Развитие SLERP для трёхмерных пространств, а также развитие дуальных чисел, векторов и кватернионов
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23 changed files with 1063 additions and 830 deletions
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@ -8,172 +8,216 @@
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inline void bgc_fp32_dual_vector3_reset(BGC_FP32_DualVector3* vector)
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{
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bgc_fp32_vector3_reset(&vector->real);
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bgc_fp32_vector3_reset(&vector->dual);
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bgc_fp32_vector3_reset(&vector->real_part);
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bgc_fp32_vector3_reset(&vector->dual_part);
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}
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inline void bgc_fp64_dual_vector3_reset(BGC_FP64_DualVector3* vector)
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{
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bgc_fp64_vector3_reset(&vector->real);
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bgc_fp64_vector3_reset(&vector->dual);
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bgc_fp64_vector3_reset(&vector->real_part);
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bgc_fp64_vector3_reset(&vector->dual_part);
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}
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// ==================== Make ==================== //
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inline void bgc_fp32_dual_vector3_make(BGC_FP32_DualVector3* vector, const BGC_FP32_Vector3* real, const BGC_FP32_Vector3* dual)
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inline void bgc_fp32_dual_vector3_make(BGC_FP32_DualVector3* vector, const BGC_FP32_Vector3* real_part, const BGC_FP32_Vector3* dual_part)
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{
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bgc_fp32_vector3_copy(&vector->real, real);
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bgc_fp32_vector3_copy(&vector->dual, dual);
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bgc_fp32_vector3_copy(&vector->real_part, real_part);
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bgc_fp32_vector3_copy(&vector->dual_part, dual_part);
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}
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inline void bgc_fp64_dual_vector3_make(BGC_FP64_DualVector3* vector, const BGC_FP64_Vector3* real, const BGC_FP64_Vector3* dual)
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inline void bgc_fp64_dual_vector3_make(BGC_FP64_DualVector3* vector, const BGC_FP64_Vector3* real_part, const BGC_FP64_Vector3* dual_part)
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{
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bgc_fp64_vector3_copy(&vector->real, real);
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bgc_fp64_vector3_copy(&vector->dual, dual);
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bgc_fp64_vector3_copy(&vector->real_part, real_part);
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bgc_fp64_vector3_copy(&vector->dual_part, dual_part);
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}
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// ==================== Copy ==================== //
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inline void bgc_fp32_dual_vector3_copy(BGC_FP32_DualVector3* destination, const BGC_FP32_DualVector3* source)
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{
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bgc_fp32_vector3_copy(&destination->real, &source->real);
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bgc_fp32_vector3_copy(&destination->dual, &source->dual);
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bgc_fp32_vector3_copy(&destination->real_part, &source->real_part);
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bgc_fp32_vector3_copy(&destination->dual_part, &source->dual_part);
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}
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inline void bgc_fp64_dual_vector3_copy(BGC_FP64_DualVector3* destination, const BGC_FP64_DualVector3* source)
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{
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bgc_fp64_vector3_copy(&destination->real, &source->real);
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bgc_fp64_vector3_copy(&destination->dual, &source->dual);
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bgc_fp64_vector3_copy(&destination->real_part, &source->real_part);
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bgc_fp64_vector3_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_vector3_swap(BGC_FP32_DualVector3* first, BGC_FP32_DualVector3* second)
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{
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bgc_fp32_vector3_swap(&first->real, &second->real);
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bgc_fp32_vector3_swap(&first->dual, &second->dual);
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bgc_fp32_vector3_swap(&first->real_part, &second->real_part);
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bgc_fp32_vector3_swap(&first->dual_part, &second->dual_part);
