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blah/include/blah_spatial.h
Noel Berry f06c38ff3e added bool Rect::contains(Rect)
2022-10-03 00:30:49 -07:00

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#pragma once
#include <blah_common.h>
#include <blah_calc.h>
namespace Blah
{
static constexpr double epsilon = 0.000001;
template<class T> struct Vec2;
template<class T> struct Vec3;
template<class T> struct Vec4;
template<class T> struct Mat3x2;
template<class T> struct Mat4x4;
template<class T> struct Rect;
template<class T> struct Quad;
template<class T> struct Line;
template<class T> struct Circle;
using Vec2f = Vec2<float>;
using Vec2d = Vec2<double>;
using Vec2i = Vec2<int>;
using Point = Vec2<int>;
using Vec3f = Vec3<float>;
using Vec3d = Vec3<double>;
using Vec4f = Vec4<float>;
using Vec4d = Vec4<double>;
using Mat3x2f = Mat3x2<float>;
using Mat3x2d = Mat3x2<double>;
using Mat4x4f = Mat4x4<float>;
using Mat4x4d = Mat4x4<double>;
using Rectf = Rect<float>;
using Rectd = Rect<double>;
using Recti = Rect<int>;
using Quadf = Quad<float>;
using Quadd = Quad<double>;
using Linef = Line<float>;
using Lined = Line<double>;
using Circlef = Circle<float>;
using Circled = Circle<double>;
template<class T>
struct Vec2
{
T x;
T y;
constexpr Vec2();
template<class X, class Y>
constexpr Vec2(X x, Y y);
template<class K>
constexpr Vec2(const Vec2<K>& vector);
constexpr Vec2 operator+(const Vec2& rhs) const;
constexpr Vec2 operator-(const Vec2& rhs) const;
constexpr Vec2 operator/(const T rhs) const;
constexpr Vec2 operator*(const T rhs) const;
constexpr Vec2 operator*(const Vec2& rhs);
constexpr Vec2 operator-() const;
constexpr Vec2& operator+=(const Vec2& rhs);
constexpr Vec2& operator-=(const Vec2& rhs);
constexpr Vec2& operator/=(const Vec2& rhs);
constexpr Vec2& operator*=(const Vec2& rhs);
constexpr Vec2& operator/=(T rhs);
constexpr Vec2& operator*=(T rhs);
constexpr bool operator==(const Vec2& rhs) const;
constexpr bool operator!=(const Vec2& rhs) const;
constexpr Vec2 abs() const;
Vec2 normal() const;
constexpr Vec2 turn_right() const;
constexpr Vec2 turn_left() const;
T length() const;
constexpr T length_squared() const;
T angle() const;
static constexpr T dot(const Vec2& a, const Vec2& b);
static constexpr Vec2 transform(const Vec2& vec, const Mat3x2<T>& matrix);
static constexpr Vec2 transform_normal(const Vec2& vec, const Mat3x2<T>& matrix);
static Vec2 from_angle(T radians, T length = 1);
static constexpr Vec2 approach(const Vec2& t, const Vec2& target, T delta);
static constexpr Vec2 lerp(const Vec2& a, const Vec2& b, T t);
static constexpr Vec2 lerp_bezier(const Vec2& a, const Vec2& b, const Vec2& end, T t);
static constexpr Vec2 lerp_bezier(const Vec2& a, const Vec2& b, const Vec2& c, const Vec2& end, T t);
static constexpr Vec2 reflect(const Vec2& vector, const Vec2& normal);
static constexpr Vec2 min(const Vec2& a, const Vec2& b);
static constexpr Vec2 max(const Vec2& a, const Vec2& b);
static const Vec2 unit_x;
static const Vec2 unit_y;
static const Vec2 right;
static const Vec2 up;
static const Vec2 down;
static const Vec2 left;
static const Vec2 zero;
static const Vec2 one;
};
template<class T> const Vec2<T> Vec2<T>::unit_x = Vec2<T>(1, 0);
template<class T> const Vec2<T> Vec2<T>::unit_y = Vec2<T>(0, 1);
