550 lines
25 KiB
C
550 lines
25 KiB
C
#include <math.h>
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#include "./quaternion.h"
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extern inline void bgc_fp32_quaternion_reset(BGC_FP32_Quaternion* const quaternion);
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extern inline void bgc_fp64_quaternion_reset(BGC_FP64_Quaternion* const quaternion);
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extern inline float bgc_fp32_quaternion_get_square_magnitude(const BGC_FP32_Quaternion* const quaternion);
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extern inline double bgc_fp64_quaternion_get_square_magnitude(const BGC_FP64_Quaternion* const quaternion);
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extern inline float bgc_fp32_quaternion_get_magnitude(const BGC_FP32_Quaternion* const quaternion);
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extern inline double bgc_fp64_quaternion_get_magnitude(const BGC_FP64_Quaternion* const quaternion);
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extern inline int bgc_fp32_quaternion_is_zero(const BGC_FP32_Quaternion* const quaternion);
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extern inline int bgc_fp64_quaternion_is_zero(const BGC_FP64_Quaternion* const quaternion);
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extern inline int bgc_fp32_quaternion_is_unit(const BGC_FP32_Quaternion* const quaternion);
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extern inline int bgc_fp64_quaternion_is_unit(const BGC_FP64_Quaternion* const quaternion);
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extern inline int bgc_fp32_quaternion_is_pure(const BGC_FP32_Quaternion* const quaternion);
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extern inline int bgc_fp64_quaternion_is_pure(const BGC_FP64_Quaternion* const quaternion);
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extern inline int bgc_fp32_quaternion_is_real(const BGC_FP32_Quaternion* const quaternion);
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extern inline int bgc_fp64_quaternion_is_real(const BGC_FP64_Quaternion* const quaternion);
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extern inline void bgc_fp32_quaternion_copy(BGC_FP32_Quaternion* const destination, const BGC_FP32_Quaternion* const source);
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extern inline void bgc_fp64_quaternion_copy(BGC_FP64_Quaternion* const destination, const BGC_FP64_Quaternion* const source);
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extern inline void bgc_fp32_quaternion_swap(BGC_FP32_Quaternion* const quarternion1, BGC_FP32_Quaternion* const quarternion2);
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extern inline void bgc_fp64_quaternion_swap(BGC_FP64_Quaternion* const quarternion1, BGC_FP64_Quaternion* const quarternion2);
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extern inline void bgc_fp32_quaternion_convert_to_fp64(BGC_FP64_Quaternion* const destination, const BGC_FP32_Quaternion* const source);
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extern inline void bgc_fp64_quaternion_convert_to_fp32(BGC_FP32_Quaternion* const destination, const BGC_FP64_Quaternion* const source);
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extern 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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extern 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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extern 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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extern 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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extern 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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extern 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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extern 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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extern 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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extern 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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extern 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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extern 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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extern 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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extern 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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extern 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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extern 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);
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extern 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);
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extern 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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extern 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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extern 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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extern 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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extern 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);
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extern 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);
