Hans Goudey
378022c797
In order to allow interpolation of integers with a float, add a separate template parameter for the factor and multiplication types. Also move some helper constexpr variables to the "base" header (reversing the dependency to "base" -> "vector"). This also adds a distance function for scalar types, which is helpful to allow sharing code between vectors and basic types. Differential Revision: https://developer.blender.org/D14446
389 lines
11 KiB
C++
389 lines
11 KiB
C++
/* SPDX-License-Identifier: GPL-2.0-or-later
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* Copyright 2022 Blender Foundation. */
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#pragma once
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/** \file
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* \ingroup bli
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*/
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#include <cmath>
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#include <type_traits>
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#include "BLI_math_base.hh"
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#include "BLI_math_vec_types.hh"
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#include "BLI_span.hh"
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#include "BLI_utildefines.h"
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namespace blender::math {
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#ifndef NDEBUG
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# define BLI_ASSERT_UNIT(v) \
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{ \
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const float _test_unit = length_squared(v); \
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BLI_assert(!(std::abs(_test_unit - 1.0f) >= BLI_ASSERT_UNIT_EPSILON) || \
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!(std::abs(_test_unit) >= BLI_ASSERT_UNIT_EPSILON)); \
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} \
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(void)0
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#else
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# define BLI_ASSERT_UNIT(v) (void)(v)
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#endif
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template<typename T, int Size> inline bool is_zero(const vec_base<T, Size> &a)
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{
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for (int i = 0; i < Size; i++) {
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if (a[i] != T(0)) {
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return false;
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}
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}
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return true;
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}
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template<typename T, int Size> inline bool is_any_zero(const vec_base<T, Size> &a)
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{
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for (int i = 0; i < Size; i++) {
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if (a[i] == T(0)) {
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return true;
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}
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}
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return false;
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}
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template<typename T, int Size> inline vec_base<T, Size> abs(const vec_base<T, Size> &a)
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{
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vec_base<T, Size> result;
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for (int i = 0; i < Size; i++) {
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result[i] = a[i] >= 0 ? a[i] : -a[i];
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}
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return result;
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}
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template<typename T, int Size>
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inline vec_base<T, Size> min(const vec_base<T, Size> &a, const vec_base<T, Size> &b)
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{
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vec_base<T, Size> result;
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for (int i = 0; i < Size; i++) {
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result[i] = a[i] < b[i] ? a[i] : b[i];
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}
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return result;
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}
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template<typename T, int Size>
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inline vec_base<T, Size> max(const vec_base<T, Size> &a, const vec_base<T, Size> &b)
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{
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vec_base<T, Size> result;
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for (int i = 0; i < Size; i++) {
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result[i] = a[i] > b[i] ? a[i] : b[i];
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}
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return result;
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}
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template<typename T, int Size>
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inline vec_base<T, Size> clamp(const vec_base<T, Size> &a,
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const vec_base<T, Size> &min,
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const vec_base<T, Size> &max)
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{
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vec_base<T, Size> result = a;
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for (int i = 0; i < Size; i++) {
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result[i] = std::clamp(result[i], min[i], max[i]);
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}
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return result;
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}
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template<typename T, int Size>
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inline vec_base<T, Size> clamp(const vec_base<T, Size> &a, const T &min, const T &max)
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{
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vec_base<T, Size> result = a;
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for (int i = 0; i < Size; i++) {
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result[i] = std::clamp(result[i], min, max);
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}
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return result;
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, Size> mod(const vec_base<T, Size> &a, const vec_base<T, Size> &b)
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{
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vec_base<T, Size> result;
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for (int i = 0; i < Size; i++) {
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BLI_assert(b[i] != 0);
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result[i] = std::fmod(a[i], b[i]);
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}
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return result;
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, Size> mod(const vec_base<T, Size> &a, const T &b)
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{
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BLI_assert(b != 0);
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vec_base<T, Size> result;
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for (int i = 0; i < Size; i++) {
