675 lines
31 KiB
C
675 lines
31 KiB
C
#ifndef _BGC_DUAL_QUATERNION_H_INCLUDED_
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#define _BGC_DUAL_QUATERNION_H_INCLUDED_
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#include "./types.h"
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#include "./quaternion.h"
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// =================== Reset ==================== //
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inline void bgc_fp32_dual_quaternion_reset(BGC_FP32_DualQuaternion* quaternion)
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{
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bgc_fp32_quaternion_reset(&quaternion->real_part);
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bgc_fp32_quaternion_reset(&quaternion->dual_part);
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}
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inline void bgc_fp64_dual_quaternion_reset(BGC_FP64_DualQuaternion* quaternion)
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{
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bgc_fp64_quaternion_reset(&quaternion->real_part);
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bgc_fp64_quaternion_reset(&quaternion->dual_part);
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}
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// ==================== Copy ==================== //
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inline void bgc_fp32_dual_quaternion_copy(BGC_FP32_DualQuaternion* destination, const BGC_FP32_DualQuaternion* source)
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{
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bgc_fp32_quaternion_copy(&destination->real_part, &source->real_part);
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bgc_fp32_quaternion_copy(&destination->dual_part, &source->dual_part);
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}
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inline void bgc_fp64_dual_quaternion_copy(BGC_FP64_DualQuaternion* destination, const BGC_FP64_DualQuaternion* source)
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{
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bgc_fp64_quaternion_copy(&destination->real_part, &source->real_part);
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bgc_fp64_quaternion_copy(&destination->dual_part, &source->dual_part);
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}
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// ==================== Swap ==================== //
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inline void bgc_fp32_dual_quaternion_swap(BGC_FP32_DualQuaternion* first, BGC_FP32_DualQuaternion* second)
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{
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bgc_fp32_quaternion_swap(&first->real_part, &second->real_part);
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bgc_fp32_quaternion_swap(&first->dual_part, &second->dual_part);
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}
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inline void bgc_fp64_dual_quaternion_swap(BGC_FP64_DualQuaternion* first, BGC_FP64_DualQuaternion* second)
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{
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bgc_fp64_quaternion_swap(&first->real_part, &second->real_part);
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bgc_fp64_quaternion_swap(&first->dual_part, &second->dual_part);
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}
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// ================== Convert =================== //
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inline void bgc_fp32_dual_quaternion_convert_to_fp64(BGC_FP64_DualQuaternion* destination, const BGC_FP32_DualQuaternion* source)
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{
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bgc_fp32_quaternion_convert_to_fp64(&destination->real_part, &source->real_part);
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bgc_fp32_quaternion_convert_to_fp64(&destination->dual_part, &source->dual_part);
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}
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inline void bgc_fp64_dual_quaternion_convert_to_fp32(BGC_FP32_DualQuaternion* destination, const BGC_FP64_DualQuaternion* source)
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{
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bgc_fp64_quaternion_convert_to_fp32(&destination->real_part, &source->real_part);
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bgc_fp64_quaternion_convert_to_fp32(&destination->dual_part, &source->dual_part);
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}
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// =================== Revert =================== //
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inline void bgc_fp32_dual_quaternion_revert(BGC_FP32_DualQuaternion* quaternion)
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{
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bgc_fp32_quaternion_revert(&quaternion->real_part);
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bgc_fp32_quaternion_revert(&quaternion->dual_part);
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}
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inline void bgc_fp64_dual_quaternion_revert(BGC_FP64_DualQuaternion* quaternion)
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{
