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suyu/src/common/vector_math.h

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// Licensed under GPLv2 or any later version
// Refer to the license.txt file included.
// Copyright 2014 Tony Wasserka
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
// * Neither the name of the owner nor the names of its contributors may
// be used to endorse or promote products derived from this software
// without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#pragma once
#include <cmath>
#include <type_traits>
namespace Math {
template <typename T>
class Vec2;
template <typename T>
class Vec3;
template <typename T>
class Vec4;
template <typename T>
static inline Vec2<T> MakeVec(const T& x, const T& y);
template <typename T>
static inline Vec3<T> MakeVec(const T& x, const T& y, const T& z);
template <typename T>
static inline Vec4<T> MakeVec(const T& x, const T& y, const T& z, const T& w);
template <typename T>
class Vec2 {
public:
T x;
T y;
T* AsArray() {
return &x;
}
Vec2() = default;
Vec2(const T& _x, const T& _y) : x(_x), y(_y) {}
template <typename T2>
Vec2<T2> Cast() const {
return Vec2<T2>((T2)x, (T2)y);
}
static Vec2 AssignToAll(const T& f) {
return Vec2<T>(f, f);
}
void Write(T a[2]) {
a[0] = x;
a[1] = y;
}
Vec2<decltype(T{} + T{})> operator+(const Vec2& other) const {
return MakeVec(x + other.x, y + other.y);
}
void operator+=(const Vec2& other) {
x += other.x;
y += other.y;
}
Vec2<decltype(T{} - T{})> operator-(const Vec2& other) const {
return MakeVec(x - other.x, y - other.y);
}
void operator-=(const Vec2& other) {
x -= other.x;
y -= other.y;
}
template <typename Q = T, class = typename std::enable_if<std::is_signed<Q>::value>::type>
Vec2<decltype(-T{})> operator-() const {
return MakeVec(-x, -y);
}
Vec2<decltype(T{} * T{})> operator*(const Vec2& other) const {
return MakeVec(x * other.x, y * other.y);
}
template <typename V>
Vec2<decltype(T{} * V{})> operator*(const V& f) const {
return MakeVec(x * f, y * f);
}
template <typename V>
void operator*=(const V& f) {
x *= f;
y *= f;
}
template <typename V>
Vec2<decltype(T{} / V{})> operator/(const V& f) const {
return MakeVec(x / f, y / f);
}
template <typename V>
void operator/=(const V& f) {
*this = *this / f;
}
T Length2() const {
return x * x + y * y;
}
// Only implemented for T=float
float Length() const;
void SetLength(const float l);
Vec2 WithLength(const float l) const;
float Distance2To(Vec2& other);
Vec2 Normalized() const;
float Normalize(); // returns the previous length, which is often useful
T& operator[](int i) // allow vector[1] = 3 (vector.y=3)
{
return *((&x) + i);
}
T operator[](const int i) const {
return *((&x) + i);
}
void SetZero() {
x = 0;
y = 0;
}
// Common aliases: UV (texel coordinates), ST (texture coordinates)
T& u() {
return x;
}
T& v() {
return y;
}
T& s() {
return x;
}
T& t() {
return y;
}
const T& u() const {
return x;
}
const T& v() const {
return y;
}
const T& s() const {
return x;
}
const T& t() const {
return y;
}
// swizzlers - create a subvector of specific components
const Vec2 yx() const {
return Vec2(y, x);
}
const Vec2 vu() const {
return Vec2(y, x);
}
const Vec2 ts() const {
return Vec2(y, x);
}
};
template <typename T, typename V>
Vec2<T> operator*(const V& f, const Vec2<T>& vec) {
return Vec2<T>(f * vec.x, f * vec.y);
}
typedef Vec2<float> Vec2f;
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;
T* AsArray() {
return &x;
}
Vec3() = default;
Vec3(const T& _x, const T& _y, const T& _z) : x(_x), y(_y), z(_z) {}
template <typename T2>
Vec3<T2> Cast() const {
return MakeVec<T2>((T2)x, (T2)y, (T2)z);