template<class T> const Vec2<T> Vec2<T>::right = Vec2<T>(1, 0);
template<class T> const Vec2<T> Vec2<T>::up = Vec2<T>(0, -1);
template<class T> const Vec2<T> Vec2<T>::down = Vec2<T>(0, 1);
template<class T> const Vec2<T> Vec2<T>::left = Vec2<T>(-1, 0);
template<class T> const Vec2<T> Vec2<T>::zero = Vec2<T>(0, 0);
template<class T> const Vec2<T> Vec2<T>::one = Vec2<T>(1, 1);
template<class T>
struct Vec3
{
T x;
T y;
T z;
constexpr Vec3();
template<class X, class Y, class Z>
constexpr Vec3(X x, Y y, Z z);
template<class K>
constexpr Vec3(const Vec3<K>& vector);
constexpr Vec3 operator +(const Vec3& rhs) const;
constexpr Vec3 operator -(const Vec3& rhs) const;
T length() const;
Vec3 normal() const;
static constexpr T dot(const Vec3& a, const Vec3& b);
static constexpr Vec3 cross(const Vec3& a, const Vec3& b);
};
template<class T>
struct Vec4
{
T x;
T y;
T z;
T w;
constexpr Vec4();
template<class X, class Y, class Z, class W>
constexpr Vec4(X x, Y y, Z z, W w);
template<class K>
constexpr Vec4(const Vec4<K>& vector);
};
template<class T>
struct Rect
{
T x;
T y;
T w;
T h;
constexpr Rect();
constexpr Rect(T x, T y, T w, T h);
template<class X, class Y, class W, class H>
constexpr Rect(X x, Y y, W w, H h);
template<class K>
constexpr Rect(const Rect<K>& rect);
constexpr Rect operator+(const Vec2<T>& rhs) const;
constexpr Rect operator-(const Vec2<T>& rhs) const;
constexpr Rect& operator+=(const Vec2<T>& rhs);
constexpr Rect& operator-=(const Vec2<T>& rhs);
constexpr bool operator==(const Rect& rhs) const;
constexpr bool operator!=(const Rect& rhs) const;
constexpr T left() const;
constexpr T right() const;
constexpr T top() const;
constexpr T bottom() const;
constexpr Vec2<T> center() const;
constexpr T center_x() const;
constexpr T center_y() const;
constexpr Vec2<T> top_left() const;
constexpr Vec2<T> top_right() const;
constexpr Vec2<T> bottom_right() const;
constexpr Vec2<T> bottom_left() const;
constexpr Vec2<T> center_left() const;
constexpr Vec2<T> center_right() const;
constexpr Vec2<T> middle_top() const;
constexpr Vec2<T> middle_bottom() const;
constexpr Line<T> left_line() const;
constexpr Line<T> right_line() const;
constexpr Line<T> top_line() const;
constexpr Line<T> bottom_line() const;
constexpr bool contains(const Vec2<T>& pt) const;
constexpr bool contains(const Rect& rect) const;
constexpr bool overlaps(const Rect& rect) const;
constexpr Rect overlap_rect(const Rect& other) const;
constexpr bool intersects(const Line<T>& line) const;
constexpr bool intersects(const Line<T>& line, Vec2<T>* out_intersection_point) const;
constexpr bool intersects(const Vec2<T>& line_from, const Vec2<T>& line_to) const;
constexpr bool intersects(const Vec2<T>& line_from, const Vec2<T>& line_to, Vec2<T>* out_intersection_point) const;
constexpr Vec2<T> intersection_point(const Line<T>& line) const;
constexpr Vec2<T> intersection_point(const Vec2<T>& line_from, const Vec2<T>& line_to) const;
constexpr Rect scale(T s) const;
constexpr Rect scale(T sx, T sy) const;
constexpr Rect inflate(T amount) const;
constexpr Rect inflate(T amount_x, T amount_y) const;
// Rect Sectors:
// 0101 0100 0110
// 0001 0000 0010
// 1001 1000 1010
// 0000 = inside rectangle, all others refer to sectors relative to the rectangle
constexpr u8 get_sector(const Vec2<T>& pt) const;