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bgc_fp64_quaternion_revert(&quaternion->real_part);
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bgc_fp64_quaternion_revert(&quaternion->dual_part);
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}
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// ================ Get Reverse ================= //
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inline void bgc_fp32_dual_quaternion_get_reverse(BGC_FP32_DualQuaternion* reverse, const BGC_FP32_DualQuaternion* quaternion)
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{
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bgc_fp32_quaternion_get_reverse(&reverse->real_part, &quaternion->real_part);
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bgc_fp32_quaternion_get_reverse(&reverse->dual_part, &quaternion->dual_part);
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}
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inline void bgc_fp64_dual_quaternion_get_reverse(BGC_FP64_DualQuaternion* reverse, const BGC_FP64_DualQuaternion* quaternion)
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{
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bgc_fp64_quaternion_get_reverse(&reverse->real_part, &quaternion->real_part);
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bgc_fp64_quaternion_get_reverse(&reverse->dual_part, &quaternion->dual_part);
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}
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// =================== Invert =================== //
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inline int bgc_fp32_dual_quaternion_invert(BGC_FP32_DualQuaternion* quaternion)
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{
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if (bgc_fp32_quaternion_get_inverse(&quaternion->real_part, &quaternion->real_part) != BGC_SUCCESS) {
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return BGC_FAILURE;
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}
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BGC_FP32_Quaternion temporary;
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_bgc_fp32_restrict_quaternion_multiply_by_quaternion(&temporary, &quaternion->real_part, &quaternion->dual_part);
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_bgc_fp32_restrict_quaternion_multiply_by_quaternion(&quaternion->dual_part, &temporary, &quaternion->real_part);
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bgc_fp32_quaternion_revert(&quaternion->dual_part);
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return BGC_SUCCESS;
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}
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inline int bgc_fp64_dual_quaternion_invert(BGC_FP64_DualQuaternion* quaternion)
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{
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if (bgc_fp64_quaternion_get_inverse(&quaternion->real_part, &quaternion->real_part) != BGC_SUCCESS) {
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return BGC_FAILURE;
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}
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BGC_FP64_Quaternion temporary;
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_bgc_fp64_restrict_quaternion_multiply_by_quaternion(&temporary, &quaternion->real_part, &quaternion->dual_part);
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_bgc_fp64_restrict_quaternion_multiply_by_quaternion(&quaternion->dual_part, &temporary, &quaternion->real_part);
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bgc_fp64_quaternion_revert(&quaternion->dual_part);
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return BGC_SUCCESS;
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}
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// ================ Get Inverse ================= //
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inline int bgc_fp32_dual_quaternion_get_inverse(BGC_FP32_DualQuaternion* inverse, const BGC_FP32_DualQuaternion* quaternion)
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{
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if (bgc_fp32_quaternion_get_inverse(&inverse->real_part, &quaternion->real_part) != BGC_SUCCESS) {
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return BGC_FAILURE;
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}
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BGC_FP32_Quaternion temporary;
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_bgc_fp32_restrict_quaternion_multiply_by_quaternion(&temporary, &inverse->real_part, &quaternion->dual_part);
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_bgc_fp32_restrict_quaternion_multiply_by_quaternion(&inverse->dual_part, &temporary, &inverse->real_part);
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bgc_fp32_quaternion_revert(&inverse->dual_part);
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return BGC_SUCCESS;
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}
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inline int bgc_fp64_dual_quaternion_get_inverse(BGC_FP64_DualQuaternion* inverse, const BGC_FP64_DualQuaternion* quaternion)
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{
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if (bgc_fp64_quaternion_get_inverse(&inverse->real_part, &quaternion->real_part) != BGC_SUCCESS) {
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return BGC_FAILURE;
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}
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BGC_FP64_Quaternion temporary;