}
// Only implemented for T=int and T=float
static Vec3 FromRGB(unsigned int rgb);
unsigned int ToRGB() const; // alpha bits set to zero
static Vec3 AssignToAll(const T& f) {
return MakeVec(f, f, f);
}
void Write(T a[3]) {
a[0] = x;
a[1] = y;
a[2] = z;
}
Vec3<decltype(T{} + T{})> operator+(const Vec3& other) const {
return MakeVec(x + other.x, y + other.y, z + other.z);
}
void operator+=(const Vec3& other) {
x += other.x;
y += other.y;
z += other.z;
}
Vec3<decltype(T{} - T{})> operator-(const Vec3& other) const {
return MakeVec(x - other.x, y - other.y, z - other.z);
}
void operator-=(const Vec3& other) {
x -= other.x;
y -= other.y;
z -= other.z;
}
template <typename Q = T, class = typename std::enable_if<std::is_signed<Q>::value>::type>
Vec3<decltype(-T{})> operator-() const {
return MakeVec(-x, -y, -z);
}
Vec3<decltype(T{} * T{})> operator*(const Vec3& other) const {
return MakeVec(x * other.x, y * other.y, z * other.z);
}
template <typename V>
Vec3<decltype(T{} * V{})> operator*(const V& f) const {
return MakeVec(x * f, y * f, z * f);
}
template <typename V>
void operator*=(const V& f) {
x *= f;
y *= f;
z *= f;
}
template <typename V>
Vec3<decltype(T{} / V{})> operator/(const V& f) const {
return MakeVec(x / f, y / f, z / f);
}
template <typename V>
void operator/=(const V& f) {
*this = *this / f;
}
T Length2() const {
return x * x + y * y + z * z;
}
// Only implemented for T=float
float Length() const;
void SetLength(const float l);
Vec3 WithLength(const float l) const;
float Distance2To(Vec3& other);
Vec3 Normalized() const;
float Normalize(); // returns the previous length, which is often useful
T& operator[](int i) // allow vector[2] = 3 (vector.z=3)
{
return *((&x) + i);
}
T operator[](const int i) const {
return *((&x) + i);
}
void SetZero() {
x = 0;
y = 0;
z = 0;
}
// Common aliases: UVW (texel coordinates), RGB (colors), STQ (texture coordinates)
T& u() {
return x;
}
T& v() {
return y;
}
T& w() {
return z;
}
T& r() {
return x;
}
T& g() {
return y;
}
T& b() {
return z;
}
T& s() {
return x;
}
T& t() {
return y;
}
T& q() {
return z;
}
const T& u() const {
return x;
}
const T& v() const {
return y;
}
const T& w() const {
return z;
}
const T& r() const {
return x;
}
const T& g() const {
return y;
}
const T& b() const {
return z;
}
const T& s() const {
return x;
}
const T& t() const {
return y;
}
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) \
const 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>
Vec3<T> operator*(const V& f, const Vec3<T>& vec) {
return Vec3<T>(f * vec.x, f * vec.y, f * 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;
}
typedef Vec3<float> Vec3f;
template <typename T>
class Vec4 {
public:
T x;
T y;
T z;
T w;
T* AsArray() {
return &x;
}
Vec4() = default;
Vec4(const T& _x, const T& _y, const T& _z, const T& _w) : x(_x), y(_y), z(_z), w(_w) {}
template <typename T2>
Vec4<T2> Cast() const {
return Vec4<T2>((T2)x, (T2)y, (T2)z, (T2)w);
}
// Only implemented for T=int and T=float
static Vec4 FromRGBA(unsigned int rgba);
unsigned int ToRGBA() const;
static Vec4 AssignToAll(const T& f) {
return Vec4<T>(f, f, f, f);
}
void Write(T a[4]) {
a[0] = x;
a[1] = y;
a[2] = z;
a[3] = w;
}
Vec4<decltype(T{} + T{})> operator+(const Vec4& other) const {
return MakeVec(x + other.x, y + other.y, z + other.z, w + other.w);
}
void operator+=(const Vec4& other) {
x += other.x;
y += other.y;
z += other.z;
w += other.w;
}
Vec4<decltype(T{} - T{})> operator-(const Vec4& other) const {
return MakeVec(x - other.x, y - other.y, z - other.z, w - other.w);
}
void operator-=(const Vec4& other) {
x -= other.x;
y -= other.y;
z -= other.z;
