Развитие SLERP для трёхмерных пространств, а также развитие дуальных чисел, векторов и кватернионов

This commit is contained in:
Andrey Pokidov 2026-02-13 20:34:11 +07:00
parent 053af33444
commit 86ea23de7d
23 changed files with 1063 additions and 830 deletions

View file

@ -8,172 +8,216 @@
inline void bgc_fp32_dual_vector3_reset(BGC_FP32_DualVector3* vector)
{
bgc_fp32_vector3_reset(&vector->real);
bgc_fp32_vector3_reset(&vector->dual);
bgc_fp32_vector3_reset(&vector->real_part);
bgc_fp32_vector3_reset(&vector->dual_part);
}
inline void bgc_fp64_dual_vector3_reset(BGC_FP64_DualVector3* vector)
{
bgc_fp64_vector3_reset(&vector->real);
bgc_fp64_vector3_reset(&vector->dual);
bgc_fp64_vector3_reset(&vector->real_part);
bgc_fp64_vector3_reset(&vector->dual_part);
}
// ==================== Make ==================== //
inline void bgc_fp32_dual_vector3_make(BGC_FP32_DualVector3* vector, const BGC_FP32_Vector3* real, const BGC_FP32_Vector3* dual)
inline void bgc_fp32_dual_vector3_make(BGC_FP32_DualVector3* vector, const BGC_FP32_Vector3* real_part, const BGC_FP32_Vector3* dual_part)
{
bgc_fp32_vector3_copy(&vector->real, real);
bgc_fp32_vector3_copy(&vector->dual, dual);
bgc_fp32_vector3_copy(&vector->real_part, real_part);
bgc_fp32_vector3_copy(&vector->dual_part, dual_part);
}
inline void bgc_fp64_dual_vector3_make(BGC_FP64_DualVector3* vector, const BGC_FP64_Vector3* real, const BGC_FP64_Vector3* dual)
inline void bgc_fp64_dual_vector3_make(BGC_FP64_DualVector3* vector, const BGC_FP64_Vector3* real_part, const BGC_FP64_Vector3* dual_part)
{
bgc_fp64_vector3_copy(&vector->real, real);
bgc_fp64_vector3_copy(&vector->dual, dual);
bgc_fp64_vector3_copy(&vector->real_part, real_part);
bgc_fp64_vector3_copy(&vector->dual_part, dual_part);
}
// ==================== Copy ==================== //
inline void bgc_fp32_dual_vector3_copy(BGC_FP32_DualVector3* destination, const BGC_FP32_DualVector3* source)
{
bgc_fp32_vector3_copy(&destination->real, &source->real);
bgc_fp32_vector3_copy(&destination->dual, &source->dual);
bgc_fp32_vector3_copy(&destination->real_part, &source->real_part);
bgc_fp32_vector3_copy(&destination->dual_part, &source->dual_part);
}
inline void bgc_fp64_dual_vector3_copy(BGC_FP64_DualVector3* destination, const BGC_FP64_DualVector3* source)
{
bgc_fp64_vector3_copy(&destination->real, &source->real);
bgc_fp64_vector3_copy(&destination->dual, &source->dual);
bgc_fp64_vector3_copy(&destination->real_part, &source->real_part);
bgc_fp64_vector3_copy(&destination->dual_part, &source->dual_part);
}
// ==================== Swap ==================== //
inline void bgc_fp32_dual_vector3_swap(BGC_FP32_DualVector3* first, BGC_FP32_DualVector3* second)
{
bgc_fp32_vector3_swap(&first->real, &second->real);
bgc_fp32_vector3_swap(&first->dual, &second->dual);
bgc_fp32_vector3_swap(&first->real_part, &second->real_part);
bgc_fp32_vector3_swap(&first->dual_part, &second->dual_part);
}
inline void bgc_fp64_dual_vector3_swap(BGC_FP64_DualVector3* first, BGC_FP64_DualVector3* second)
{
bgc_fp64_vector3_swap(&first->real, &second->real);
bgc_fp64_vector3_swap(&first->dual, &second->dual);
}
// ================== Set Real ================== //
inline void bgc_fp32_dual_vector3_set_real_values(BGC_FP32_DualVector3* vector, const float x1, const float x2, const float x3)
{
vector->real.x1 = x1;
vector->real.x2 = x2;
vector->real.x3 = x3;
}
inline void bgc_fp64_dual_vector3_set_real_values(BGC_FP64_DualVector3* vector, const double x1, const double x2, const double x3)
{
vector->real.x1 = x1;
vector->real.x2 = x2;
vector->real.x3 = x3;
}
// ================== Set Dual ================== //
inline void bgc_fp32_dual_vector3_set_dual_values(BGC_FP32_DualVector3* vector, const float x1, const float x2, const float x3)
{
vector->dual.x1 = x1;