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result[i] = std::fmod(a[i], b);
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}
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return result;
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline T safe_mod(const vec_base<T, Size> &a, const vec_base<T, Size> &b)
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{
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vec_base<T, Size> result;
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for (int i = 0; i < Size; i++) {
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result[i] = (b[i] != 0) ? std::fmod(a[i], b[i]) : 0;
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}
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return result;
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline T safe_mod(const vec_base<T, Size> &a, const T &b)
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{
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if (b == 0) {
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return vec_base<T, Size>(0);
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}
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vec_base<T, Size> result;
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for (int i = 0; i < Size; i++) {
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result[i] = std::fmod(a[i], b);
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}
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return result;
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}
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template<typename T, int Size>
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inline void min_max(const vec_base<T, Size> &vector,
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vec_base<T, Size> &min,
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vec_base<T, Size> &max)
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{
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min = math::min(vector, min);
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max = math::max(vector, max);
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, Size> safe_divide(const vec_base<T, Size> &a, const vec_base<T, Size> &b)
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{
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vec_base<T, Size> result;
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for (int i = 0; i < Size; i++) {
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result[i] = (b[i] == 0) ? 0 : a[i] / b[i];
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}
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return result;
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, Size> safe_divide(const vec_base<T, Size> &a, const T &b)
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{
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return (b != 0) ? a / b : vec_base<T, Size>(0.0f);
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, Size> floor(const vec_base<T, Size> &a)
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{
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vec_base<T, Size> result;
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for (int i = 0; i < Size; i++) {
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result[i] = std::floor(a[i]);
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}
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return result;
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, Size> ceil(const vec_base<T, Size> &a)
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{
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vec_base<T, Size> result;
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for (int i = 0; i < Size; i++) {
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result[i] = std::ceil(a[i]);
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}
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return result;
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, Size> fract(const vec_base<T, Size> &a)
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{
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vec_base<T, Size> result;
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for (int i = 0; i < Size; i++) {
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result[i] = a[i] - std::floor(a[i]);
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}
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return result;
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline T dot(const vec_base<T, Size> &a, const vec_base<T, Size> &b)
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{
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T result = a[0] * b[0];
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for (int i = 1; i < Size; i++) {
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result += a[i] * b[i];
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}
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return result;
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}
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template<typename T, int Size> inline T length_manhattan(const vec_base<T, Size> &a)
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{
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T result = std::abs(a[0]);
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for (int i = 1; i < Size; i++) {
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result += std::abs(a[i]);
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}
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return result;
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline T length_squared(const vec_base<T, Size> &a)
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{
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return dot(a, a);
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline T length(const vec_base<T, Size> &a)
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{
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return std::sqrt(length_squared(a));
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline T distance_manhattan(const vec_base<T, Size> &a, const vec_base<T, Size> &b)
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{
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return length_manhattan(a - b);
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline T distance_squared(const vec_base<T, Size> &a, const vec_base<T, Size> &b)
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{
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return length_squared(a - b);
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline T distance(const vec_base<T, Size> &a, const vec_base<T, Size> &b)
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{
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return length(a - b);
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, Size> reflect(const vec_base<T, Size> &incident,
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const vec_base<T, Size> &normal)
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{
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BLI_ASSERT_UNIT(normal);
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return incident - 2.0 * dot(normal, incident) * normal;
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, Size> refract(const vec_base<T, Size> &incident,
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const vec_base<T, Size> &normal,
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const T &eta)
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{
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float dot_ni = dot(normal, incident);
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float k = 1.0f - eta * eta * (1.0f - dot_ni * dot_ni);
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if (k < 0.0f) {
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return vec_base<T, Size>(0.0f);
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}
