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yuzu/src/common/vector_math.h

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// SPDX-FileCopyrightText: 2014 Tony Wasserka
// SPDX-FileCopyrightText: 2014 Dolphin Emulator Project
// SPDX-License-Identifier: BSD-3-Clause AND GPL-2.0-or-later
#pragma once
#include <cmath>
#include <type_traits>
namespace Common {
template <typename T>
class Vec2;
template <typename T>
class Vec3;
template <typename T>
class Vec4;
template <typename T>
class Vec2 {
public:
T x{};
T y{};
constexpr Vec2() = default;
constexpr Vec2(const T& x_, const T& y_) : x(x_), y(y_) {}
template <typename T2>
[[nodiscard]] constexpr Vec2<T2> Cast() const {
return Vec2<T2>(static_cast<T2>(x), static_cast<T2>(y));
}
[[nodiscard]] static constexpr Vec2 AssignToAll(const T& f) {
return Vec2{f, f};
}
[[nodiscard]] constexpr Vec2<decltype(T{} + T{})> operator+(const Vec2& other) const {
return {x + other.x, y + other.y};
}
constexpr Vec2& operator+=(const Vec2& other) {
x += other.x;
y += other.y;
return *this;
}
[[nodiscard]] constexpr Vec2<decltype(T{} - T{})> operator-(const Vec2& other) const {
return {x - other.x, y - other.y};
}
constexpr Vec2& operator-=(const Vec2& other) {
x -= other.x;
y -= other.y;
return *this;
}
template <typename U = T>
[[nodiscard]] constexpr Vec2<std::enable_if_t<std::is_signed_v<U>, U>> operator-() const {
return {-x, -y};
}
[[nodiscard]] constexpr Vec2<decltype(T{} * T{})> operator*(const Vec2& other) const {
return {x * other.x, y * other.y};
}
template <typename V>
[[nodiscard]] constexpr Vec2<decltype(T{} * V{})> operator*(const V& f) const {
using TV = decltype(T{} * V{});
using C = std::common_type_t<T, V>;
return {
static_cast<TV>(static_cast<C>(x) * static_cast<C>(f)),
static_cast<TV>(static_cast<C>(y) * static_cast<C>(f)),
};
}
template <typename V>
constexpr Vec2& operator*=(const V& f) {
*this = *this * f;
return *this;
}
template <typename V>
[[nodiscard]] constexpr Vec2<decltype(T{} / V{})> operator/(const V& f) const {
using TV = decltype(T{} / V{});
using C = std::common_type_t<T, V>;
return {
static_cast<TV>(static_cast<C>(x) / static_cast<C>(f)),
static_cast<TV>(static_cast<C>(y) / static_cast<C>(f)),
};
}
template <typename V>
constexpr Vec2& operator/=(const V& f) {
*this = *this / f;
return *this;
}
[[nodiscard]] constexpr T Length2() const {
return x * x + y * y;
}
// Only implemented for T=float
[[nodiscard]] float Length() const;
[[nodiscard]] float Normalize(); // returns the previous length, which is often useful
[[nodiscard]] constexpr T& operator[](std::size_t i) {
return *((&x) + i);
}
[[nodiscard]] constexpr const T& operator[](std::size_t i) const {
return *((&x) + i);
}
constexpr void SetZero() {
x = 0;
y = 0;
}
// Common aliases: UV (texel coordinates), ST (texture coordinates)
[[nodiscard]] constexpr T& u() {
return x;
}
[[nodiscard]] constexpr T& v() {
return y;
}
[[nodiscard]] constexpr T& s() {
return x;
}
[[nodiscard]] constexpr T& t() {
return y;
}
[[nodiscard]] constexpr const T& u() const {
return x;
}