static constexpr Rect transform(const Rect& rect, const Mat3x2<T>& matrix);
static constexpr Rect from_points(const Vec2<T>& from, const Vec2<T>& to);
};
template<class T>
struct Circle
{
Vec2<T> center;
T radius;
constexpr Circle();
constexpr Circle(T x, T y, T radius);
constexpr Circle(const Vec2<T>& center, T radius);
template<class K>
constexpr Circle(const Circle<K>& circle);
constexpr void project(const Vec2<T>& axis, T* min, T* max) const;
};
template<class T>
struct Quad
{
Vec2<T> a;
Vec2<T> b;
Vec2<T> c;
Vec2<T> d;
constexpr Quad();
constexpr Quad(const Vec2<T>& a, const Vec2<T>& b, const Vec2<T>& c, const Vec2<T>& d);
constexpr void project(const Vec2<T>& axis, T* min, T* max) const;
};
template<class T>
struct Line
{
Vec2<T> a;
Vec2<T> b;
constexpr Line();
constexpr Line(const Vec2<T>& a, const Vec2<T>& b);
constexpr Line(T x0, T y0, T x1, T y1);
constexpr Rect<T> bounds() const;
constexpr Vec2<T> closest_point(const Vec2<T>& pt) const;
constexpr bool intersects(const Rect<T>& rect, Vec2<T>* out_intersection_point = nullptr) const;
constexpr bool intersects(const Line<T>& line, Vec2<T>* out_intersection_point = nullptr) const;
constexpr void project(const Vec2<T>& axis, T* min, T* max) const;
constexpr Line operator +(const Vec2<T>& rhs) const;
constexpr Line operator -(const Vec2<T>& rhs) const;
};
template<class T>
struct Mat3x2
{
T m11;
T m12;
T m21;
T m22;
T m31;
T m32;
constexpr Mat3x2();
constexpr Mat3x2(T m11, T m12, T m21, T m22, T m31, T m32);
template<class K>
constexpr Mat3x2(const Mat3x2<K>& matrix);
static const Mat3x2 identity;
constexpr Mat3x2 invert() const;
T scaling_factor() const;
static constexpr Mat3x2 create_translation(const Vec2<T>& position);
static constexpr Mat3x2 create_translation(T x, T y);
static constexpr Mat3x2 create_scale(T scale);
static constexpr Mat3x2 create_scale(T x, T y);
static constexpr Mat3x2 create_scale(const Vec2<T>& scale);
static constexpr Mat3x2 create_scale(T scale, const Vec2<T>& center_point);
static constexpr Mat3x2 create_scale(const Vec2<T>& scale, const Vec2<T>& center_point);
static constexpr Mat3x2 create_scale(T scale_x, T scale_y, const Vec2<T>& center_point);
static Mat3x2 create_rotation(T radians);
static Mat3x2 create_transform(const Vec2<T>& position, const Vec2<T>& origin, const Vec2<T>& scale, T rotation);
static constexpr Mat3x2 add(const Mat3x2& a, const Mat3x2& b);
static constexpr Mat3x2 subtract(const Mat3x2& a, const Mat3x2& b);
static constexpr Mat3x2 multiply(const Mat3x2& a, const Mat3x2& b);
constexpr Mat3x2 operator *(const Mat3x2& rhs) const;
constexpr Mat3x2 operator +(const Mat3x2& rhs) const;
constexpr Mat3x2 operator -(const Mat3x2& rhs) const;
constexpr Mat3x2& operator *=(const Mat3x2& rhs);
constexpr bool operator==(const Mat3x2& rhs);
constexpr bool operator!=(const Mat3x2& rhs);
};
template<class T> const Mat3x2<T> Mat3x2<T>::identity = Mat3x2<T>(1, 0, 0, 1, 0, 0);
template<class T>
struct Mat4x4
{
T m11;
T m12;
T m13;
T m14;
T m21;
T m22;
T m23;
T m24;
T m31;
T m32;
T m33;
T m34;
T m41;
T m42;
T m43;
T m44;
Mat4x4();
Mat4x4(
T m11, T m12, T m13, T m14,
T m21, T m22, T m23, T m24,
T m31, T m32, T m33, T m34,
T m41, T m42, T m43, T m44);
static const Mat4x4 identity;
static constexpr Mat4x4 create_ortho(T width, T height, T z_near_plane, T z_far_plane);