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extern inline int bgc_fp32_quaternion_divide_by_real_number(BGC_FP32_Quaternion* const quotient, const BGC_FP32_Quaternion* const dividend, const float divisor);
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extern inline int bgc_fp64_quaternion_divide_by_real_number(BGC_FP64_Quaternion* const quotient, const BGC_FP64_Quaternion* const dividend, const double divisor);
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extern 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);
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extern 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);
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extern 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);
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extern 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);
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extern inline void bgc_fp32_quaternion_get_mean2(BGC_FP32_Quaternion* const mean, const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2);
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extern inline void bgc_fp64_quaternion_get_mean2(BGC_FP64_Quaternion* const mean, const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2);
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extern 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);
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extern 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);
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extern 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);
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extern 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);
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extern inline float bgc_fp32_quaternion_get_dot_product(const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2);
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extern inline double bgc_fp64_quaternion_get_dot_product(const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2);
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extern inline void bgc_fp32_quaternion_conjugate(BGC_FP32_Quaternion* const quaternion);
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extern inline void bgc_fp64_quaternion_conjugate(BGC_FP64_Quaternion* const quaternion);
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extern inline void bgc_fp32_quaternion_get_conjugate(BGC_FP32_Quaternion* const conjugate, const BGC_FP32_Quaternion* const quaternion);
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extern inline void bgc_fp64_quaternion_get_conjugate(BGC_FP64_Quaternion* const conjugate, const BGC_FP64_Quaternion* const quaternion);
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extern inline void bgc_fp32_quaternion_revert(BGC_FP32_Quaternion* const quaternion);
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extern inline void bgc_fp64_quaternion_revert(BGC_FP64_Quaternion* const quaternion);
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extern inline void bgc_fp32_quaternion_get_reverse(BGC_FP32_Quaternion* const reverse, const BGC_FP32_Quaternion* const quaternion);
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extern inline void bgc_fp64_quaternion_get_reverse(BGC_FP64_Quaternion* const reverse, const BGC_FP64_Quaternion* const quaternion);
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extern inline int bgc_fp32_quaternion_invert(BGC_FP32_Quaternion* const quaternion);
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extern inline int bgc_fp64_quaternion_invert(BGC_FP64_Quaternion* const quaternion);
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extern inline int bgc_fp32_quaternion_get_inverse(BGC_FP32_Quaternion* const inverse, const BGC_FP32_Quaternion* const quaternion);
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extern inline int bgc_fp64_quaternion_get_inverse(BGC_FP64_Quaternion* const inverse, const BGC_FP64_Quaternion* const quaternion);
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extern inline int bgc_fp32_quaternion_normalize(BGC_FP32_Quaternion* const quaternion);
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extern inline int bgc_fp64_quaternion_normalize(BGC_FP64_Quaternion* const quaternion);
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extern inline int bgc_fp32_quaternion_get_normalized(BGC_FP32_Quaternion* const normalized, const BGC_FP32_Quaternion* const quaternion);
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extern inline int bgc_fp64_quaternion_get_normalized(BGC_FP64_Quaternion* const normalized, const BGC_FP64_Quaternion* const quaternion);
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extern 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);
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extern 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);
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extern 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);
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extern 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);
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extern 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);
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extern 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);
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extern 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);
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extern 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);
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extern inline int bgc_fp32_quaternion_get_both_matrices(BGC_FP32_Matrix3x3* const rotation, BGC_FP32_Matrix3x3* const reverse, const BGC_FP32_Quaternion* const quaternion);
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extern inline int bgc_fp64_quaternion_get_both_matrices(BGC_FP64_Matrix3x3* const rotation, BGC_FP64_Matrix3x3* const reverse, const BGC_FP64_Quaternion* const quaternion);
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extern inline int bgc_fp32_quaternion_are_close(const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2);
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extern inline int bgc_fp64_quaternion_are_close(const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2);
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// =============== Get Exponation =============== //
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int bgc_fp32_quaternion_get_power(BGC_FP32_Quaternion* const power, const BGC_FP32_Quaternion* const base, const float exponent)
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{
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const float ss = base->s * base->s;
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const float xx = base->x * base->x;
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const float yy = base->y * base->y;
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const float zz = base->z * base->z;
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const float square_vector = xx + (yy + zz);
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const float square_modulus = (ss + xx) + (yy + zz);
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// isnan(square_modulus) means checking for NaN value at square_modulus
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if (isnan(square_modulus)) {
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return BGC_FAILURE;
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}
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if (square_vector <= BGC_FP32_SQUARE_EPSILON) {
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if (base->s < 0.0f) {
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return BGC_FAILURE;
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}
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power->s = powf(base->s, exponent);
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power->x = 0.0f;
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power->y = 0.0f;
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power->z = 0.0f;
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return BGC_SUCCESS;
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}
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const float vector_modulus = sqrtf(square_vector);
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const float power_angle = atan2f(vector_modulus, base->s) * exponent;
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const float power_modulus = powf(square_modulus, 0.5f * exponent);
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const float multiplier = power_modulus * sinf(power_angle) / vector_modulus;
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power->s = power_modulus * cosf(power_angle);
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power->x = base->x * multiplier;
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power->y = base->y * multiplier;
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power->z = base->z * multiplier;
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return BGC_SUCCESS;
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}
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int bgc_fp64_quaternion_get_power(BGC_FP64_Quaternion* const power, const BGC_FP64_Quaternion* const base, const double exponent)
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{
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const double ss = base->s * base->s;
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const double xx = base->x * base->x;
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const double yy = base->y * base->y;
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const double zz = base->z * base->z;
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const double square_vector = xx + (yy + zz);
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const double square_modulus = (ss + xx) + (yy + zz);
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// isnan(square_modulus) means checking for NaN value at square_modulus
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if (isnan(square_modulus)) {
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return BGC_FAILURE;
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}
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if (square_vector <= BGC_FP64_SQUARE_EPSILON) {
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if (base->s < 0.0) {
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return BGC_FAILURE;
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}
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power->s = pow(base->s, exponent);
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power->x = 0.0;
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power->y = 0.0;
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power->z = 0.0;
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return BGC_SUCCESS;
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}
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const double vector_modulus = sqrt(square_vector);
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const double power_angle = atan2(vector_modulus, base->s) * exponent;