[[nodiscard]] constexpr const T& v() const {
return y;
}
[[nodiscard]] constexpr const T& s() const {
return x;
}
[[nodiscard]] constexpr const T& t() const {
return y;
}
// swizzlers - create a subvector of specific components
[[nodiscard]] constexpr Vec2 yx() const {
return Vec2(y, x);
}
[[nodiscard]] constexpr Vec2 vu() const {
return Vec2(y, x);
}
[[nodiscard]] constexpr Vec2 ts() const {
return Vec2(y, x);
}
};
template <typename T, typename V>
[[nodiscard]] constexpr Vec2<T> operator*(const V& f, const Vec2<T>& vec) {
using C = std::common_type_t<T, V>;
return Vec2<T>(static_cast<T>(static_cast<C>(f) * static_cast<C>(vec.x)),
static_cast<T>(static_cast<C>(f) * static_cast<C>(vec.y)));
}
using Vec2f = Vec2<float>;
template <>
inline float Vec2<float>::Length() const {
return std::sqrt(x * x + y * y);
}
template <>
inline float Vec2<float>::Normalize() {
float length = Length();
*this /= length;
return length;
}
template <typename T>
class Vec3 {
public:
T x{};
T y{};
T z{};
constexpr Vec3() = default;
constexpr Vec3(const T& x_, const T& y_, const T& z_) : x(x_), y(y_), z(z_) {}
template <typename T2>
[[nodiscard]] constexpr Vec3<T2> Cast() const {
return Vec3<T2>(static_cast<T2>(x), static_cast<T2>(y), static_cast<T2>(z));
}
[[nodiscard]] static constexpr Vec3 AssignToAll(const T& f) {
return Vec3(f, f, f);
}
[[nodiscard]] constexpr Vec3<decltype(T{} + T{})> operator+(const Vec3& other) const {
return {x + other.x, y + other.y, z + other.z};
}
constexpr Vec3& operator+=(const Vec3& other) {
x += other.x;
y += other.y;
z += other.z;
return *this;
}
[[nodiscard]] constexpr Vec3<decltype(T{} - T{})> operator-(const Vec3& other) const {
return {x - other.x, y - other.y, z - other.z};
}
constexpr Vec3& operator-=(const Vec3& other) {
x -= other.x;
y -= other.y;
z -= other.z;
return *this;
}
template <typename U = T>
[[nodiscard]] constexpr Vec3<std::enable_if_t<std::is_signed_v<U>, U>> operator-() const {
return {-x, -y, -z};
}
[[nodiscard]] constexpr Vec3<decltype(T{} * T{})> operator*(const Vec3& other) const {
return {x * other.x, y * other.y, z * other.z};
}
template <typename V>
[[nodiscard]] constexpr Vec3<decltype(T{} * V{})> operator*(const V& f) const {
using TV = decltype(T{} * V{});
using C = std::common_type_t<T, V>;
return {
static_cast<TV>(static_cast<C>(x) * static_cast<C>(f)),
static_cast<TV>(static_cast<C>(y) * static_cast<C>(f)),
static_cast<TV>(static_cast<C>(z) * static_cast<C>(f)),
};
}
template <typename V>
constexpr Vec3& operator*=(const V& f) {
*this = *this * f;
return *this;
}
template <typename V>
[[nodiscard]] constexpr Vec3<decltype(T{} / V{})> operator/(const V& f) const {
using TV = decltype(T{} / V{});
using C = std::common_type_t<T, V>;
return {
static_cast<TV>(static_cast<C>(x) / static_cast<C>(f)),
static_cast<TV>(static_cast<C>(y) / static_cast<C>(f)),
static_cast<TV>(static_cast<C>(z) / static_cast<C>(f)),
};
}
template <typename V>
constexpr Vec3& operator/=(const V& f) {
*this = *this / f;
return *this;
}
[[nodiscard]] constexpr T Length2() const {