static constexpr Mat4x4 create_ortho_offcenter(T left, T right, T bottom, T top, T z_near_plane, T z_far_plane);
static Mat4x4 create_perspective(T field_of_view, T ratio, T z_near_plane, T z_far_plane);
static constexpr Mat4x4 create_translation(T x, T y, T z);
static constexpr Mat4x4 create_scale(T x, T y, T z);
static Mat4x4 create_lookat(const Vec3<T>& position, const Vec3<T>& target, const Vec3<T>& up);
constexpr Mat4x4 operator* (const Mat4x4& rhs);
};
template<class T> const Mat4x4<T> Mat4x4<T>::identity = Mat4x4<T>(
1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f);
template<class T>
constexpr Vec2<T>::Vec2()
: x(0), y(0) {}
template<class T>
template<class X, class Y>
constexpr Vec2<T>::Vec2(X x, Y y)
: x(static_cast<T>(x)), y(static_cast<T>(y)) {}
template<class T>
template<class K>
constexpr Vec2<T>::Vec2(const Vec2<K>& vector)
: x(static_cast<T>(vector.x)), y(static_cast<T>(vector.y)) {}
template<class T>
constexpr Vec2<T> Vec2<T>::operator+(const Vec2& rhs) const {
return Vec2(x + rhs.x, y + rhs.y);
}
template<class T>
constexpr Vec2<T> Vec2<T>::operator-(const Vec2& rhs) const {
return Vec2(x - rhs.x, y - rhs.y);
}
template<class T>
constexpr Vec2<T> Vec2<T>::operator-() const {
return Vec2(-x, -y);
}
template<class T>
constexpr Vec2<T> Vec2<T>::operator/(const T rhs) const {
return Vec2(x / rhs, y / rhs);
}
template<class T>
constexpr Vec2<T> Vec2<T>::operator* (const T rhs) const {
return Vec2(x * rhs, y * rhs);
}
template<class T>
constexpr Vec2<T> Vec2<T>::operator *(const Vec2& rhs) {
return Vec2(x * rhs.x, y * rhs.y);
}
template<class T>
constexpr Vec2<T>& Vec2<T>::operator += (const Vec2& rhs) {
x += rhs.x;
y += rhs.y;
return *this;
}
template<class T>
constexpr Vec2<T>& Vec2<T>::operator -= (const Vec2& rhs) {
x -= rhs.x;
y -= rhs.y;
return *this;
}
template<class T>
constexpr Vec2<T>& Vec2<T>::operator /= (T rhs) {
x /= rhs;
y /= rhs;
return *this;
}
template<class T>
constexpr Vec2<T>& Vec2<T>::operator *= (const Vec2 & rhs) {
x *= rhs.x;
y *= rhs.y;
return this;
}
template<class T>
constexpr Vec2<T>& Vec2<T>::operator *=(T rhs) {
x *= rhs;
y *= rhs;
return *this;
}
template<class T>
constexpr bool Vec2<T>::operator ==(const Vec2& rhs) const {
return Calc::abs(x - rhs.x) < epsilon && Calc::abs(y - rhs.y) < epsilon;
}
template<class T>
constexpr bool Vec2<T>::operator !=(const Vec2& rhs) const {
return !(*this == rhs);
}
template<class T>
constexpr Vec2<T> Vec2<T>::abs() const {
return Vec2(Calc::abs(x), Calc::abs(y));
}
template<class T>
Vec2<T> Vec2<T>::normal() const {
auto len = Calc::sqrt(x * x + y * y);
if (len <= 0)
return Vec2<T>(0, 0);
return Vec2(x / len, y / len);
}
template<class T>
constexpr Vec2<T> Vec2<T>::turn_right() const {
return Vec2(-y, x);
}
template<class T>
constexpr Vec2<T> Vec2<T>::turn_left() const {
return Vec2(y, -x);
}
template<class T>
T Vec2<T>::length() const {
return static_cast<T>(Calc::sqrt(static_cast<f32>(x * x + y * y)));
}
template<class T>
constexpr T Vec2<T>::length_squared() const {
return x * x + y * y;
}
template<class T>
T Vec2<T>::angle() const {
return Calc::atan2(y, x);
}
template<class T>
constexpr T Vec2<T>::dot(const Vec2& a, const Vec2& b) {
return a.x * b.x + a.y * b.y;
}
template<class T>
constexpr Vec2<T> Vec2<T>::transform(const Vec2& vec, const Mat3x2<T>& matrix) {
return Vec2(