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const double power_modulus = pow(square_modulus, 0.5 * exponent);
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const double multiplier = power_modulus * sin(power_angle) / vector_modulus;
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power->s = power_modulus * cos(power_angle);
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power->x = base->x * multiplier;
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power->y = base->y * multiplier;
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power->z = base->z * multiplier;
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return BGC_SUCCESS;
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}
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// ============ Get Rotation Matrix ============= //
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int bgc_fp32_quaternion_get_rotation_matrix(BGC_FP32_Matrix3x3* const rotation, 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(rotation);
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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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rotation->r1c1 = corrector1 * ((ss + xx) - (yy + zz));
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rotation->r2c2 = corrector1 * ((ss + yy) - (xx + zz));
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rotation->r3c3 = corrector1 * ((ss + zz) - (xx + yy));
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rotation->r1c2 = corrector2 * (xy - sz);
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rotation->r2c3 = corrector2 * (yz - sx);
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rotation->r3c1 = corrector2 * (xz - sy);
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rotation->r2c1 = corrector2 * (xy + sz);
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rotation->r3c2 = corrector2 * (yz + sx);
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rotation->r1c3 = corrector2 * (xz + sy);
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return BGC_SUCCESS;
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}
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int bgc_fp64_quaternion_get_rotation_matrix(BGC_FP64_Matrix3x3* const rotation, 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(rotation);
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return BGC_FAILURE;
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}
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const double corrector1 = 1.0 / square_modulus;
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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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const double corrector2 = 2.0 * corrector1;
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rotation->r1c1 = corrector1 * ((ss + xx) - (yy + zz));
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rotation->r2c2 = corrector1 * ((ss + yy) - (xx + zz));
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rotation->r3c3 = corrector1 * ((ss + zz) - (xx + yy));
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rotation->r1c2 = corrector2 * (xy - sz);
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rotation->r2c3 = corrector2 * (yz - sx);
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rotation->r3c1 = corrector2 * (xz - sy);
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rotation->r2c1 = corrector2 * (xy + sz);
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rotation->r3c2 = corrector2 * (yz + sx);
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rotation->r1c3 = corrector2 * (xz + sy);
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return BGC_SUCCESS;
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}
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// ============ Set Rotation Matrix ============= //
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|
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int bgc_fp32_quaternion_set_rotation_matrix(BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Matrix3x3* const matrix)
|
|
{
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|
if (!bgc_fp32_matrix3x3_is_rotation(matrix)) {
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return BGC_FAILURE;
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|
}
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const float ss_4 = (1 + matrix->r1c1) + (matrix->r2c2 + matrix->r3c3);
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const float xx_4 = (1 + matrix->r1c1) - (matrix->r2c2 + matrix->r3c3);
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const float yy_4 = (1 + matrix->r2c2) - (matrix->r1c1 + matrix->r3c3);
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const float zz_4 = (1 + matrix->r3c3) - (matrix->r1c1 + matrix->r2c2);
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const float sx_4 = matrix->r3c2 - matrix->r2c3;
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const float sy_4 = matrix->r1c3 - matrix->r3c1;
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const float sz_4 = matrix->r2c1 - matrix->r1c2;
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const float yz_4 = matrix->r3c2 + matrix->r2c3;
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const float xz_4 = matrix->r1c3 + matrix->r3c1;
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const float xy_4 = matrix->r2c1 + matrix->r1c2;
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float max = ss_4;
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int index = 0;
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|
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if (xx_4 > max) {
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max = xx_4;
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index = 1;
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|
}
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|
|
if (yy_4 > max) {
|
|
max = yy_4;
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|
index = 2;
|
|
}
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|
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if (zz_4 > max) {
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max = zz_4;
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index = 3;
|
|
}
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|
|
switch (index) {
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|
case 0:
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|
quaternion->s = ss_4;
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|
quaternion->x = sx_4;
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quaternion->y = sy_4;
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quaternion->z = sz_4;
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|
break;
|
|
|
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case 1:
|
|
quaternion->s = sx_4;
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|
quaternion->x = xx_4;
|
|
quaternion->y = xy_4;
|
|
quaternion->z = xz_4;
|
|
break;
|
|
|
|
case 2:
|
|
quaternion->s = sy_4;
|
|
quaternion->x = xy_4;
|
|
quaternion->y = yy_4;
|
|
quaternion->z = yz_4;
|
|
break;
|
|
|
|
case 3:
|
|
quaternion->s = sz_4;
|
|
quaternion->x = xz_4;
|
|
quaternion->y = yz_4;
|
|
quaternion->z = zz_4;
|
|
break;
|
|
}
|
|
|
|
if (quaternion->s < 0.0f) {
|
|
quaternion->s = -quaternion->s;
|
|
quaternion->x = -quaternion->x;
|
|
quaternion->y = -quaternion->y;
|
|
quaternion->z = -quaternion->z;
|
|
}
|
|
|
|
const float multiplicator = sqrtf(1.0f / bgc_fp32_quaternion_get_square_magnitude(quaternion));
|
|
|
|
quaternion->s *= multiplicator;
|
|
quaternion->x *= multiplicator;
|
|
quaternion->y *= multiplicator;
|
|
quaternion->z *= multiplicator;
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
int bgc_fp64_quaternion_set_rotation_matrix(BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Matrix3x3* const matrix)
|
|
{
|
|
if (!bgc_fp64_matrix3x3_is_rotation(matrix)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const double ss_4 = (1 + matrix->r1c1) + (matrix->r2c2 + matrix->r3c3);
|
|
const double xx_4 = (1 + matrix->r1c1) - (matrix->r2c2 - matrix->r3c3);
|
|
const double yy_4 = (1 + matrix->r2c2) - (matrix->r1c1 - matrix->r3c3);
|
|
const double zz_4 = (1 + matrix->r3c3) - (matrix->r1c1 - matrix->r2c2);
|
|
|
|
const double sx_4 = matrix->r3c2 - matrix->r2c3;
|
|
const double sy_4 = matrix->r1c3 - matrix->r3c1;
|
|
const double sz_4 = matrix->r2c1 - matrix->r1c2;
|
|
|
|
const double yz_4 = matrix->r3c2 + matrix->r2c3;
|
|
const double xz_4 = matrix->r1c3 + matrix->r3c1;
|
|
const double xy_4 = matrix->r2c1 + matrix->r1c2;
|
|
|
|
double max = ss_4;
|
|
int index = 0;
|
|
|
|
if (xx_4 > max) {
|
|
max = xx_4;
|
|
index = 1;
|
|
}
|
|
|
|
if (yy_4 > max) {
|
|
max = yy_4;
|
|
index = 2;
|
|
}
|
|
|
|
if (zz_4 > max) {
|
|
max = zz_4;
|
|
index = 3;
|
|
}
|
|
|
|
switch (index) {
|
|
case 0:
|
|
quaternion->s = ss_4;
|
|
quaternion->x = sx_4;
|
|
quaternion->y = sy_4;
|
|
quaternion->z = sz_4;
|
|
break;
|
|
|
|
case 1:
|
|
quaternion->s = sx_4;
|
|
quaternion->x = xx_4;
|
|
quaternion->y = xy_4;
|
|
quaternion->z = xz_4;
|
|
break;
|
|
|
|
case 2:
|
|
quaternion->s = sy_4;
|
|
quaternion->x = xy_4;
|
|
quaternion->y = yy_4;
|
|
quaternion->z = yz_4;
|
|
break;
|
|
|
|
case 3:
|
|
quaternion->s = sz_4;
|
|
quaternion->x = xz_4;
|
|
quaternion->y = yz_4;
|
|
quaternion->z = zz_4;
|
|
break;
|
|
}
|
|
|
|
if (quaternion->s < 0.0) {
|
|
quaternion->s = -quaternion->s;
|
|
quaternion->x = -quaternion->x;
|
|
quaternion->y = -quaternion->y;
|
|
quaternion->z = -quaternion->z;
|
|
}
|
|
|
|
const double multiplicator = sqrt(1.0 / bgc_fp64_quaternion_get_square_magnitude(quaternion));
|
|
|
|
quaternion->s *= multiplicator;
|
|
quaternion->x *= multiplicator;
|
|
quaternion->y *= multiplicator;
|
|
quaternion->z *= multiplicator;
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
// ============= Get Reverse Matrix ============= //
|
|
|
|
int bgc_fp32_quaternion_get_reverse_matrix(BGC_FP32_Matrix3x3* const reverse, 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(reverse);
|
|
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;
|
|
|
|
reverse->r1c1 = corrector1 * ((ss + xx) - (yy + zz));
|
|
reverse->r2c2 = corrector1 * ((ss + yy) - (xx + zz));
|
|
reverse->r3c3 = corrector1 * ((ss + zz) - (xx + yy));
|
|
|
|
reverse->r1c2 = corrector2 * (xy + sz);
|
|
reverse->r2c3 = corrector2 * (yz + sx);
|
|
reverse->r3c1 = corrector2 * (xz + sy);
|
|
|
|
reverse->r2c1 = corrector2 * (xy - sz);
|
|
reverse->r3c2 = corrector2 * (yz - sx);
|
|
reverse->r1c3 = corrector2 * (xz - sy);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
int bgc_fp64_quaternion_get_reverse_matrix(BGC_FP64_Matrix3x3* const reverse, 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(reverse);
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const double corrector1 = 1.0 / 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 = 2.0 * corrector1;
|
|
|
|
reverse->r1c1 = corrector1 * ((ss + xx) - (yy + zz));
|
|
reverse->r2c2 = corrector1 * ((ss + yy) - (xx + zz));
|
|
reverse->r3c3 = corrector1 * ((ss + zz) - (xx + yy));
|
|
|
|
reverse->r1c2 = corrector2 * (xy + sz);
|
|
reverse->r2c3 = corrector2 * (yz + sx);
|
|
reverse->r3c1 = corrector2 * (xz + sy);
|
|
|
|
reverse->r2c1 = corrector2 * (xy - sz);
|
|
reverse->r3c2 = corrector2 * (yz - sx);
|
|
reverse->r1c3 = corrector2 * (xz - sy);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|