return x * x + y * y + z * z;
}
// Only implemented for T=float
[[nodiscard]] float Length() const;
[[nodiscard]] Vec3 Normalized() const;
[[nodiscard]] float Normalize(); // returns the previous length, which is often useful
[[nodiscard]] constexpr T& operator[](std::size_t i) {
return *((&x) + i);
}
[[nodiscard]] constexpr const T& operator[](std::size_t i) const {
return *((&x) + i);
}
constexpr void SetZero() {
x = 0;
y = 0;
z = 0;
}
// Common aliases: UVW (texel coordinates), RGB (colors), STQ (texture coordinates)
[[nodiscard]] constexpr T& u() {
return x;
}
[[nodiscard]] constexpr T& v() {
return y;
}
[[nodiscard]] constexpr T& w() {
return z;
}
[[nodiscard]] constexpr T& r() {
return x;
}
[[nodiscard]] constexpr T& g() {
return y;
}
[[nodiscard]] constexpr T& b() {
return z;
}
[[nodiscard]] constexpr T& s() {
return x;
}
[[nodiscard]] constexpr T& t() {
return y;
}
[[nodiscard]] constexpr T& q() {
return z;
}
[[nodiscard]] constexpr const T& u() const {
return x;
}
[[nodiscard]] constexpr const T& v() const {
return y;
}
[[nodiscard]] constexpr const T& w() const {
return z;
}
[[nodiscard]] constexpr const T& r() const {
return x;
}
[[nodiscard]] constexpr const T& g() const {
return y;
}
[[nodiscard]] constexpr const T& b() const {
return z;
}
[[nodiscard]] constexpr const T& s() const {
return x;
}
[[nodiscard]] constexpr const T& t() const {
return y;
}
[[nodiscard]] constexpr const T& q() const {
return z;
}
// swizzlers - create a subvector of specific components
// e.g. Vec2 uv() { return Vec2(x,y); }
// _DEFINE_SWIZZLER2 defines a single such function, DEFINE_SWIZZLER2 defines all of them for all
// component names (x<->r) and permutations (xy<->yx)
#define _DEFINE_SWIZZLER2(a, b, name) \
[[nodiscard]] constexpr Vec2<T> name() const { \
return Vec2<T>(a, b); \
}
#define DEFINE_SWIZZLER2(a, b, a2, b2, a3, b3, a4, b4) \
_DEFINE_SWIZZLER2(a, b, a##b); \
_DEFINE_SWIZZLER2(a, b, a2##b2); \
_DEFINE_SWIZZLER2(a, b, a3##b3); \
_DEFINE_SWIZZLER2(a, b, a4##b4); \
_DEFINE_SWIZZLER2(b, a, b##a); \
_DEFINE_SWIZZLER2(b, a, b2##a2); \
_DEFINE_SWIZZLER2(b, a, b3##a3); \
_DEFINE_SWIZZLER2(b, a, b4##a4)
DEFINE_SWIZZLER2(x, y, r, g, u, v, s, t);
DEFINE_SWIZZLER2(x, z, r, b, u, w, s, q);
DEFINE_SWIZZLER2(y, z, g, b, v, w, t, q);
#undef DEFINE_SWIZZLER2
#undef _DEFINE_SWIZZLER2
};
template <typename T, typename V>
[[nodiscard]] constexpr Vec3<T> operator*(const V& f, const Vec3<T>& vec) {
using C = std::common_type_t<T, V>;
return Vec3<T>(static_cast<T>(static_cast<C>(f) * static_cast<C>(vec.x)),
static_cast<T>(static_cast<C>(f) * static_cast<C>(vec.y)),
static_cast<T>(static_cast<C>(f) * static_cast<C>(vec.z)));
}
template <>
inline float Vec3<float>::Length() const {
return std::sqrt(x * x + y * y + z * z);
}
template <>
inline Vec3<float> Vec3<float>::Normalized() const {
return *this / Length();
}
template <>
inline float Vec3<float>::Normalize() {
float length = Length();
*this /= length;
return length;
}
using Vec3f = Vec3<float>;
template <typename T>
class Vec4 {
public:
T x{};
T y{};
T z{};
T w{};