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}
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inline void bgc_fp64_dual_vector3_swap(BGC_FP64_DualVector3* first, BGC_FP64_DualVector3* second)
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{
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bgc_fp64_vector3_swap(&first->real, &second->real);
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bgc_fp64_vector3_swap(&first->dual, &second->dual);
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}
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// ================== Set Real ================== //
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inline void bgc_fp32_dual_vector3_set_real_values(BGC_FP32_DualVector3* vector, const float x1, const float x2, const float x3)
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{
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vector->real.x1 = x1;
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vector->real.x2 = x2;
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vector->real.x3 = x3;
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}
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inline void bgc_fp64_dual_vector3_set_real_values(BGC_FP64_DualVector3* vector, const double x1, const double x2, const double x3)
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{
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vector->real.x1 = x1;
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vector->real.x2 = x2;
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vector->real.x3 = x3;
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}
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// ================== Set Dual ================== //
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inline void bgc_fp32_dual_vector3_set_dual_values(BGC_FP32_DualVector3* vector, const float x1, const float x2, const float x3)
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{
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vector->dual.x1 = x1;
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vector->dual.x2 = x2;
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vector->dual.x3 = x3;
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}
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inline void bgc_fp64_dual_vector3_set_dual_values(BGC_FP64_DualVector3* vector, const double x1, const double x2, const double x3)
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{
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vector->dual.x1 = x1;
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vector->dual.x2 = x2;
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vector->dual.x3 = x3;
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bgc_fp64_vector3_swap(&first->real_part, &second->real_part);
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bgc_fp64_vector3_swap(&first->dual_part, &second->dual_part);
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}
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// ==================== Add ===================== //
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inline void bgc_fp32_dual_vector3_add(BGC_FP32_DualVector3* sum, const BGC_FP32_DualVector3* first, const BGC_FP32_DualVector3* second)
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{
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bgc_fp32_vector3_add(&sum->real, &first->real, &second->real);
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bgc_fp32_vector3_add(&sum->dual, &first->dual, &second->dual);
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bgc_fp32_vector3_add(&sum->real_part, &first->real_part, &second->real_part);
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bgc_fp32_vector3_add(&sum->dual_part, &first->dual_part, &second->dual_part);
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}
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inline void bgc_fp64_dual_vector3_add(BGC_FP64_DualVector3* sum, const BGC_FP64_DualVector3* first, const BGC_FP64_DualVector3* second)
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{
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bgc_fp64_vector3_add(&sum->real, &first->real, &second->real);
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bgc_fp64_vector3_add(&sum->dual, &first->dual, &second->dual);
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bgc_fp64_vector3_add(&sum->real_part, &first->real_part, &second->real_part);
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bgc_fp64_vector3_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_vector3_add_scaled(BGC_FP32_DualVector3* sum, const BGC_FP32_DualVector3* base_vector, const BGC_FP32_DualVector3* scalable_vector, const float scale)
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{
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bgc_fp32_vector3_add_scaled(&sum->real, &base_vector->real, &scalable_vector->real, scale);
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bgc_fp32_vector3_add_scaled(&sum->dual, &base_vector->dual, &scalable_vector->dual, scale);
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bgc_fp32_vector3_add_scaled(&sum->real_part, &base_vector->real_part, &scalable_vector->real_part, scale);
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bgc_fp32_vector3_add_scaled(&sum->dual_part, &base_vector->dual_part, &scalable_vector->dual_part, scale);