vector->dual.x2 = x2;
vector->dual.x3 = x3;
}
inline void bgc_fp64_dual_vector3_set_dual_values(BGC_FP64_DualVector3* vector, const double x1, const double x2, const double x3)
{
vector->dual.x1 = x1;
vector->dual.x2 = x2;
vector->dual.x3 = x3;
bgc_fp64_vector3_swap(&first->real_part, &second->real_part);
bgc_fp64_vector3_swap(&first->dual_part, &second->dual_part);
}
// ==================== Add ===================== //
inline void bgc_fp32_dual_vector3_add(BGC_FP32_DualVector3* sum, const BGC_FP32_DualVector3* first, const BGC_FP32_DualVector3* second)
{
bgc_fp32_vector3_add(&sum->real, &first->real, &second->real);
bgc_fp32_vector3_add(&sum->dual, &first->dual, &second->dual);
bgc_fp32_vector3_add(&sum->real_part, &first->real_part, &second->real_part);
bgc_fp32_vector3_add(&sum->dual_part, &first->dual_part, &second->dual_part);
}
inline void bgc_fp64_dual_vector3_add(BGC_FP64_DualVector3* sum, const BGC_FP64_DualVector3* first, const BGC_FP64_DualVector3* second)
{
bgc_fp64_vector3_add(&sum->real, &first->real, &second->real);
bgc_fp64_vector3_add(&sum->dual, &first->dual, &second->dual);
bgc_fp64_vector3_add(&sum->real_part, &first->real_part, &second->real_part);
bgc_fp64_vector3_add(&sum->dual_part, &first->dual_part, &second->dual_part);
}
// ================= Add Scaled ================= //
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)
{
bgc_fp32_vector3_add_scaled(&sum->real, &base_vector->real, &scalable_vector->real, scale);
bgc_fp32_vector3_add_scaled(&sum->dual, &base_vector->dual, &scalable_vector->dual, scale);
bgc_fp32_vector3_add_scaled(&sum->real_part, &base_vector->real_part, &scalable_vector->real_part, scale);
bgc_fp32_vector3_add_scaled(&sum->dual_part, &base_vector->dual_part, &scalable_vector->dual_part, scale);
}
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)
{
bgc_fp64_vector3_add_scaled(&sum->real, &base_vector->real, &scalable_vector->real, scale);
bgc_fp64_vector3_add_scaled(&sum->dual, &base_vector->dual, &scalable_vector->dual, scale);
bgc_fp64_vector3_add_scaled(&sum->real_part, &base_vector->real_part, &scalable_vector->real_part, scale);
bgc_fp64_vector3_add_scaled(&sum->dual_part, &base_vector->dual_part, &scalable_vector->dual_part, scale);
}
// ================== Subtract ================== //
inline void bgc_fp32_dual_vector3_subtract(BGC_FP32_DualVector3* difference, const BGC_FP32_DualVector3* minuend, const BGC_FP32_DualVector3* subtrahend)
{
bgc_fp32_vector3_subtract(&difference->real, &minuend->real, &subtrahend->real);
bgc_fp32_vector3_subtract(&difference->dual, &minuend->dual, &subtrahend->dual);
bgc_fp32_vector3_subtract(&difference->real_part, &minuend->real_part, &subtrahend->real_part);
bgc_fp32_vector3_subtract(&difference->dual_part, &minuend->dual_part, &subtrahend->dual_part);
}
inline void bgc_fp64_dual_vector3_subtract(BGC_FP64_DualVector3* difference, const BGC_FP64_DualVector3* minuend, const BGC_FP64_DualVector3* subtrahend)
{
bgc_fp64_vector3_subtract(&difference->real, &minuend->real, &subtrahend->real);
bgc_fp64_vector3_subtract(&difference->dual, &minuend->dual, &subtrahend->dual);
bgc_fp64_vector3_subtract(&difference->real_part, &minuend->real_part, &subtrahend->real_part);
bgc_fp64_vector3_subtract(&difference->dual_part, &minuend->dual_part, &subtrahend->dual_part);
}
// ================== Multiply ================== //
inline void bgc_fp32_dual_vector3_multiply(BGC_FP32_DualVector3* product, const BGC_FP32_DualVector3* multiplicand, const float multiplier)
inline void bgc_fp32_dual_vector3_multiply_by_real(BGC_FP32_DualVector3* product, const BGC_FP32_DualVector3* multiplicand, const float multiplier)
{
bgc_fp32_vector3_multiply_by_real(&product->real, &multiplicand->real, multiplier);
bgc_fp32_vector3_multiply_by_real(&product->dual, &multiplicand->dual, multiplier);