constexpr Vec4() = default;
constexpr Vec4(const T& x_, const T& y_, const T& z_, const T& w_)
: x(x_), y(y_), z(z_), w(w_) {}
template <typename T2>
[[nodiscard]] constexpr Vec4<T2> Cast() const {
return Vec4<T2>(static_cast<T2>(x), static_cast<T2>(y), static_cast<T2>(z),
static_cast<T2>(w));
}
[[nodiscard]] static constexpr Vec4 AssignToAll(const T& f) {
return Vec4(f, f, f, f);
}
[[nodiscard]] constexpr Vec4<decltype(T{} + T{})> operator+(const Vec4& other) const {
return {x + other.x, y + other.y, z + other.z, w + other.w};
}
constexpr Vec4& operator+=(const Vec4& other) {
x += other.x;
y += other.y;
z += other.z;
w += other.w;
return *this;
}
[[nodiscard]] constexpr Vec4<decltype(T{} - T{})> operator-(const Vec4& other) const {
return {x - other.x, y - other.y, z - other.z, w - other.w};
}
constexpr Vec4& operator-=(const Vec4& other) {
x -= other.x;
y -= other.y;
z -= other.z;
w -= other.w;
return *this;
}
template <typename U = T>
[[nodiscard]] constexpr Vec4<std::enable_if_t<std::is_signed_v<U>, U>> operator-() const {
return {-x, -y, -z, -w};
}
[[nodiscard]] constexpr Vec4<decltype(T{} * T{})> operator*(const Vec4& other) const {
return {x * other.x, y * other.y, z * other.z, w * other.w};
}
template <typename V>
[[nodiscard]] constexpr Vec4<decltype(T{} * V{})> operator*(const V& f) const {
using TV = decltype(T{} * V{});
using C = std::common_type_t<T, V>;
return {
static_cast<TV>(static_cast<C>(x) * static_cast<C>(f)),
static_cast<TV>(static_cast<C>(y) * static_cast<C>(f)),
static_cast<TV>(static_cast<C>(z) * static_cast<C>(f)),
static_cast<TV>(static_cast<C>(w) * static_cast<C>(f)),
};
}
template <typename V>
constexpr Vec4& operator*=(const V& f) {
*this = *this * f;
return *this;
}
template <typename V>
[[nodiscard]] constexpr Vec4<decltype(T{} / V{})> operator/(const V& f) const {
using TV = decltype(T{} / V{});
using C = std::common_type_t<T, V>;
return {
static_cast<TV>(static_cast<C>(x) / static_cast<C>(f)),
static_cast<TV>(static_cast<C>(y) / static_cast<C>(f)),
static_cast<TV>(static_cast<C>(z) / static_cast<C>(f)),
static_cast<TV>(static_cast<C>(w) / static_cast<C>(f)),
};
}
template <typename V>
constexpr Vec4& operator/=(const V& f) {
*this = *this / f;
return *this;
}
[[nodiscard]] constexpr T Length2() const {
return x * x + y * y + z * z + w * w;
}
[[nodiscard]] constexpr T& operator[](std::size_t i) {
return *((&x) + i);
}
[[nodiscard]] constexpr const T& operator[](std::size_t i) const {
return *((&x) + i);
}
constexpr void SetZero() {
x = 0;
y = 0;
z = 0;
w = 0;
}
// Common alias: RGBA (colors)
[[nodiscard]] constexpr T& r() {
return x;
}
[[nodiscard]] constexpr T& g() {
return y;
}
[[nodiscard]] constexpr T& b() {
return z;
}
[[nodiscard]] constexpr T& a() {
return w;
}
[[nodiscard]] constexpr const T& r() const {
return x;
}
[[nodiscard]] constexpr const T& g() const {
return y;
}
[[nodiscard]] constexpr const T& b() const {
return z;
}
[[nodiscard]] constexpr const T& a() const {
return w;
}
// Swizzlers - Create a subvector of specific components