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}
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inline void bgc_fp64_dual_vector3_add_scaled(BGC_FP64_DualVector3* sum, const BGC_FP64_DualVector3* base_vector, const BGC_FP64_DualVector3* scalable_vector, const double scale)
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{
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bgc_fp64_vector3_add_scaled(&sum->real, &base_vector->real, &scalable_vector->real, scale);
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bgc_fp64_vector3_add_scaled(&sum->dual, &base_vector->dual, &scalable_vector->dual, scale);
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bgc_fp64_vector3_add_scaled(&sum->real_part, &base_vector->real_part, &scalable_vector->real_part, scale);
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bgc_fp64_vector3_add_scaled(&sum->dual_part, &base_vector->dual_part, &scalable_vector->dual_part, scale);
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}
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// ================== Subtract ================== //
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inline void bgc_fp32_dual_vector3_subtract(BGC_FP32_DualVector3* difference, const BGC_FP32_DualVector3* minuend, const BGC_FP32_DualVector3* subtrahend)
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{
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bgc_fp32_vector3_subtract(&difference->real, &minuend->real, &subtrahend->real);
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bgc_fp32_vector3_subtract(&difference->dual, &minuend->dual, &subtrahend->dual);
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bgc_fp32_vector3_subtract(&difference->real_part, &minuend->real_part, &subtrahend->real_part);
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bgc_fp32_vector3_subtract(&difference->dual_part, &minuend->dual_part, &subtrahend->dual_part);
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}
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inline void bgc_fp64_dual_vector3_subtract(BGC_FP64_DualVector3* difference, const BGC_FP64_DualVector3* minuend, const BGC_FP64_DualVector3* subtrahend)
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{
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bgc_fp64_vector3_subtract(&difference->real, &minuend->real, &subtrahend->real);
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bgc_fp64_vector3_subtract(&difference->dual, &minuend->dual, &subtrahend->dual);
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bgc_fp64_vector3_subtract(&difference->real_part, &minuend->real_part, &subtrahend->real_part);
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bgc_fp64_vector3_subtract(&difference->dual_part, &minuend->dual_part, &subtrahend->dual_part);
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}
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// ================== Multiply ================== //
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inline void bgc_fp32_dual_vector3_multiply(BGC_FP32_DualVector3* product, const BGC_FP32_DualVector3* multiplicand, const float multiplier)
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inline void bgc_fp32_dual_vector3_multiply_by_real(BGC_FP32_DualVector3* product, const BGC_FP32_DualVector3* multiplicand, const float multiplier)
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{
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bgc_fp32_vector3_multiply_by_real(&product->real, &multiplicand->real, multiplier);
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bgc_fp32_vector3_multiply_by_real(&product->dual, &multiplicand->dual, multiplier);
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bgc_fp32_vector3_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier);
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bgc_fp32_vector3_multiply_by_real(&product->dual_part, &multiplicand->dual_part, multiplier);
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}
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inline void bgc_fp64_dual_vector3_multiply(BGC_FP64_DualVector3* product, const BGC_FP64_DualVector3* multiplicand, const double multiplier)
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inline void bgc_fp64_dual_vector3_multiply_by_real(BGC_FP64_DualVector3* product, const BGC_FP64_DualVector3* multiplicand, const double multiplier)
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{
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bgc_fp64_vector3_multiply_by_real(&product->real, &multiplicand->real, multiplier);
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bgc_fp64_vector3_multiply_by_real(&product->dual, &multiplicand->dual, multiplier);
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bgc_fp64_vector3_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier);
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bgc_fp64_vector3_multiply_by_real(&product->dual_part, &multiplicand->dual_part, multiplier);
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}
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inline void bgc_fp32_dual_vector3_multiply_by_dual(BGC_FP32_DualVector3* product, const BGC_FP32_DualVector3* multiplicand, const BGC_FP32_DualScalar* multiplier)
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{
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const float real_x1 = multiplicand->real_part.x1 * multiplier->real_part;
