->s0 = from->s0;
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to->x1 = from->x1;
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to->x2 = from->x2;
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to->x3 = from->x3;
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}
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// ==================== Swap ==================== //
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inline void bgc_quaternion_swap_fp32(BgcQuaternionFP32* quarternion1, BgcQuaternionFP32* 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_quaternion_swap_fp64(BgcQuaternionFP64* quarternion1, BgcQuaternionFP64* 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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// ============= Copy to twin type ============== //
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inline void bgc_quaternion_convert_fp64_to_fp32(const BgcQuaternionFP64* quaternion, BgcQuaternionFP32* result)
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{
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result->s0 = (float) quaternion->s0;
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result->x1 = (float) quaternion->x1;
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result->x2 = (float) quaternion->x2;
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result->x3 = (float) quaternion->x3;
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}
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inline void bgc_quaternion_convert_fp32_to_fp64(const BgcQuaternionFP32* quaternion, BgcQuaternionFP64* result)
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{
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result->s0 = quaternion->s0;
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result->x1 = quaternion->x1;
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result->x2 = quaternion->x2;
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result->x3 = quaternion->x3;
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}
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// ================= Inversion ================== //
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inline void bgc_quaternion_conjugate_fp32(BgcQuaternionFP32* quaternion)
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{
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quaternion->x1 = -quaternion->x1;
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quaternion->x2 = -quaternion->x2;
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quaternion->x3 = -quaternion->x3;
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}
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inline void bgc_quaternion_conjugate_fp64(BgcQuaternionFP64* quaternion)
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{
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quaternion->x1 = -quaternion->x1;
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quaternion->x2 = -quaternion->x2;
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quaternion->x3 = -quaternion->x3;
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}
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// ================ Set Conjugate =============== //
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inline void bgc_quaternion_set_conjugate_fp32(const BgcQuaternionFP32* quaternion, BgcQuaternionFP32* result)
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{
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result->s0 = quaternion->s0;
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result->x1 = -quaternion->x1;
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result->x2 = -quaternion->x2;
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result->x3 = -quaternion->x3;
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}
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inline void bgc_quaternion_set_conjugate_fp64(const BgcQuaternionFP64* quaternion, BgcQuaternionFP64* result)
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{
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result->s0 = quaternion->s0;
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result->x1 = -quaternion->x1;
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result->x2 = -quaternion->x2;
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result->x3 = -quaternion->x3;
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}
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// ================ Set Conjugate =============== //
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inline void bgc_quaternion_set_conjugate_fp64_to_fp32(const BgcQuaternionFP64* quaternion, BgcQuaternionFP32* result)
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{
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result->s0 = (float) quaternion->s0;
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result->x1 = (float) -quaternion->x1;
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result->x2 = (float) -quaternion->x2;
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result->x3 = (float) -quaternion->x3;
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}
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inline void bgc_quaternion_set_conjugate_fp32_to_fp64(const BgcQuaternionFP32* quaternion, BgcQuaternionFP64* result)
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{
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result->s0 = quaternion->s0;
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result->x1 = -quaternion->x1;
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result->x2 = -quaternion->x2;
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result->x3 = -quaternion->x3;
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}
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// ============= Get Square Modulus ============= //
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inline float bgc_quaternion_get_square_modulus_fp32(const BgcQuaternionFP32* 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_quaternion_get_square_modulus_fp64(const BgcQuaternionFP64* 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_quaternion_get_modulus_fp32(const BgcQuaternionFP32* quaternion)
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{
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return sqrtf(bgc_quaternion_get_square_modulus_fp32(quaternion));
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}
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inline double bgc_quaternion_get_modulus_fp64(const BgcQuaternionFP64* quaternion)
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{
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return sqrt(bgc_quaternion_get_square_modulus_fp64(quaternion));
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}
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// =============== Normalization ================ //
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inline int bgc_quaternion_normalize_fp32(BgcQuaternionFP32* quaternion)
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{
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const float square_modulus = bgc_quaternion_get_square_modulus_fp32(quaternion);
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if (1.0f - BGC_TWO_EPSYLON_FP32 <= square_modulus && square_modulus <= 1.0f + BGC_TWO_EPSYLON_FP32) {
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return 1;
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}
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if (square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
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bgc_quaternion_reset_fp32(quaternion);
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return 0;
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}
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const float multiplier = sqrtf(1.0f / square_modulus);
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quaternion->s0 *= multiplier;
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quaternion->x1 *= multiplier;
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quaternion->x2 *= multiplier;
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quaternion->x3 *= multiplier;
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return 1;
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}
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inline int bgc_quaternion_normalize_fp64(BgcQuaternionFP64* quaternion)
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{
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const double square_modulus = bgc_quaternion_get_square_modulus_fp64(quaternion);
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if (1.0 - BGC_TWO_EPSYLON_FP64 <= square_modulus && square_modulus <= 1.0 + BGC_TWO_EPSYLON_FP64) {
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return 1;
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}
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if (square_modulus <= BGC_SQUARE_EPSYLON_FP32) {
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bgc_quaternion_reset_fp64(quaternion);
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return 0;
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}
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const double multiplier = sqrt(1.0 / square_modulus);
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quaternion->s0 *= multiplier;
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quaternion->x1 *= multiplier;
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quaternion->x2 *= multiplier;
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quaternion->x3 *= multiplier;
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return 1;
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}
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// ============ Make Rotation Matrix ============ //
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inline void bgc_quaternion_get_rotation_matrix_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* matrix)
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{
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const float s0s0 = quaternion->s0 * quaternion->s0;
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const float x1x1 = quaternion->x1 * quaternion->x1;
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const float x2x2 = quaternion->x2 * quaternion->x2;
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const float x3x3 = quaternion->x3 * quaternion->x3;
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const float square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);
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if (-BGC_EPSYLON_FP32 <= square_modulus && square_modulus <= BGC_EPSYLON_FP32)
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{
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bgc_matrix3x3_set_to_identity_fp32(matrix);
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return;
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}
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const float corrector1 = 1.0f / square_modulus;
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const float corrector2 = 2.0f * corrector1;
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const float s0x1 = quaternion->s0 * quaternion->x1;
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const float s0x2 = quaternion->s0 * quaternion->x2;
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const float s0x3 = quaternion->s0 * quaternion->x3;
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const float x1x2 = quaternion->x1 * quaternion->x2;
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const float x1x3 = quaternion->x1 * quaternion->x3;
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const float x2x3 = quaternion->x2 * quaternion->x3;
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matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
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matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
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matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
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matrix->r1c2 = corrector2 * (x1x2 - s0x3);
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matrix->r2c3 = corrector2 * (x2x3 - s0x1);
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matrix->r3c1 = corrector2 * (x1x3 - s0x2);
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matrix->r2c1 = corrector2 * (x1x2 + s0x3);
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matrix->r3c2 = corrector2 * (x2x3 + s0x1);
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matrix->r1c3 = corrector2 * (x1x3 + s0x2);
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}
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inline void bgc_quaternion_get_rotation_matrix_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* matrix)
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{
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const double s0s0 = quaternion->s0 * quaternion->s0;
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const double x1x1 = quaternion->x1 * quaternion->x1;
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const double x2x2 = quaternion->x2 * quaternion->x2;
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const double x3x3 = quaternion->x3 * quaternion->x3;
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const double square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);
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if (-BGC_EPSYLON_FP64 <= square_modulus && square_modulus <= BGC_EPSYLON_FP64)
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{
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bgc_matrix3x3_set_to_identity_fp64(matrix);
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return;
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}
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const double corrector1 = 1.0f / square_modulus;
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const double corrector2 = 2.0f * corrector1;
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const double s0x1 = quaternion->s0 * quaternion->x1;
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const double s0x2 = quaternion->s0 * quaternion->x2;
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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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matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
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matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
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matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
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matrix->r1c2 = corrector2 * (x1x2 - s0x3);
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matrix->r2c3 = corrector2 * (x2x3 - s0x1);
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matrix->r3c1 = corrector2 * (x1x3 - s0x2);
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matrix->r2c1 = corrector2 * (x1x2 + s0x3);
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matrix->r3c2 = corrector2 * (x2x3 + s0x1);
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matrix->r1c3 = corrector2 * (x1x3 + s0x2);
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}
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// ============ Make Reverse Matrix ============= //
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inline void bgc_quaternion_get_reverse_matrix_fp32(const BgcQuaternionFP32* quaternion, BgcMatrix3x3FP32* matrix)
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{
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const float s0s0 = quaternion->s0 * quaternion->s0;
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const float x1x1 = quaternion->x1 * quaternion->x1;
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const float x2x2 = quaternion->x2 * quaternion->x2;
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const float x3x3 = quaternion->x3 * quaternion->x3;
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const float square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);
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if (-BGC_EPSYLON_FP32 <= square_modulus && square_modulus <= BGC_EPSYLON_FP32)
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{
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bgc_matrix3x3_set_to_identity_fp32(matrix);
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return;
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}
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const float corrector1 = 1.0f / square_modulus;
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const float corrector2 = 2.0f * corrector1;
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const float s0x1 = quaternion->s0 * quaternion->x1;
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const float s0x2 = quaternion->s0 * quaternion->x2;
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const float s0x3 = quaternion->s0 * quaternion->x3;
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const float x1x2 = quaternion->x1 * quaternion->x2;
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const float x1x3 = quaternion->x1 * quaternion->x3;
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const float x2x3 = quaternion->x2 * quaternion->x3;
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matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
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matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
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matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
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matrix->r1c2 = corrector2 * (x1x2 + s0x3);
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matrix->r2c3 = corrector2 * (x2x3 + s0x1);
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matrix->r3c1 = corrector2 * (x1x3 + s0x2);
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matrix->r2c1 = corrector2 * (x1x2 - s0x3);
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matrix->r3c2 = corrector2 * (x2x3 - s0x1);
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matrix->r1c3 = corrector2 * (x1x3 - s0x2);
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}
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inline void bgc_quaternion_get_reverse_matrix_fp64(const BgcQuaternionFP64* quaternion, BgcMatrix3x3FP64* matrix)
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{
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const double s0s0 = quaternion->s0 * quaternion->s0;
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const double x1x1 = quaternion->x1 * quaternion->x1;
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const double x2x2 = quaternion->x2 * quaternion->x2;
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const double x3x3 = quaternion->x3 * quaternion->x3;
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const double square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);
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if (-BGC_EPSYLON_FP64 <= square_modulus && square_modulus <= BGC_EPSYLON_FP64)
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{
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bgc_matrix3x3_set_to_identity_fp64(matrix);
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return;
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}
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const double corrector1 = 1.0f / square_modulus;
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const double corrector2 = 2.0f * corrector1;
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const double s0x1 = quaternion->s0 * quaternion->x1;
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const double s0x2 = quaternion->s0 * quaternion->x2;
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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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matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
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matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
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matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));
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matrix->r1c2 = corrector2 * (x1x2 + s0x3);
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matrix->r2c3 = corrector2 * (x2x3 + s0x1);
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matrix->r3c1 = corrector2 * (x1x3 + s0x2);
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matrix->r2c1 = corrector2 * (x1x2 - s0x3);
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matrix->r3c2 = corrector2 * (x2x3 - s0x1);
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matrix->r1c3 = corrector2 * (x1x3 - s0x2);
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}
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// ==================== Add ===================== //
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inline void bgc_quaternion_add_fp32(const BgcQuaternionFP32 * quaternion1, const BgcQuaternionFP32 * quaternion2, BgcQuaternionFP32 * sum)
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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_quaternion_add_fp64(const BgcQuaternionFP64 * quaternion1, const BgcQuaternionFP64 * quaternion2, BgcQuaternionFP64 * sum)
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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_quaternion_add_scaled_fp32(const BgcQuaternionFP32 * basic_quaternion, const BgcQuaternionFP32 * scalable_quaternion, const float scale, BgcQuaternionFP32 * sum)
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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_quaternion_add_scaled_fp64(const BgcQuaternionFP64 * basic_quaternion, const BgcQuaternionFP64 * scalable_quaternion, const double scale, BgcQuaternionFP64 * sum)
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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_quaternion_subtract_fp32(const BgcQuaternionFP32 * minuend, const BgcQuaternionFP32 * subtrahend, BgcQuaternionFP32 * difference)
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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_quaternion_subtract_fp64(const BgcQuaternionFP64 * minuend, const BgcQuaternionFP64 * subtrahend, BgcQuaternionFP64 * difference)
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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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// =============== Multiplication =============== //
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inline void bgc_quaternion_multiply_fp32(const BgcQuaternionFP32* multiplicand, const float multipier, BgcQuaternionFP32* product)
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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_quaternion_multiply_fp64(const BgcQuaternionFP64* multiplicand, const double multipier, BgcQuaternionFP64* product)
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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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// ================== Division ================== //
|
|
|
|
inline void bgc_quaternion_divide_fp32(const BgcQuaternionFP32* dividend, const float divisor, BgcQuaternionFP32* quotient)
|
|
{
|
|
bgc_quaternion_multiply_fp32(dividend, 1.0f / divisor, quotient);
|
|
}
|
|
|
|
inline void bgc_quaternion_divide_fp64(const BgcQuaternionFP64* dividend, const double divisor, BgcQuaternionFP64* quotient)
|
|
{
|
|
bgc_quaternion_multiply_fp64(dividend, 1.0 / divisor, quotient);
|
|
}
|
|
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|
// ================== Product =================== //
|
|
|
|
inline void bgc_quaternion_get_product_fp32(const BgcQuaternionFP32* left, const BgcQuaternionFP32* right, BgcQuaternionFP32* product)
|
|
{
|
|
const float s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
|
|
const float x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
|
|
const float x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
|
|
const float x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);
|
|
|
|
product->s0 = s0;
|
|
product->x1 = x1;
|
|
product->x2 = x2;
|
|
product->x3 = x3;
|
|
}
|
|
|
|
inline void bgc_quaternion_get_product_fp64(const BgcQuaternionFP64* left, const BgcQuaternionFP64* right, BgcQuaternionFP64* product)
|
|
{
|
|
const double s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
|
|
const double x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
|
|
const double x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
|
|
const double x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);
|
|
|
|
product->s0 = s0;
|
|
product->x1 = x1;
|
|
product->x2 = x2;
|
|
product->x3 = x3;
|
|
}
|
|
|
|
#endif // _BGC_QUATERNION_H_
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