bgc_fp32_vector3_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier);
bgc_fp32_vector3_multiply_by_real(&product->dual_part, &multiplicand->dual_part, multiplier);
}
inline void bgc_fp64_dual_vector3_multiply(BGC_FP64_DualVector3* product, const BGC_FP64_DualVector3* multiplicand, const double multiplier)
inline void bgc_fp64_dual_vector3_multiply_by_real(BGC_FP64_DualVector3* product, const BGC_FP64_DualVector3* multiplicand, const double multiplier)
{
bgc_fp64_vector3_multiply_by_real(&product->real, &multiplicand->real, multiplier);
bgc_fp64_vector3_multiply_by_real(&product->dual, &multiplicand->dual, multiplier);
bgc_fp64_vector3_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier);
bgc_fp64_vector3_multiply_by_real(&product->dual_part, &multiplicand->dual_part, multiplier);
}
inline void bgc_fp32_dual_vector3_multiply_by_dual(BGC_FP32_DualVector3* product, const BGC_FP32_DualVector3* multiplicand, const BGC_FP32_DualScalar* multiplier)
{
const float real_x1 = multiplicand->real_part.x1 * multiplier->real_part;
const float real_x2 = multiplicand->real_part.x2 * multiplier->real_part;
const float real_x3 = multiplicand->real_part.x3 * multiplier->real_part;
const float dual_x1 = multiplicand->dual_part.x1 * multiplier->real_part + multiplicand->real_part.x1 * multiplier->dual_part;
const float dual_x2 = multiplicand->dual_part.x2 * multiplier->real_part + multiplicand->real_part.x2 * multiplier->dual_part;
const float dual_x3 = multiplicand->dual_part.x3 * multiplier->real_part + multiplicand->real_part.x3 * multiplier->dual_part;
product->real_part.x1 = real_x1;
product->real_part.x2 = real_x2;
product->real_part.x3 = real_x3;
product->dual_part.x1 = dual_x1;
product->dual_part.x2 = dual_x2;
product->dual_part.x3 = dual_x3;
}
inline void bgc_fp64_dual_vector3_multiply_by_dual(BGC_FP64_DualVector3* product, const BGC_FP64_DualVector3* multiplicand, const BGC_FP64_DualScalar* multiplier)
{
const double real_x1 = multiplicand->real_part.x1 * multiplier->real_part;
const double real_x2 = multiplicand->real_part.x2 * multiplier->real_part;
const double real_x3 = multiplicand->real_part.x3 * multiplier->real_part;
const double dual_x1 = multiplicand->dual_part.x1 * multiplier->real_part + multiplicand->real_part.x1 * multiplier->dual_part;
const double dual_x2 = multiplicand->dual_part.x2 * multiplier->real_part + multiplicand->real_part.x2 * multiplier->dual_part;
const double dual_x3 = multiplicand->dual_part.x3 * multiplier->real_part + multiplicand->real_part.x3 * multiplier->dual_part;
product->real_part.x1 = real_x1;
product->real_part.x2 = real_x2;
product->real_part.x3 = real_x3;
product->dual_part.x1 = dual_x1;
product->dual_part.x2 = dual_x2;
product->dual_part.x3 = dual_x3;
}
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)
{
const float real_x1 = multiplicand->real_part.x1 * multiplier_to_conjugate->real_part;
const float real_x2 = multiplicand->real_part.x2 * multiplier_to_conjugate->real_part;
const float real_x3 = multiplicand->real_part.x3 * multiplier_to_conjugate->real_part;
const float dual_x1 = multiplicand->dual_part.x1 * multiplier_to_conjugate->real_part - multiplicand->real_part.x1 * multiplier_to_conjugate->dual_part;
const float dual_x2 = multiplicand->dual_part.x2 * multiplier_to_conjugate->real_part - multiplicand->real_part.x2 * multiplier_to_conjugate->dual_part;
const float dual_x3 = multiplicand->dual_part.x3 * multiplier_to_conjugate->real_part - multiplicand->real_part.x3 * multiplier_to_conjugate->dual_part;
product->real_part.x1 = real_x1;
product->real_part.x2 = real_x2;
product->real_part.x3 = real_x3;
product->dual_part.x1 = dual_x1;
product->dual_part.x2 = dual_x2;
product->dual_part.x3 = dual_x3;
}
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)
{
const double real_x1 = multiplicand->real_part.x1 * multiplier_to_conjugate->real_part;
const double real_x2 = multiplicand->real_part.x2 * multiplier_to_conjugate->real_part;
const double real_x3 = multiplicand->real_part.x3 * multiplier_to_conjugate->real_part;
const double dual_x1 = multiplicand->dual_part.x1 * multiplier_to_conjugate->real_part - multiplicand->real_part.x1 * multiplier_to_conjugate->dual_part;
const double dual_x2 = multiplicand->dual_part.x2 * multiplier_to_conjugate->real_part - multiplicand->real_part.x2 * multiplier_to_conjugate->dual_part;
const double dual_x3 = multiplicand->dual_part.x3 * multiplier_to_conjugate->real_part - multiplicand->real_part.x3 * multiplier_to_conjugate->dual_part;
product->real_part.x1 = real_x1;
product->real_part.x2 = real_x2;
product->real_part.x3 = real_x3;
product->dual_part.x1 = dual_x1;
product->dual_part.x2 = dual_x2;
product->dual_part.x3 = dual_x3;
}
// =================== Divide =================== //
inline int bgc_fp32_dual_vector3_divide(BGC_FP32_DualVector3* quotient, const BGC_FP32_DualVector3* dividend, const float divisor)
inline int bgc_fp32_dual_vector3_divide_by_real(BGC_FP32_DualVector3* quotient, const BGC_FP32_DualVector3* dividend, const float divisor)
{
if (bgc_fp32_is_zero(divisor) || isnan(divisor)) {
if (bgc_fp32_is_zero(divisor)) {
return BGC_FAILURE;
}
const float multiplier = 1.0f / divisor;
bgc_fp32_vector3_multiply_by_real(&quotient->real, &dividend->real, multiplier);
bgc_fp32_vector3_multiply_by_real(&quotient->dual, &dividend->dual, multiplier);
bgc_fp32_vector3_multiply_by_real(&quotient->real_part, &dividend->real_part, multiplier);
bgc_fp32_vector3_multiply_by_real(&quotient->dual_part, &dividend->dual_part, multiplier);
return BGC_SUCCESS;
}
inline int bgc_fp64_dual_vector3_divide(BGC_FP64_DualVector3* quotient, const BGC_FP64_DualVector3* dividend, const double divisor)
inline int bgc_fp64_dual_vector3_divide_by_real(BGC_FP64_DualVector3* quotient, const BGC_FP64_DualVector3* dividend, const double divisor)
{
if (bgc_fp64_is_zero(divisor) || isnan(divisor)) {
if (bgc_fp64_is_zero(divisor)) {
return BGC_FAILURE;
}
const double multiplier = 1.0 / divisor;
bgc_fp64_vector3_multiply_by_real(&quotient->real, &dividend->real, multiplier);
bgc_fp64_vector3_multiply_by_real(&quotient->dual, &dividend->dual, multiplier);
bgc_fp64_vector3_multiply_by_real(&quotient->real_part, &dividend->real_part, multiplier);
bgc_fp64_vector3_multiply_by_real(&quotient->dual_part, &dividend->dual_part, multiplier);
return BGC_SUCCESS;
}
@ -182,70 +226,70 @@ inline int bgc_fp64_dual_vector3_divide(BGC_FP64_DualVector3* quotient, const BG
inline void bgc_fp32_dual_vector3_get_mean2(BGC_FP32_DualVector3* mean, const BGC_FP32_DualVector3* vector1, const BGC_FP32_DualVector3* vector2)
{
bgc_fp32_vector3_get_mean2(&mean->real, &vector1->real, &vector2->real);
bgc_fp32_vector3_get_mean2(&mean->dual, &vector1->dual, &vector2->dual);
bgc_fp32_vector3_get_mean2(&mean->real_part, &vector1->real_part, &vector2->real_part);
bgc_fp32_vector3_get_mean2(&mean->dual_part, &vector1->dual_part, &vector2->dual_part);
}
inline void bgc_fp64_dual_vector3_get_mean2(BGC_FP64_DualVector3* mean, const BGC_FP64_DualVector3* vector1, const BGC_FP64_DualVector3* vector2)
{
bgc_fp64_vector3_get_mean2(&mean->real, &vector1->real, &vector2->real);
bgc_fp64_vector3_get_mean2(&mean->dual, &vector1->dual, &vector2->dual);
bgc_fp64_vector3_get_mean2(&mean->real_part, &vector1->real_part, &vector2->real_part);
bgc_fp64_vector3_get_mean2(&mean->dual_part, &vector1->dual_part, &vector2->dual_part);
}
// =============== Mean of Three ================ //
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);
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