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const float real_x2 = multiplicand->real_part.x2 * multiplier->real_part;
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const float real_x3 = multiplicand->real_part.x3 * multiplier->real_part;
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const float dual_x1 = multiplicand->dual_part.x1 * multiplier->real_part + multiplicand->real_part.x1 * multiplier->dual_part;
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const float dual_x2 = multiplicand->dual_part.x2 * multiplier->real_part + multiplicand->real_part.x2 * multiplier->dual_part;
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const float dual_x3 = multiplicand->dual_part.x3 * multiplier->real_part + multiplicand->real_part.x3 * multiplier->dual_part;
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product->real_part.x1 = real_x1;
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product->real_part.x2 = real_x2;
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product->real_part.x3 = real_x3;
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product->dual_part.x1 = dual_x1;
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product->dual_part.x2 = dual_x2;
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product->dual_part.x3 = dual_x3;
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}
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inline void bgc_fp64_dual_vector3_multiply_by_dual(BGC_FP64_DualVector3* product, const BGC_FP64_DualVector3* multiplicand, const BGC_FP64_DualScalar* multiplier)
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{
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const double real_x1 = multiplicand->real_part.x1 * multiplier->real_part;
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const double real_x2 = multiplicand->real_part.x2 * multiplier->real_part;
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const double real_x3 = multiplicand->real_part.x3 * multiplier->real_part;
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const double dual_x1 = multiplicand->dual_part.x1 * multiplier->real_part + multiplicand->real_part.x1 * multiplier->dual_part;
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const double dual_x2 = multiplicand->dual_part.x2 * multiplier->real_part + multiplicand->real_part.x2 * multiplier->dual_part;
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const double dual_x3 = multiplicand->dual_part.x3 * multiplier->real_part + multiplicand->real_part.x3 * multiplier->dual_part;
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product->real_part.x1 = real_x1;
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product->real_part.x2 = real_x2;
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product->real_part.x3 = real_x3;
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product->dual_part.x1 = dual_x1;
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product->dual_part.x2 = dual_x2;
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product->dual_part.x3 = dual_x3;
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}
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inline void bgc_fp32_dual_vector3_multiply_by_conjugate(BGC_FP32_DualVector3* product, const BGC_FP32_DualVector3* multiplicand, const BGC_FP32_DualScalar* multiplier_to_conjugate)
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{
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const float real_x1 = multiplicand->real_part.x1 * multiplier_to_conjugate->real_part;
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const float real_x2 = multiplicand->real_part.x2 * multiplier_to_conjugate->real_part;
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const float real_x3 = multiplicand->real_part.x3 * multiplier_to_conjugate->real_part;
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const float dual_x1 = multiplicand->dual_part.x1 * multiplier_to_conjugate->real_part - multiplicand->real_part.x1 * multiplier_to_conjugate->dual_part;
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const float dual_x2 = multiplicand->dual_part.x2 * multiplier_to_conjugate->real_part - multiplicand->real_part.x2 * multiplier_to_conjugate->dual_part;
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const float dual_x3 = multiplicand->dual_part.x3 * multiplier_to_conjugate->real_part - multiplicand->real_part.x3 * multiplier_to_conjugate->dual_part;
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product->real_part.x1 = real_x1;
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product->real_part.x2 = real_x2;
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product->real_part.x3 = real_x3;
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product->dual_part.x1 = dual_x1;
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product->dual_part.x2 = dual_x2;
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product->dual_part.x3 = dual_x3;
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}
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inline void bgc_fp64_dual_vector3_multiply_by_conjugate(BGC_FP64_DualVector3* product, const BGC_FP64_DualVector3* multiplicand, const BGC_FP64_DualScalar* multiplier_to_conjugate)
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{
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const double real_x1 = multiplicand->real_part.x1 * multiplier_to_conjugate->real_part;