// e.g. Vec2 uv() { return Vec2(x,y); }
// _DEFINE_SWIZZLER2 defines a single such function
// DEFINE_SWIZZLER2_COMP1 defines one-component functions for all component names (x<->r)
// DEFINE_SWIZZLER2_COMP2 defines two component functions for all component names (x<->r) and
// permutations (xy<->yx)
#define _DEFINE_SWIZZLER2(a, b, name) \
[[nodiscard]] constexpr Vec2<T> name() const { \
return Vec2<T>(a, b); \
}
#define DEFINE_SWIZZLER2_COMP1(a, a2) \
_DEFINE_SWIZZLER2(a, a, a##a); \
_DEFINE_SWIZZLER2(a, a, a2##a2)
#define DEFINE_SWIZZLER2_COMP2(a, b, a2, b2) \
_DEFINE_SWIZZLER2(a, b, a##b); \
_DEFINE_SWIZZLER2(a, b, a2##b2); \
_DEFINE_SWIZZLER2(b, a, b##a); \
_DEFINE_SWIZZLER2(b, a, b2##a2)
DEFINE_SWIZZLER2_COMP2(x, y, r, g);
DEFINE_SWIZZLER2_COMP2(x, z, r, b);
DEFINE_SWIZZLER2_COMP2(x, w, r, a);
DEFINE_SWIZZLER2_COMP2(y, z, g, b);
DEFINE_SWIZZLER2_COMP2(y, w, g, a);
DEFINE_SWIZZLER2_COMP2(z, w, b, a);
DEFINE_SWIZZLER2_COMP1(x, r);
DEFINE_SWIZZLER2_COMP1(y, g);
DEFINE_SWIZZLER2_COMP1(z, b);
DEFINE_SWIZZLER2_COMP1(w, a);
#undef DEFINE_SWIZZLER2_COMP1
#undef DEFINE_SWIZZLER2_COMP2
#undef _DEFINE_SWIZZLER2
#define _DEFINE_SWIZZLER3(a, b, c, name) \
[[nodiscard]] constexpr Vec3<T> name() const { \
return Vec3<T>(a, b, c); \
}
#define DEFINE_SWIZZLER3_COMP1(a, a2) \
_DEFINE_SWIZZLER3(a, a, a, a##a##a); \
_DEFINE_SWIZZLER3(a, a, a, a2##a2##a2)
#define DEFINE_SWIZZLER3_COMP3(a, b, c, a2, b2, c2) \
_DEFINE_SWIZZLER3(a, b, c, a##b##c); \
_DEFINE_SWIZZLER3(a, c, b, a##c##b); \
_DEFINE_SWIZZLER3(b, a, c, b##a##c); \
_DEFINE_SWIZZLER3(b, c, a, b##c##a); \
_DEFINE_SWIZZLER3(c, a, b, c##a##b); \
_DEFINE_SWIZZLER3(c, b, a, c##b##a); \
_DEFINE_SWIZZLER3(a, b, c, a2##b2##c2); \
_DEFINE_SWIZZLER3(a, c, b, a2##c2##b2); \
_DEFINE_SWIZZLER3(b, a, c, b2##a2##c2); \
_DEFINE_SWIZZLER3(b, c, a, b2##c2##a2); \
_DEFINE_SWIZZLER3(c, a, b, c2##a2##b2); \
_DEFINE_SWIZZLER3(c, b, a, c2##b2##a2)
DEFINE_SWIZZLER3_COMP3(x, y, z, r, g, b);
DEFINE_SWIZZLER3_COMP3(x, y, w, r, g, a);
DEFINE_SWIZZLER3_COMP3(x, z, w, r, b, a);
DEFINE_SWIZZLER3_COMP3(y, z, w, g, b, a);
DEFINE_SWIZZLER3_COMP1(x, r);
DEFINE_SWIZZLER3_COMP1(y, g);
DEFINE_SWIZZLER3_COMP1(z, b);
DEFINE_SWIZZLER3_COMP1(w, a);
#undef DEFINE_SWIZZLER3_COMP1
#undef DEFINE_SWIZZLER3_COMP3
#undef _DEFINE_SWIZZLER3
};
template <typename T, typename V>
[[nodiscard]] constexpr Vec4<decltype(V{} * T{})> operator*(const V& f, const Vec4<T>& vec) {
using TV = decltype(V{} * T{});
using C = std::common_type_t<T, V>;
return {
static_cast<TV>(static_cast<C>(f) * static_cast<C>(vec.x)),
static_cast<TV>(static_cast<C>(f) * static_cast<C>(vec.y)),
static_cast<TV>(static_cast<C>(f) * static_cast<C>(vec.z)),
static_cast<TV>(static_cast<C>(f) * static_cast<C>(vec.w)),
};
}
using Vec4f = Vec4<float>;
template <typename T>
constexpr decltype(T{} * T{} + T{} * T{}) Dot(const Vec2<T>& a, const Vec2<T>& b) {
return a.x * b.x + a.y * b.y;
}
template <typename T>
[[nodiscard]] constexpr decltype(T{} * T{} + T{} * T{}) Dot(const Vec3<T>& a, const Vec3<T>& b) {
return a.x * b.x + a.y * b.y + a.z * b.z;
}
template <typename T>
[[nodiscard]] constexpr decltype(T{} * T{} + T{} * T{}) Dot(const Vec4<T>& a, const Vec4<T>& b) {
return a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w;
}
template <typename T>
[[nodiscard]] constexpr Vec3<decltype(T{} * T{} - T{} * T{})> Cross(const Vec3<T>& a,
const Vec3<T>& b) {
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};
}
// linear interpolation via float: 0.0=begin, 1.0=end
template <typename X>
[[nodiscard]] constexpr decltype(X{} * float{} + X{} * float{})
Lerp(const X& begin, const X& end, const float t) {
return begin * (1.f - t) + end * t;
}
// linear interpolation via int: 0=begin, base=end
template <typename X, int base>
[[nodiscard]] constexpr decltype((X{} * int{} + X{} * int{}) / base) LerpInt(const X& begin,
const X& end,
const int t) {
return (begin * (base - t) + end * t) / base;
}
// bilinear interpolation. s is for interpolating x00-x01 and x10-x11, and t is for the second
// interpolation.
template <typename X>
[[nodiscard]] constexpr auto BilinearInterp(const X& x00, const X& x01, const X& x10, const X& x11,
const float s, const float t) {
auto y0 = Lerp(x00, x01, s);
auto y1 = Lerp(x10, x11, s);
return Lerp(y0, y1, t);
}
// Utility vector factories
template <typename T>
[[nodiscard]] constexpr Vec2<T> MakeVec(const T& x, const T& y) {
return Vec2<T>{x, y};
}
template <typename T>
[[nodiscard]] constexpr Vec3<T> MakeVec(const T& x, const T& y, const T& z) {
return Vec3<T>{x, y, z};
}
template <typename T>
[[nodiscard]] constexpr Vec4<T> MakeVec(const T& x, const T& y, const Vec2<T>& zw) {
return MakeVec(x, y, zw[0], zw[1]);
}
template <typename T>
[[nodiscard]] constexpr Vec3<T> MakeVec(const Vec2<T>& xy, const T& z) {
return MakeVec(xy[0], xy[1], z);
}
template <typename T>
[[nodiscard]] constexpr Vec3<T> MakeVec(const T& x, const Vec2<T>& yz) {
return MakeVec(x, yz[0], yz[1]);
}
template <typename T>
[[nodiscard]] constexpr Vec4<T> MakeVec(const T& x, const T& y, const T& z, const T& w) {
return Vec4<T>{x, y, z, w};
}
template <typename T>
[[nodiscard]] constexpr Vec4<T> MakeVec(const Vec2<T>& xy, const T& z, const T& w) {
return MakeVec(xy[0], xy[1], z, w);
}
template <typename T>
[[nodiscard]] constexpr Vec4<T> MakeVec(const T& x, const Vec2<T>& yz, const T& w) {
return MakeVec(x, yz[0], yz[1], w);
}
// NOTE: This has priority over "Vec2<Vec2<T>> MakeVec(const Vec2<T>& x, const Vec2<T>& y)".
// Even if someone wanted to use an odd object like Vec2<Vec2<T>>, the compiler would error
// out soon enough due to misuse of the returned structure.
template <typename T>
[[nodiscard]] constexpr Vec4<T> MakeVec(const Vec2<T>& xy, const Vec2<T>& zw) {
return MakeVec(xy[0], xy[1], zw[0], zw[1]);
}
template <typename T>
[[nodiscard]] constexpr Vec4<T> MakeVec(const Vec3<T>& xyz, const T& w) {
return MakeVec(xyz[0], xyz[1], xyz[2], w);
}
template <typename T>
[[nodiscard]] constexpr Vec4<T> MakeVec(const T& x, const Vec3<T>& yzw) {
return MakeVec(x, yzw[0], yzw[1], yzw[2]);
}
} // namespace Common
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