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return eta * incident - (eta * dot_ni + sqrt(k)) * normal;
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, Size> project(const vec_base<T, Size> &p, const vec_base<T, Size> &v_proj)
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{
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if (UNLIKELY(is_zero(v_proj))) {
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return vec_base<T, Size>(0.0f);
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}
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return v_proj * (dot(p, v_proj) / dot(v_proj, v_proj));
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, Size> normalize_and_get_length(const vec_base<T, Size> &v, T &out_length)
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{
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out_length = length_squared(v);
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/* A larger value causes normalize errors in a scaled down models with camera extreme close. */
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constexpr T threshold = std::is_same_v<T, double> ? 1.0e-70 : 1.0e-35f;
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if (out_length > threshold) {
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out_length = sqrt(out_length);
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return v / out_length;
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}
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/* Either the vector is small or one of it's values contained `nan`. */
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out_length = 0.0;
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return vec_base<T, Size>(0.0);
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, Size> normalize(const vec_base<T, Size> &v)
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{
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T len;
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return normalize_and_get_length(v, len);
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}
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template<typename T, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, 3> cross(const vec_base<T, 3> &a, const vec_base<T, 3> &b)
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{
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return {a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x};
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}
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inline vec_base<float, 3> cross_high_precision(const vec_base<float, 3> &a,
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const vec_base<float, 3> &b)
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{
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return {(float)((double)a.y * b.z - (double)a.z * b.y),
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(float)((double)a.z * b.x - (double)a.x * b.z),
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(float)((double)a.x * b.y - (double)a.y * b.x)};
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}
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template<typename T, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, 3> cross_poly(Span<vec_base<T, 3>> poly)
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{
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/* Newell's Method. */
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int nv = static_cast<int>(poly.size());
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if (nv < 3) {
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return vec_base<T, 3>(0, 0, 0);
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}
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const vec_base<T, 3> *v_prev = &poly[nv - 1];
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const vec_base<T, 3> *v_curr = &poly[0];
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vec_base<T, 3> n(0, 0, 0);
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for (int i = 0; i < nv;) {
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n[0] = n[0] + ((*v_prev)[1] - (*v_curr)[1]) * ((*v_prev)[2] + (*v_curr)[2]);
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n[1] = n[1] + ((*v_prev)[2] - (*v_curr)[2]) * ((*v_prev)[0] + (*v_curr)[0]);
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n[2] = n[2] + ((*v_prev)[0] - (*v_curr)[0]) * ((*v_prev)[1] + (*v_curr)[1]);
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v_prev = v_curr;
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++i;
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if (i < nv) {
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v_curr = &poly[i];
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}
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}
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return n;
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}
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template<typename T, typename FactorT, int Size, BLI_ENABLE_IF((is_math_float_type<FactorT>))>
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inline vec_base<T, Size> interpolate(const vec_base<T, Size> &a,
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const vec_base<T, Size> &b,
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const FactorT &t)
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{
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return a * (1 - t) + b * t;
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, Size> midpoint(const vec_base<T, Size> &a, const vec_base<T, Size> &b)
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{
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return (a + b) * 0.5;
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}
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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inline vec_base<T, Size> faceforward(const vec_base<T, Size> &vector,
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const vec_base<T, Size> &incident,
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const vec_base<T, Size> &reference)
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{
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return (dot(reference, incident) < 0) ? vector : -vector;
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}
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template<typename T> inline int dominant_axis(const vec_base<T, 3> &a)
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{
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vec_base<T, 3> b = abs(a);
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return ((b.x > b.y) ? ((b.x > b.z) ? 0 : 2) : ((b.y > b.z) ? 1 : 2));
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}
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/** Intersections. */
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template<typename T> struct isect_result {
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enum {
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LINE_LINE_COLINEAR = -1,
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LINE_LINE_NONE = 0,
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LINE_LINE_EXACT = 1,
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LINE_LINE_CROSS = 2,
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} kind;
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typename T::base_type lambda;
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};
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template<typename T, int Size, BLI_ENABLE_IF((is_math_float_type<T>))>
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isect_result<vec_base<T, Size>> isect_seg_seg(const vec_base<T, Size> &v1,
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const vec_base<T, Size> &v2,
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const vec_base<T, Size> &v3,
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const vec_base<T, Size> &v4);
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} // namespace blender::math
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