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const double real_x2 = multiplicand->real_part.x2 * multiplier_to_conjugate->real_part;
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const double real_x3 = multiplicand->real_part.x3 * multiplier_to_conjugate->real_part;
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const double dual_x1 = multiplicand->dual_part.x1 * multiplier_to_conjugate->real_part - multiplicand->real_part.x1 * multiplier_to_conjugate->dual_part;
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const double dual_x2 = multiplicand->dual_part.x2 * multiplier_to_conjugate->real_part - multiplicand->real_part.x2 * multiplier_to_conjugate->dual_part;
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const double dual_x3 = multiplicand->dual_part.x3 * multiplier_to_conjugate->real_part - multiplicand->real_part.x3 * multiplier_to_conjugate->dual_part;
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product->real_part.x1 = real_x1;
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product->real_part.x2 = real_x2;
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product->real_part.x3 = real_x3;
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product->dual_part.x1 = dual_x1;
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product->dual_part.x2 = dual_x2;
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product->dual_part.x3 = dual_x3;
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}
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// =================== Divide =================== //
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inline int bgc_fp32_dual_vector3_divide(BGC_FP32_DualVector3* quotient, const BGC_FP32_DualVector3* dividend, const float divisor)
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inline int bgc_fp32_dual_vector3_divide_by_real(BGC_FP32_DualVector3* quotient, const BGC_FP32_DualVector3* dividend, const float divisor)
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{
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if (bgc_fp32_is_zero(divisor) || isnan(divisor)) {
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if (bgc_fp32_is_zero(divisor)) {
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return BGC_FAILURE;
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}
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const float multiplier = 1.0f / divisor;
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bgc_fp32_vector3_multiply_by_real("ient->real, ÷nd->real, multiplier);
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bgc_fp32_vector3_multiply_by_real("ient->dual, ÷nd->dual, multiplier);
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bgc_fp32_vector3_multiply_by_real("ient->real_part, ÷nd->real_part, multiplier);
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bgc_fp32_vector3_multiply_by_real("ient->dual_part, ÷nd->dual_part, multiplier);
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return BGC_SUCCESS;
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}
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inline int bgc_fp64_dual_vector3_divide(BGC_FP64_DualVector3* quotient, const BGC_FP64_DualVector3* dividend, const double divisor)
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inline int bgc_fp64_dual_vector3_divide_by_real(BGC_FP64_DualVector3* quotient, const BGC_FP64_DualVector3* dividend, const double divisor)
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{
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if (bgc_fp64_is_zero(divisor) || isnan(divisor)) {
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if (bgc_fp64_is_zero(divisor)) {
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return BGC_FAILURE;
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}
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const double multiplier = 1.0 / divisor;
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bgc_fp64_vector3_multiply_by_real("ient->real, ÷nd->real, multiplier);
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bgc_fp64_vector3_multiply_by_real("ient->dual, ÷nd->dual, multiplier);
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bgc_fp64_vector3_multiply_by_real("ient->real_part, ÷nd->real_part, multiplier);
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bgc_fp64_vector3_multiply_by_real("ient->dual_part, ÷nd->dual_part, multiplier);
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return BGC_SUCCESS;
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}
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@ -182,70 +226,70 @@ inline int bgc_fp64_dual_vector3_divide(BGC_FP64_DualVector3* quotient, const BG
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inline void bgc_fp32_dual_vector3_get_mean2(BGC_FP32_DualVector3* mean, const BGC_FP32_DualVector3* vector1, const BGC_FP32_DualVector3* vector2)
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{
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bgc_fp32_vector3_get_mean2(&mean->real, &vector1->real, &vector2->real);
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bgc_fp32_vector3_get_mean2(&mean->dual, &vector1->dual, &vector2->dual);
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bgc_fp32_vector3_get_mean2(&mean->real_part, &vector1->real_part, &vector2->real_part);
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bgc_fp32_vector3_get_mean2(&mean->dual_part, &vector1->dual_part, &vector2->dual_part);