w -= other.w;
}
template <typename Q = T>
Vec4<decltype(-T{})> operator-() const {
return MakeVec(-x, -y, -z, -w);
}
Vec4<decltype(T{} * T{})> operator*(const Vec4& other) const {
return MakeVec(x * other.x, y * other.y, z * other.z, w * other.w);
}
template <typename V>
Vec4<decltype(T{} * V{})> operator*(const V& f) const {
return MakeVec(x * f, y * f, z * f, w * f);
}
template <typename V>
void operator*=(const V& f) {
x *= f;
y *= f;
z *= f;
w *= f;
}
template <typename V>
Vec4<decltype(T{} / V{})> operator/(const V& f) const {
return MakeVec(x / f, y / f, z / f, w / f);
}
template <typename V>
void operator/=(const V& f) {
*this = *this / f;
}
T Length2() const {
return x * x + y * y + z * z + w * w;
}
// Only implemented for T=float
float Length() const;
void SetLength(const float l);
Vec4 WithLength(const float l) const;
float Distance2To(Vec4& other);
Vec4 Normalized() const;
float Normalize(); // returns the previous length, which is often useful
T& operator[](int i) // allow vector[2] = 3 (vector.z=3)
{
return *((&x) + i);
}
T operator[](const int i) const {
return *((&x) + i);
}
void SetZero() {
x = 0;
y = 0;
z = 0;
w = 0;
}
// Common alias: RGBA (colors)
T& r() {
return x;
}
T& g() {
return y;
}
T& b() {
return z;
}
T& a() {
return w;
}
const T& r() const {
return x;
}
const T& g() const {
return y;
}
const T& b() const {
return z;
}
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) \
const 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) \
const 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>
Vec4<decltype(V{} * T{})> operator*(const V& f, const Vec4<T>& vec) {
return MakeVec(f * vec.x, f * vec.y, f * vec.z, f * vec.w);
}
typedef Vec4<float> Vec4f;
template <typename T>
static inline 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>
static inline 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>
static inline 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>
static inline Vec3<decltype(T{} * T{} - T{} * T{})> Cross(const Vec3<T>& a, const Vec3<T>& b) {
return MakeVec(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>
static inline 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>
static inline 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>
inline 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>
static inline Vec2<T> MakeVec(const T& x, const T& y) {
return Vec2<T>{x, y};
}
template <typename T>
static inline Vec3<T> MakeVec(const T& x, const T& y, const T& z) {
return Vec3<T>{x, y, z};
}
template <typename T>
static inline Vec4<T> MakeVec(const T& x, const T& y, const Vec2<T>& zw) {
return MakeVec(x, y, zw[0], zw[1]);
}
template <typename T>
static inline Vec3<T> MakeVec(const Vec2<T>& xy, const T& z) {
return MakeVec(xy[0], xy[1], z);
}
template <typename T>
static inline Vec3<T> MakeVec(const T& x, const Vec2<T>& yz) {
return MakeVec(x, yz[0], yz[1]);
}
template <typename T>
static inline 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>
static inline Vec4<T> MakeVec(const Vec2<T>& xy, const T& z, const T& w) {
return MakeVec(xy[0], xy[1], z, w);
}
template <typename T>
static inline 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>
static inline Vec4<T> MakeVec(const Vec2<T>& xy, const Vec2<T>& zw) {
return MakeVec(xy[0], xy[1], zw[0], zw[1]);
}
template <typename T>
static inline Vec4<T> MakeVec(const Vec3<T>& xyz, const T& w) {
return MakeVec(xyz[0], xyz[1], xyz[2], w);
}
template <typename T>
static inline Vec4<T> MakeVec(const T& x, const Vec3<T>& yzw) {
return MakeVec(x, yzw[0], yzw[1], yzw[2]);
}
} // namespace
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