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_bgc_fp64_restrict_quaternion_multiply_by_quaternion(&temporary, &inverse->real_part, &quaternion->dual_part);
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_bgc_fp64_restrict_quaternion_multiply_by_quaternion(&inverse->dual_part, &temporary, &inverse->real_part);
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bgc_fp64_quaternion_revert(&inverse->dual_part);
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return BGC_SUCCESS;
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}
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// ============ Component Conjugate ============= //
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inline void bgc_fp32_dual_quaternion_component_conjugate(BGC_FP32_DualQuaternion* quaternion)
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{
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bgc_fp32_quaternion_conjugate(&quaternion->real_part);
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bgc_fp32_quaternion_conjugate(&quaternion->dual_part);
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}
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inline void bgc_fp64_dual_quaternion_component_conjugate(BGC_FP64_DualQuaternion* quaternion)
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{
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bgc_fp64_quaternion_conjugate(&quaternion->real_part);
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bgc_fp64_quaternion_conjugate(&quaternion->dual_part);
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}
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// ========== Get Component Conjugate =========== //
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inline void bgc_fp32_dual_quaternion_get_component_conjugate(BGC_FP32_DualQuaternion* conjugate, const BGC_FP32_DualQuaternion* quaternion)
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{
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bgc_fp32_quaternion_get_conjugate(&conjugate->real_part, &quaternion->real_part);
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bgc_fp32_quaternion_get_conjugate(&conjugate->dual_part, &quaternion->dual_part);
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}
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inline void bgc_fp64_dual_quaternion_get_component_conjugate(BGC_FP64_DualQuaternion* conjugate, const BGC_FP64_DualQuaternion* quaternion)
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{
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bgc_fp64_quaternion_get_conjugate(&conjugate->real_part, &quaternion->real_part);
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bgc_fp64_quaternion_get_conjugate(&conjugate->dual_part, &quaternion->dual_part);
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}
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// =============== Dual Conjugate =============== //
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inline void bgc_fp32_dual_quaternion_dual_conjugate(BGC_FP32_DualQuaternion* quaternion)
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{
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bgc_fp32_quaternion_revert(&quaternion->dual_part);
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}
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inline void bgc_fp64_dual_quaternion_dual_conjugate(BGC_FP64_DualQuaternion* quaternion)
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{
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bgc_fp64_quaternion_revert(&quaternion->dual_part);
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}
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// ============= Get Dual Conjugate ============= //
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inline void bgc_fp32_dual_quaternion_get_dual_conjugate(BGC_FP32_DualQuaternion* conjugate, const BGC_FP32_DualQuaternion* quaternion)
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{
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bgc_fp32_quaternion_copy(&conjugate->real_part, &quaternion->real_part);
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bgc_fp32_quaternion_get_reverse(&conjugate->real_part, &quaternion->dual_part);
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}
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inline void bgc_fp64_dual_quaternion_get_dual_conjugate(BGC_FP64_DualQuaternion* conjugate, const BGC_FP64_DualQuaternion* quaternion)
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{
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bgc_fp64_quaternion_copy(&conjugate->real_part, &quaternion->real_part);
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bgc_fp64_quaternion_get_reverse(&conjugate->real_part, &quaternion->dual_part);
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}
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// ============== Fully Conjugate =============== //
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inline void bgc_fp32_dual_quaternion_fully_conjugate(BGC_FP32_DualQuaternion* quaternion)
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{
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quaternion->real_part.x1 = -quaternion->real_part.x1;
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quaternion->real_part.x2 = -quaternion->real_part.x2;
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quaternion->real_part.x3 = -quaternion->real_part.x3;
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quaternion->dual_part.s0 = -quaternion->dual_part.s0;
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}
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inline void bgc_fp64_dual_quaternion_fully_conjugate(BGC_FP64_DualQuaternion* quaternion)
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{
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quaternion->real_part.x1 = -quaternion->real_part.x1;
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quaternion->real_part.x2 = -quaternion->real_part.x2;
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quaternion->real_part.x3 = -quaternion->real_part.x3;
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quaternion->dual_part.s0 = -quaternion->dual_part.s0;
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}
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// ============ Get Fully Conjugate ============= //
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inline void bgc_fp32_dual_quaternion_get_fully_conjugate(BGC_FP32_DualQuaternion* conjugate, const BGC_FP32_DualQuaternion* quaternion)
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{
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conjugate->real_part.s0 = quaternion->real_part.s0;
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conjugate->real_part.x1 = -quaternion->real_part.x1;
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conjugate->real_part.x2 = -quaternion->real_part.x2;
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conjugate->real_part.x3 = -quaternion->real_part.x3;
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conjugate->dual_part.s0 = -quaternion->dual_part.s0;
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conjugate->dual_part.x1 = quaternion->dual_part.x1;
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conjugate->dual_part.x2 = quaternion->dual_part.x2;
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conjugate->dual_part.x3 = quaternion->dual_part.x3;
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}
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inline void bgc_fp64_dual_quaternion_get_fully_conjugate(BGC_FP64_DualQuaternion* conjugate, const BGC_FP64_DualQuaternion* quaternion)
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{
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conjugate->real_part.s0 = quaternion->real_part.s0;
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conjugate->real_part.x1 = -quaternion->real_part.x1;
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conjugate->real_part.x2 = -quaternion->real_part.x2;
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conjugate->real_part.x3 = -quaternion->real_part.x3;
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conjugate->dual_part.s0 = -quaternion->dual_part.s0;
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conjugate->dual_part.x1 = quaternion->dual_part.x1;
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conjugate->dual_part.x2 = quaternion->dual_part.x2;
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conjugate->dual_part.x3 = quaternion->dual_part.x3;
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}
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// ================= Normalize ================== //
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void _bgc_fp32_dual_quaternion_normalize_parts(BGC_FP32_DualQuaternion* quaternion, const float square_magnitude);
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void _bgc_fp64_dual_quaternion_normalize_parts(BGC_FP64_DualQuaternion* quaternion, const double square_magnitude);
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inline void bgc_fp32_dual_quaternion_normalize(BGC_FP32_DualQuaternion* quaternion)
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{
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const float square_magnitude = bgc_fp32_quaternion_get_square_magnitude(&quaternion->real_part);
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if (!bgc_fp32_is_square_unit(square_magnitude)) {
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_bgc_fp32_quaternion_normalize_normalize_parts(quaternion, square_magnitude);
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}
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const float dot_product = bgc_fp32_quaternion_get_dot_product(&quaternion->real_part, &quaternion->dual_part);
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bgc_fp32_quaternion_subtract_scaled(&quaternion->dual_part, &quaternion->dual_part, &quaternion->real_part, dot_product);
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}
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inline void bgc_fp64_dual_quaternion_normalize(BGC_FP64_DualQuaternion* quaternion)
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{
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const double square_magnitude = bgc_fp64_quaternion_get_square_magnitude(&quaternion->real_part);
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if (!bgc_fp64_is_square_unit(square_magnitude)) {
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_bgc_fp64_quaternion_normalize_normalize_parts(quaternion, square_magnitude);
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}
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const double dot_product = bgc_fp64_quaternion_get_dot_product(&pose->_real_part, &pose->_dual_part);
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bgc_fp64_quaternion_subtract_scaled(&pose->_dual_part, &pose->_dual_part, &pose->_real_part, dot_product);
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}
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// ==================== Add ===================== //
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inline void bgc_fp32_dual_quaternion_add(BGC_FP32_DualQuaternion* sum, const BGC_FP32_DualQuaternion* first, const BGC_FP32_DualQuaternion* second)
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{
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bgc_fp32_quaternion_add(&sum->real_part, &first->real_part, &second->real_part);
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bgc_fp32_quaternion_add(&sum->dual_part, &first->dual_part, &second->dual_part);
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}
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inline void bgc_fp64_dual_quaternion_add(BGC_FP64_DualQuaternion* sum, const BGC_FP64_DualQuaternion* first, const BGC_FP64_DualQuaternion* second)
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{
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bgc_fp64_quaternion_add(&sum->real_part, &first->real_part, &second->real_part);
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bgc_fp64_quaternion_add(&sum->dual_part, &first->dual_part, &second->dual_part);
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}
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// ================= Add Scaled ================= //
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inline void bgc_fp32_dual_quaternion_add_scaled(BGC_FP32_DualQuaternion* sum, const BGC_FP32_DualQuaternion* base_quaternion, const BGC_FP32_DualQuaternion* scalable_quaternion, const float scale)
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{
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bgc_fp32_quaternion_add_scaled(&sum->real_part, &base_quaternion->real_part, &scalable_quaternion->real_part, scale);
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bgc_fp32_quaternion_add_scaled(&sum->dual_part, &base_quaternion->dual_part, &scalable_quaternion->dual_part, scale);
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}
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inline void bgc_fp64_dual_quaternion_add_scaled(BGC_FP64_DualQuaternion* sum, const BGC_FP64_DualQuaternion* base_quaternion, const BGC_FP64_DualQuaternion* scalable_quaternion, const double scale)
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{
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bgc_fp64_quaternion_add_scaled(&sum->real_part, &base_quaternion->real_part, &scalable_quaternion->real_part, scale);
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bgc_fp64_quaternion_add_scaled(&sum->dual_part, &base_quaternion->dual_part, &scalable_quaternion->dual_part, scale);
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}
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// ================== Subtract ================== //
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inline void bgc_fp32_dual_quaternion_subtract(BGC_FP32_DualQuaternion* difference, const BGC_FP32_DualQuaternion* minuend, const BGC_FP32_DualQuaternion* subtrahend)
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{
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bgc_fp32_quaternion_subtract(&difference->real_part, &minuend->real_part, &subtrahend->real_part);
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bgc_fp32_quaternion_subtract(&difference->dual_part, &minuend->dual_part, &subtrahend->dual_part);
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}
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inline void bgc_fp64_dual_quaternion_subtract(BGC_FP64_DualQuaternion* difference, const BGC_FP64_DualQuaternion* minuend, const BGC_FP64_DualQuaternion* subtrahend)
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{
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bgc_fp64_quaternion_subtract(&difference->real_part, &minuend->real_part, &subtrahend->real_part);
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bgc_fp64_quaternion_subtract(&difference->dual_part, &minuend->dual_part, &subtrahend->dual_part);
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}
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// ============== Subtract Scaled =============== //
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inline void bgc_fp32_dual_quaternion_subtract_scaled(BGC_FP32_DualQuaternion* difference, const BGC_FP32_DualQuaternion* base_quaternion, const BGC_FP32_DualQuaternion* scalable_quaternion, const float scale)
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{
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bgc_fp32_quaternion_subtract_scaled(&difference->real_part, &base_quaternion->real_part, &scalable_quaternion->real_part, scale);
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bgc_fp32_quaternion_subtract_scaled(&difference->dual_part, &base_quaternion->dual_part, &scalable_quaternion->dual_part, scale);
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}
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inline void bgc_fp64_dual_quaternion_subtract_scaled(BGC_FP64_DualQuaternion* difference, const BGC_FP64_DualQuaternion* base_quaternion, const BGC_FP64_DualQuaternion* scalable_quaternion, const double scale)
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{
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bgc_fp64_quaternion_subtract_scaled(&difference->real_part, &base_quaternion->real_part, &scalable_quaternion->real_part, scale);
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bgc_fp64_quaternion_subtract_scaled(&difference->dual_part, &base_quaternion->dual_part, &scalable_quaternion->dual_part, scale);
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}
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// ================== Multiply ================== //
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inline void bgc_fp32_dual_quaternion_multiply_by_real_number(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const float multiplier)
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{
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bgc_fp32_quaternion_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier);
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bgc_fp32_quaternion_multiply_by_real(&product->dual_part, &multiplicand->dual_part, multiplier);
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}
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inline void bgc_fp64_dual_quaternion_multiply_by_real_number(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const double multiplier)
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{
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bgc_fp64_quaternion_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier);
|
|
bgc_fp64_quaternion_multiply_by_real(&product->dual_part, &multiplicand->dual_part, multiplier);
|
|
}
|
|
|
|
// ========== Multiply by Dual Number =========== //
|
|
|
|
inline void bgc_fp32_dual_quaternion_multiply_by_dual_number(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const BGC_FP32_DualNumber* multiplier)
|
|
{
|
|
BGC_FP32_Quaternion dual_part;
|
|
|
|
bgc_fp32_quaternion_multiply_by_real(&dual_part, &multiplicand->dual_part, multiplier->real_part);
|
|
bgc_fp32_quaternion_add_scaled(&dual_part, &dual_part, &multiplicand->real_part, multiplier->dual_part);
|
|
|
|
bgc_fp32_quaternion_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier->real_part);
|
|
bgc_fp32_quaternion_copy(&product->dual_part, &dual_part);
|
|
}
|
|
|
|
inline void bgc_fp64_dual_quaternion_multiply_by_dual_number(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const BGC_FP64_DualNumber* multiplier)
|
|
{
|
|
BGC_FP64_Quaternion dual_part;
|
|
|
|
bgc_fp64_quaternion_multiply_by_real(&dual_part, &multiplicand->dual_part, multiplier->real_part);
|
|
bgc_fp64_quaternion_add_scaled(&dual_part, &dual_part, &multiplicand->real_part, multiplier->dual_part);
|
|
|
|
bgc_fp64_quaternion_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier->real_part);
|
|
bgc_fp64_quaternion_copy(&product->dual_part, &dual_part);
|
|
}
|
|
|
|
// ===== Multiply by Conjugate Dual Number ====== //
|
|
|
|
inline void bgc_fp32_dual_quaternion_multiply_by_conjugate_dual_number(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const BGC_FP32_DualNumber* multiplier_to_conjugate)
|
|
{
|
|
BGC_FP32_Quaternion dual_part;
|
|
|
|
bgc_fp32_quaternion_multiply_by_real(&dual_part, &multiplicand->dual_part, multiplier_to_conjugate->real_part);
|
|
bgc_fp32_quaternion_subtract_scaled(&dual_part, &dual_part, &multiplicand->real_part, multiplier_to_conjugate->dual_part);
|
|
|
|
bgc_fp32_quaternion_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier_to_conjugate->real_part);
|
|
bgc_fp32_quaternion_copy(&product->dual_part, &dual_part);
|
|
}
|
|
|
|
inline void bgc_fp64_dual_quaternion_multiply_by_conjugate_dual_number(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const BGC_FP64_DualNumber* multiplier_to_conjugate)
|
|
{
|
|
BGC_FP64_Quaternion dual_part;
|
|
|
|
bgc_fp64_quaternion_multiply_by_real(&dual_part, &multiplicand->dual_part, multiplier_to_conjugate->real_part);
|
|
bgc_fp64_quaternion_subtract_scaled(&dual_part, &dual_part, &multiplicand->real_part, multiplier_to_conjugate->dual_part);
|
|
|
|
bgc_fp64_quaternion_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier_to_conjugate->real_part);
|
|
bgc_fp64_quaternion_copy(&product->dual_part, &dual_part);
|
|
}
|
|
|
|
// ====== Multiply by (Regular) Quaternion ====== //
|
|
|
|
inline void bgc_fp32_dual_quaternion_multiply_by_quaternion(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const BGC_FP32_Quaternion* multiplier)
|
|
{
|
|
bgc_fp32_quaternion_multiply_by_quaternion(&product->real_part, &multiplicand->real_part, multiplier);
|
|
bgc_fp32_quaternion_multiply_by_quaternion(&product->dual_part, &multiplicand->dual_part, multiplier);
|
|
}
|
|
|
|
inline void bgc_fp64_dual_quaternion_multiply_by_quaternion(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const BGC_FP64_Quaternion* multiplier)
|
|
{
|
|
bgc_fp64_quaternion_multiply_by_quaternion(&product->real_part, &multiplicand->real_part, multiplier);
|
|
bgc_fp64_quaternion_multiply_by_quaternion(&product->dual_part, &multiplicand->dual_part, multiplier);
|
|
}
|
|
|
|
// ====== Multiply by Conjugate Quaternion ====== //
|
|
|
|
inline void bgc_fp32_dual_quaternion_multiply_by_conjugate_quaternion(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const BGC_FP32_Quaternion* multiplier_to_conjugate)
|
|
{
|
|
bgc_fp32_quaternion_multiply_by_conjugate(&product->real_part, &multiplicand->real_part, multiplier_to_conjugate);
|
|
bgc_fp32_quaternion_multiply_by_conjugate(&product->dual_part, &multiplicand->dual_part, multiplier_to_conjugate);
|
|
}
|
|
|
|
inline void bgc_fp64_dual_quaternion_multiply_by_conjugate_quaternion(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const BGC_FP64_Quaternion* multiplier_to_conjugate)
|
|
{
|
|
bgc_fp64_quaternion_multiply_by_conjugate(&product->real_part, &multiplicand->real_part, multiplier_to_conjugate);
|
|
bgc_fp64_quaternion_multiply_by_conjugate(&product->dual_part, &multiplicand->dual_part, multiplier_to_conjugate);
|
|
}
|
|
|
|
// ======== Multiply by Dual Quaternion ========= //
|
|
|
|
inline void bgc_fp32_dual_quaternion_multiply_by_dual_quaternion(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* left, const BGC_FP32_DualQuaternion* right)
|
|
{
|
|
BGC_FP32_Quaternion dual_part1, dual_part2;
|
|
|
|
_bgc_fp32_restrict_quaternion_multiply_by_quaternion(&dual_part1, &left->real_part, &right->dual_part);
|
|
_bgc_fp32_restrict_quaternion_multiply_by_quaternion(&dual_part2, &left->dual_part, &right->real_part);
|
|
|
|
bgc_fp32_quaternion_multiply_by_quaternion(&product->real_part, &left->real_part, &right->real_part);
|
|
bgc_fp32_quaternion_add(&product->dual_part, &dual_part1, &dual_part2);
|
|
}
|
|
|
|
inline void bgc_fp64_dual_quaternion_multiply_by_dual_quaternion(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* left, const BGC_FP64_DualQuaternion* right)
|
|
{
|
|
BGC_FP64_Quaternion dual_part1, dual_part2;
|
|
|
|
bgc_fp64_quaternion_multiply_by_quaternion(&dual_part1, &left->real_part, &right->dual_part);
|
|
bgc_fp64_quaternion_multiply_by_quaternion(&dual_part2, &left->dual_part, &right->real_part);
|
|
|
|
bgc_fp64_quaternion_multiply_by_quaternion(&product->real_part, &left->real_part, &right->real_part);
|
|
bgc_fp64_quaternion_add(&product->dual_part, &dual_part1, &dual_part2);
|
|
}
|
|
|
|
// =================== Divide =================== //
|
|
|
|
inline int bgc_fp32_dual_quaternion_divide_by_real_number(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* dividend, const float divisor)
|
|
{
|
|
if (bgc_fp32_is_zero(divisor)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const float multiplier = 1.0f / divisor;
|
|
|
|
bgc_fp32_quaternion_multiply_by_real("ient->real_part, ÷nd->real_part, multiplier);
|
|
bgc_fp32_quaternion_multiply_by_real("ient->dual_part, ÷nd->dual_part, multiplier);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_dual_quaternion_divide_by_real_number(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* dividend, const double divisor)
|
|
{
|
|
if (bgc_fp64_is_zero(divisor)) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const double multiplier = 1.0 / divisor;
|
|
|
|
bgc_fp64_quaternion_multiply_by_real("ient->real_part, ÷nd->real_part, multiplier);
|
|
bgc_fp64_quaternion_multiply_by_real("ient->dual_part, ÷nd->dual_part, multiplier);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
// =========== Divide by Dual Number ============ //
|
|
|
|
inline int bgc_fp32_dual_quaternion_divide_by_dual_number(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* dividend, const BGC_FP32_DualNumber* divisor)
|
|
{
|
|
const float square_modulus = divisor->real_part * divisor->real_part;
|
|
|
|
if (square_modulus <= BGC_FP32_SQUARE_EPSILON) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
bgc_fp32_dual_quaternion_multiply_by_conjugate_dual_number(quotient, dividend, divisor);
|
|
bgc_fp32_dual_quaternion_multiply_by_real_number(quotient, quotient, 1.0f / square_modulus);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_dual_quaternion_divide_by_dual_number(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* dividend, const BGC_FP64_DualNumber* divisor)
|
|
{
|
|
const double square_modulus = divisor->real_part * divisor->real_part;
|
|
|
|
if (square_modulus <= BGC_FP64_SQUARE_EPSILON) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
bgc_fp64_dual_quaternion_multiply_by_conjugate_dual_number(quotient, dividend, divisor);
|
|
bgc_fp64_dual_quaternion_multiply_by_real_number(quotient, quotient, 1.0 / square_modulus);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
// ====== Divide by Conjugate Dual Number ======= //
|
|
|
|
inline int bgc_fp32_dual_quaternion_divide_by_conjugate_dual_number(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* dividend, const BGC_FP32_DualNumber* divisor_to_conjugate)
|
|
{
|
|
const float square_modulus = divisor_to_conjugate->real_part * divisor_to_conjugate->real_part;
|
|
|
|
if (square_modulus <= BGC_FP32_SQUARE_EPSILON) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
bgc_fp32_dual_quaternion_multiply_by_dual_number(quotient, dividend, divisor_to_conjugate);
|
|
bgc_fp32_dual_quaternion_multiply_by_real_number(quotient, quotient, 1.0f / square_modulus);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_dual_quaternion_divide_by_conjugate_dual_number(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* dividend, const BGC_FP64_DualNumber* divisor_to_conjugate)
|
|
{
|
|
const double square_modulus = divisor_to_conjugate->real_part * divisor_to_conjugate->real_part;
|
|
|
|
if (square_modulus <= BGC_FP64_SQUARE_EPSILON) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
bgc_fp64_dual_quaternion_multiply_by_dual_number(quotient, dividend, divisor_to_conjugate);
|
|
bgc_fp64_dual_quaternion_multiply_by_real_number(quotient, quotient, 1.0 / square_modulus);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
// ======= Divide by (Regular) Quaternion ======= //
|
|
|
|
inline int bgc_fp32_dual_quaternion_divide_by_quaternion(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* dividend, const BGC_FP32_Quaternion* divisor)
|
|
{
|
|
const float square_magnitude = bgc_fp32_quaternion_get_square_magnitude(divisor);
|
|
|
|
if (square_magnitude <= BGC_FP32_SQUARE_EPSILON) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const float multiplier = 1.0f / square_magnitude;
|
|
|
|
bgc_fp32_quaternion_multiply_by_conjugate("ient->real_part, ÷nd->real_part, divisor);
|
|
bgc_fp32_quaternion_multiply_by_conjugate("ient->dual_part, ÷nd->dual_part, divisor);
|
|
|
|
bgc_fp32_quaternion_multiply_by_real("ient->real_part, "ient->real_part, multiplier);
|
|
bgc_fp32_quaternion_multiply_by_real("ient->dual_part, "ient->dual_part, multiplier);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_dual_quaternion_divide_by_quaternion(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* dividend, const BGC_FP64_Quaternion* divisor)
|
|
{
|
|
const double square_magnitude = bgc_fp64_quaternion_get_square_magnitude(divisor);
|
|
|
|
if (square_magnitude <= BGC_FP64_SQUARE_EPSILON) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const double multiplier = 1.0 / square_magnitude;
|
|
|
|
bgc_fp64_quaternion_multiply_by_conjugate("ient->real_part, ÷nd->real_part, divisor);
|
|
bgc_fp64_quaternion_multiply_by_conjugate("ient->dual_part, ÷nd->dual_part, divisor);
|
|
|
|
bgc_fp64_quaternion_multiply_by_real("ient->real_part, "ient->real_part, multiplier);
|
|
bgc_fp64_quaternion_multiply_by_real("ient->dual_part, "ient->dual_part, multiplier);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
// ======= Divide by Conjugate Quaternion ======= //
|
|
|
|
inline int bgc_fp32_dual_quaternion_divide_by_conjugate_quaternion(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* dividend, const BGC_FP32_Quaternion* divisor_to_conjugate)
|
|
{
|
|
const float square_magnitude = bgc_fp32_quaternion_get_square_magnitude(divisor_to_conjugate);
|
|
|
|
if (square_magnitude <= BGC_FP32_SQUARE_EPSILON) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const float multiplier = 1.0f / square_magnitude;
|
|
|
|
bgc_fp32_quaternion_multiply_by_quaternion("ient->real_part, ÷nd->real_part, divisor_to_conjugate);
|
|
bgc_fp32_quaternion_multiply_by_quaternion("ient->dual_part, ÷nd->dual_part, divisor_to_conjugate);
|
|
|
|
bgc_fp32_quaternion_multiply_by_real("ient->real_part, "ient->real_part, multiplier);
|
|
bgc_fp32_quaternion_multiply_by_real("ient->dual_part, "ient->dual_part, multiplier);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
inline int bgc_fp64_dual_quaternion_divide_by_conjugate_quaternion(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* dividend, const BGC_FP64_Quaternion* divisor_to_conjugate)
|
|
{
|
|
const double square_magnitude = bgc_fp64_quaternion_get_square_magnitude(divisor_to_conjugate);
|
|
|
|
if (square_magnitude <= BGC_FP64_SQUARE_EPSILON) {
|
|
return BGC_FAILURE;
|
|
}
|
|
|
|
const double multiplier = 1.0 / square_magnitude;
|
|
|
|
bgc_fp64_quaternion_multiply_by_quaternion("ient->real_part, ÷nd->real_part, divisor_to_conjugate);
|
|
bgc_fp64_quaternion_multiply_by_quaternion("ient->dual_part, ÷nd->dual_part, divisor_to_conjugate);
|
|
|
|
bgc_fp64_quaternion_multiply_by_real("ient->real_part, "ient->real_part, multiplier);
|
|
bgc_fp64_quaternion_multiply_by_real("ient->dual_part, "ient->dual_part, multiplier);
|
|
|
|
return BGC_SUCCESS;
|
|
}
|
|
|
|
// ================ Mean of Two ================= //
|
|
|
|
inline void bgc_fp32_dual_quaternion_get_mean2(BGC_FP32_DualQuaternion* mean, const BGC_FP32_DualQuaternion* quaternion1, const BGC_FP32_DualQuaternion* quaternion2)
|
|
{
|
|
bgc_fp32_quaternion_get_mean2(&mean->real_part, &quaternion1->real_part, &quaternion2->real_part);
|
|
bgc_fp32_quaternion_get_mean2(&mean->dual_part, &quaternion1->dual_part, &quaternion2->dual_part);
|
|
}
|
|
|
|
inline void bgc_fp64_dual_quaternion_get_mean2(BGC_FP64_DualQuaternion* mean, const BGC_FP64_DualQuaternion* quaternion1, const BGC_FP64_DualQuaternion* quaternion2)
|
|
{
|
|
bgc_fp64_quaternion_get_mean2(&mean->real_part, &quaternion1->real_part, &quaternion2->real_part);
|
|
bgc_fp64_quaternion_get_mean2(&mean->dual_part, &quaternion1->dual_part, &quaternion2->dual_part);
|
|
}
|
|
|
|
// =============== Mean of Three ================ //
|
|
|
|
inline void bgc_fp32_dual_quaternion_get_mean3(BGC_FP32_DualQuaternion* mean, const BGC_FP32_DualQuaternion* quaternion1, const BGC_FP32_DualQuaternion* quaternion2, const BGC_FP32_DualQuaternion* quaternion3)
|
|
{
|
|
bgc_fp32_quaternion_get_mean3(&mean->real_part, &quaternion1->real_part, &quaternion2->real_part, &quaternion3->real_part);
|
|
bgc_fp32_quaternion_get_mean3(&mean->dual_part, &quaternion1->dual_part, &quaternion2->dual_part, &quaternion3->dual_part);
|
|
}
|
|
|
|
inline void bgc_fp64_dual_quaternion_get_mean3(BGC_FP64_DualQuaternion* mean, const BGC_FP64_DualQuaternion* quaternion1, const BGC_FP64_DualQuaternion* quaternion2, const BGC_FP64_DualQuaternion* quaternion3)
|
|
{
|
|
bgc_fp64_quaternion_get_mean3(&mean->real_part, &quaternion1->real_part, &quaternion2->real_part, &quaternion3->real_part);
|
|
bgc_fp64_quaternion_get_mean3(&mean->dual_part, &quaternion1->dual_part, &quaternion2->dual_part, &quaternion3->dual_part);
|
|
}
|
|
|
|
// ============ Linear Interpolation ============ //
|
|
|
|
inline void bgc_fp32_dual_quaternion_interpolate(BGC_FP32_DualQuaternion* interpolation, const BGC_FP32_DualQuaternion* first, const BGC_FP32_DualQuaternion* second, const float phase)
|
|
{
|
|
bgc_fp32_quaternion_interpolate(&interpolation->real_part, &first->real_part, &second->real_part, phase);
|
|
bgc_fp32_quaternion_interpolate(&interpolation->dual_part, &first->dual_part, &second->dual_part, phase);
|
|
}
|
|
|
|
inline void bgc_fp64_dual_quaternion_interpolate(BGC_FP64_DualQuaternion* interpolation, const BGC_FP64_DualQuaternion* first, const BGC_FP64_DualQuaternion* second, const double phase)
|
|
{
|
|
bgc_fp64_quaternion_interpolate(&interpolation->real_part, &first->real_part, &second->real_part, phase);
|
|
bgc_fp64_quaternion_interpolate(&interpolation->dual_part, &first->dual_part, &second->dual_part, phase);
|
|
}
|
|
|
|
#endif
|