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}
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inline void bgc_fp64_dual_vector3_get_mean2(BGC_FP64_DualVector3* mean, const BGC_FP64_DualVector3* vector1, const BGC_FP64_DualVector3* vector2)
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{
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bgc_fp64_vector3_get_mean2(&mean->real, &vector1->real, &vector2->real);
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bgc_fp64_vector3_get_mean2(&mean->dual, &vector1->dual, &vector2->dual);
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bgc_fp64_vector3_get_mean2(&mean->real_part, &vector1->real_part, &vector2->real_part);
|
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bgc_fp64_vector3_get_mean2(&mean->dual_part, &vector1->dual_part, &vector2->dual_part);
|
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}
|
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|
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// =============== Mean of Three ================ //
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||||
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inline void bgc_fp32_dual_vector3_get_mean3(BGC_FP32_DualVector3* mean, const BGC_FP32_DualVector3* vector1, const BGC_FP32_DualVector3* vector2, const BGC_FP32_DualVector3* vector3)
|
||||
{
|
||||
bgc_fp32_vector3_get_mean3(&mean->real, &vector1->real, &vector2->real, &vector3->real);
|
||||
bgc_fp32_vector3_get_mean3(&mean->dual, &vector1->dual, &vector2->dual, &vector3->dual);
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bgc_fp32_vector3_get_mean3(&mean->real_part, &vector1->real_part, &vector2->real_part, &vector3->real_part);
|
||||
bgc_fp32_vector3_get_mean3(&mean->dual_part, &vector1->dual_part, &vector2->dual_part, &vector3->dual_part);
|
||||
}
|
||||
|
||||
inline void bgc_fp64_dual_vector3_get_mean3(BGC_FP64_DualVector3* mean, const BGC_FP64_DualVector3* vector1, const BGC_FP64_DualVector3* vector2, const BGC_FP64_DualVector3* vector3)
|
||||
{
|
||||
bgc_fp64_vector3_get_mean3(&mean->real, &vector1->real, &vector2->real, &vector3->real);
|
||||
bgc_fp64_vector3_get_mean3(&mean->dual, &vector1->dual, &vector2->dual, &vector3->dual);
|
||||
bgc_fp64_vector3_get_mean3(&mean->real_part, &vector1->real_part, &vector2->real_part, &vector3->real_part);
|
||||
bgc_fp64_vector3_get_mean3(&mean->dual_part, &vector1->dual_part, &vector2->dual_part, &vector3->dual_part);
|
||||
}
|
||||
|
||||
// ============ Linear Interpolation ============ //
|
||||
|
||||
inline void bgc_fp32_dual_vector3_interpolate(BGC_FP32_DualVector3* interpolation, const BGC_FP32_DualVector3* first, const BGC_FP32_DualVector3* second, const float phase)
|
||||
{
|
||||
bgc_fp32_vector3_interpolate(&interpolation->real, &first->real, &second->real, phase);
|
||||
bgc_fp32_vector3_interpolate(&interpolation->dual, &first->dual, &second->dual, phase);
|
||||
bgc_fp32_vector3_interpolate(&interpolation->real_part, &first->real_part, &second->real_part, phase);
|
||||
bgc_fp32_vector3_interpolate(&interpolation->dual_part, &first->dual_part, &second->dual_part, phase);
|
||||
}
|
||||
|
||||
inline void bgc_fp64_dual_vector3_interpolate(BGC_FP64_DualVector3* interpolation, const BGC_FP64_DualVector3* first, const BGC_FP64_DualVector3* second, const double phase)
|
||||
{
|
||||
bgc_fp64_vector3_interpolate(&interpolation->real, &first->real, &second->real, phase);
|
||||
bgc_fp64_vector3_interpolate(&interpolation->dual, &first->dual, &second->dual, phase);
|
||||
bgc_fp64_vector3_interpolate(&interpolation->real_part, &first->real_part, &second->real_part, phase);
|
||||
bgc_fp64_vector3_interpolate(&interpolation->dual_part, &first->dual_part, &second->dual_part, phase);
|
||||
}
|
||||
|
||||
// =================== Revert =================== //
|
||||
|
||||
inline void bgc_fp32_dual_vector3_revert(BGC_FP32_DualVector3* vector)
|
||||
{
|
||||
bgc_fp32_vector3_revert(&vector->real);
|
||||
bgc_fp32_vector3_revert(&vector->dual);
|
||||
bgc_fp32_vector3_revert(&vector->real_part);
|
||||
bgc_fp32_vector3_revert(&vector->dual_part);
|
||||
}
|
||||
|
||||
inline void bgc_fp64_dual_vector3_revert(BGC_FP64_DualVector3* vector)
|
||||
{
|
||||
bgc_fp64_vector3_revert(&vector->real);
|
||||
bgc_fp64_vector3_revert(&vector->dual);
|
||||
bgc_fp64_vector3_revert(&vector->real_part);
|
||||
bgc_fp64_vector3_revert(&vector->dual_part);
|
||||
}
|
||||
|
||||
// ================ Get Reverse ================= //
|
||||
|
||||
inline void bgc_fp32_dual_vector3_get_reverse(BGC_FP32_DualVector3* reverse, const BGC_FP32_DualVector3* vector)
|
||||
{
|
||||
bgc_fp32_vector3_get_reverse(&reverse->real, &vector->real);
|
||||
bgc_fp32_vector3_get_reverse(&reverse->dual, &vector->dual);
|
||||
bgc_fp32_vector3_get_reverse(&reverse->real_part, &vector->real_part);
|
||||
bgc_fp32_vector3_get_reverse(&reverse->dual_part, &vector->dual_part);
|
||||
}
|
||||
|
||||
inline void bgc_fp64_dual_vector3_get_reverse(BGC_FP64_DualVector3* reverse, const BGC_FP64_DualVector3* vector)
|
||||
{
|
||||
bgc_fp64_vector3_get_reverse(&reverse->real, &vector->real);
|
||||
bgc_fp64_vector3_get_reverse(&reverse->dual, &vector->dual);
|
||||
bgc_fp64_vector3_get_reverse(&reverse->real_part, &vector->real_part);
|
||||
bgc_fp64_vector3_get_reverse(&reverse->dual_part, &vector->dual_part);
|
||||
}
|
||||
|
||||
#endif
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue