520 lines
17 KiB
C
520 lines
17 KiB
C
#ifndef _BASIC_GEOMETRY_QUATERNION_H_
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#define _BASIC_GEOMETRY_QUATERNION_H_
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#include <math.h>
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#include "basis.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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} quaternion_fp32_t;
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typedef struct {
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double s0, x1, x2, x3;
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} quaternion_fp64_t;
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// ==================== Reset =================== //
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inline void quaternion_reset_fp32(quaternion_fp32_t * 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 quaternion_reset_fp64(quaternion_fp64_t * 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 quaternion_fp32_set_identity(quaternion_fp32_t * 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 quaternion_fp64_set_identity(quaternion_fp64_t * 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 quaternion_fp32_set_values(const float s0, const float x1, const float x2, const float x3, quaternion_fp32_t * 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 quaternion_fp64_set_values(const double s0, const double x1, const double x2, const double x3, quaternion_fp64_t * 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 quaternion_copy_fp32(const quaternion_fp32_t* from, quaternion_fp32_t* 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 quaternion_copy_fp64(const quaternion_fp64_t* from, quaternion_fp64_t* 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 quaternion_swap_fp32(quaternion_fp32_t* quarternion1, quaternion_fp32_t* 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 quaternion_swap_fp64(quaternion_fp64_t* quarternion1, quaternion_fp64_t* 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 quaternion_fp32_set_from_fp64(const quaternion_fp64_t* quaternion, quaternion_fp32_t* 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 quaternion_fp64_set_from_fp32(const quaternion_fp32_t* quaternion, quaternion_fp64_t* 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 quaternion_fp32_conjugate(quaternion_fp32_t* 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 quaternion_fp64_conjugate(quaternion_fp64_t* 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 quaternion_fp32_set_conjugate(const quaternion_fp32_t* quaternion, quaternion_fp32_t* 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 quaternion_fp64_set_conjugate(const quaternion_fp64_t* quaternion, quaternion_fp64_t* 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 quaternion_fp32_set_conjugate_fp64(const quaternion_fp64_t* quaternion, quaternion_fp32_t* 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 quaternion_fp64_set_conjugate_fp32(const quaternion_fp32_t* quaternion, quaternion_fp64_t* 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 quaternion_get_square_modulus_fp32(const quaternion_fp32_t* 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 quaternion_get_square_modulus_fp64(const quaternion_fp64_t* 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 quaternion_get_modulus_fp32(const quaternion_fp32_t* quaternion)
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{
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return sqrtf(quaternion_get_square_modulus_fp32(quaternion));
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}
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inline double quaternion_get_modulus_fp64(const quaternion_fp64_t* quaternion)
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{
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return sqrt(quaternion_get_square_modulus_fp64(quaternion));
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}
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// =============== Normalization ================ //
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inline int quaternion_fp32_normalize(quaternion_fp32_t* quaternion)
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{
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const float square_modulus = quaternion_get_square_modulus_fp32(quaternion);
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if (1.0f - FP32_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0f + FP32_TWO_EPSYLON) {
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return 1;
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}
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if (square_modulus <= FP32_SQUARE_EPSYLON) {
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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 quaternion_fp64_normalize(quaternion_fp64_t* quaternion)
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{
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const double square_modulus = quaternion_get_square_modulus_fp64(quaternion);
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if (1.0 - FP64_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0 + FP64_TWO_EPSYLON) {
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return 1;
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}
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if (square_modulus <= FP32_SQUARE_EPSYLON) {
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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 quaternion_fp32_get_rotation_matrix(const quaternion_fp32_t* quaternion, matrix3x3_fp32_t* 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 (-FP32_EPSYLON <= square_modulus && square_modulus <= FP32_EPSYLON)
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{
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matrix3x3_fp32_set_to_identity(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 quaternion_fp64_get_rotation_matrix(const quaternion_fp64_t* quaternion, matrix3x3_fp64_t* 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 (-FP64_EPSYLON <= square_modulus && square_modulus <= FP64_EPSYLON)
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{
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matrix3x3_fp64_set_to_identity(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 quaternion_fp32_get_reverse_matrix(const quaternion_fp32_t* quaternion, matrix3x3_fp32_t* 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 (-FP32_EPSYLON <= square_modulus && square_modulus <= FP32_EPSYLON)
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{
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matrix3x3_fp32_set_to_identity(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 quaternion_fp64_get_reverse_matrix(const quaternion_fp64_t* quaternion, matrix3x3_fp64_t* 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 (-FP64_EPSYLON <= square_modulus && square_modulus <= FP64_EPSYLON)
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{
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matrix3x3_fp64_set_to_identity(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 quaternion_fp32_add(const quaternion_fp32_t * quaternion1, const quaternion_fp32_t * quaternion2, quaternion_fp32_t * result)
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{
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result->s0 = quaternion1->s0 + quaternion2->s0;
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result->x1 = quaternion1->x1 + quaternion2->x1;
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result->x2 = quaternion1->x2 + quaternion2->x2;
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result->x3 = quaternion1->x3 + quaternion2->x3;
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}
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inline void quaternion_fp64_add(const quaternion_fp64_t * quaternion1, const quaternion_fp64_t * quaternion2, quaternion_fp64_t * result)
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{
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result->s0 = quaternion1->s0 + quaternion2->s0;
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result->x1 = quaternion1->x1 + quaternion2->x1;
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result->x2 = quaternion1->x2 + quaternion2->x2;
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result->x3 = quaternion1->x3 + quaternion2->x3;
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}
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// ================== Subtract ================== //
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inline void quaternion_fp32_subtract(const quaternion_fp32_t * minuend, const quaternion_fp32_t * subtrahend, quaternion_fp32_t * 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 quaternion_fp64_subtract(const quaternion_fp64_t * minuend, const quaternion_fp64_t * subtrahend, quaternion_fp64_t * 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 quaternion_fp32_multiply(const quaternion_fp32_t* multiplicand, const float multipier, quaternion_fp32_t* 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 quaternion_fp64_multiply(const quaternion_fp64_t* multiplicand, const double multipier, quaternion_fp64_t* 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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// ================== Division ================== //
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inline void quaternion_fp32_divide(const quaternion_fp32_t* dividend, const float divisor, quaternion_fp32_t* quotient)
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{
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quaternion_fp32_multiply(dividend, 1.0f / divisor, quotient);
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}
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inline void quaternion_fp64_divide(const quaternion_fp64_t* dividend, const double divisor, quaternion_fp64_t* quotient)
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{
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quaternion_fp64_multiply(dividend, 1.0 / divisor, quotient);
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}
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// ================== Product =================== //
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inline void quaternion_fp32_get_product(const quaternion_fp32_t* left, const quaternion_fp32_t* right, quaternion_fp32_t* product)
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{
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const float s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
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const float x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
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const float x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
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const float x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);
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product->s0 = s0;
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product->x1 = x1;
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product->x2 = x2;
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product->x3 = x3;
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}
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inline void quaternion_fp64_get_product(const quaternion_fp64_t* left, const quaternion_fp64_t* right, quaternion_fp64_t* product)
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{
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const double s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
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const double x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
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const double x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
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const double x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);
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product->s0 = s0;
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product->x1 = x1;
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product->x2 = x2;
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product->x3 = x3;
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}
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#endif // _GEOMETRY_QUATERNION_H_
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