(vec.x * matrix.m11) + (vec.y * matrix.m21) + matrix.m31,
(vec.x * matrix.m12) + (vec.y * matrix.m22) + matrix.m32);
}
template<class T>
constexpr Vec2<T> Vec2<T>::transform_normal(const Vec2& vec, const Mat3x2<T>& matrix) {
return Vec2(
vec.x * matrix.m11 + vec.y * matrix.m21,
vec.x * matrix.m12 + vec.y * matrix.m22);
}
template<class T>
Vec2<T> Vec2<T>::from_angle(T radians, T length) {
return Vec2(
Calc::cos(radians) * length,
Calc::sin(radians) * length);
}
template<class T>
constexpr Vec2<T> Vec2<T>::approach(const Vec2& value, const Vec2& target, T delta) {
if ((value - target).length_squared() <= delta * delta)
return target;
return value + (target - value).normal() * delta;
}
template<class T>
constexpr Vec2<T> Vec2<T>::lerp(const Vec2& a, const Vec2& b, T t) {
if (t == 0)
return a;
else if (t == 1)
return b;
else
return a + (b - a) * t;
}
template<class T>
constexpr Vec2<T> Vec2<T>::lerp_bezier(const Vec2& a, const Vec2& b, const Vec2& end, T t) {
return lerp(lerp(a, b, t), lerp(b, end, t), t);
}
template<class T>
constexpr Vec2<T> Vec2<T>::lerp_bezier(const Vec2& a, const Vec2& b, const Vec2& c, const Vec2& end, T t) {
return lerp_bezier(lerp(a, b, t), lerp(b, c, t), lerp(c, end, t), t);
}
template<class T>
constexpr Vec2<T> Vec2<T>::reflect(const Vec2& vector, const Vec2& normal) {
auto dot = vector.x * normal.x + vector.y * normal.y;
return Vec2(
vector.x - 2 * dot * normal.x,
vector.y - 2 * dot * normal.y);
}
template<class T>
constexpr Vec2<T> Vec2<T>::min(const Vec2& a, const Vec2& b) {
return Vec2(Calc::min(a.x, b.x), Calc::min(a.y, b.y));
}
template<class T>
constexpr Vec2<T> Vec2<T>::max(const Vec2& a, const Vec2& b) {
return Vec2(Calc::max(a.x, b.x), Calc::max(a.y, b.y));
}
template<class T>
constexpr Vec3<T>::Vec3()
: x(0), y(0), z(0) {}
template<class T>
template<class X, class Y, class Z>
constexpr Vec3<T>::Vec3(X x, Y y, Z z)
: x(static_cast<T>(x)), y(static_cast<T>(y)), z(static_cast<T>(z)) {}
template<class T>
template<class K>
constexpr Vec3<T>::Vec3(const Vec3<K>& vector)
: x(static_cast<T>(vector.x)), y(static_cast<T>(vector.y)), z(static_cast<T>(vector.z)) {}
template<class T>
constexpr Vec3<T> Vec3<T>::operator+(const Vec3& rhs) const {
return Vec3(x + rhs.x, y + rhs.y, z + rhs.z);
}
template<class T>
constexpr Vec3<T> Vec3<T>::operator-(const Vec3& rhs) const {
return Vec3(x - rhs.x, y - rhs.y, z - rhs.z);
}
template<class T>
T Vec3<T>::length() const {
return Calc::sqrt(x * x + y * y + z * z);
}
template<class T>
Vec3<T> Vec3<T>::normal() const {
T len = length();
return Vec3(x / len, y / len, z / len);
}
template<class T>
constexpr T Vec3<T>::dot(const Vec3& a, const Vec3& b) {
return a.x * b.x + a.y * b.y + a.z * b.z;
}
template<class T>
constexpr Vec3<T> Vec3<T>::cross(const Vec3& a, const Vec3& b) {
return Vec3(
a.y * b.z - a.z * b.y,
a.z * b.x - a.x * b.z,
a.x * b.y - a.y * b.x);
}
template<class T>
constexpr Vec4<T>::Vec4()
: x(0), y(0), z(0), w(0) {}
template<class T>
template<class X, class Y, class Z, class W>
constexpr Vec4<T>::Vec4(X x, Y y, Z z, W w)
: x(static_cast<T>(x)), y(static_cast<T>(y)), z(static_cast<T>(z)), w(static_cast<T>(w)) {}
template<class T>
template<class K>
constexpr Vec4<T>::Vec4(const Vec4<K>& vector)
: x(static_cast<T>(vector.x)), y(static_cast<T>(vector.y)), z(static_cast<T>(vector.z)), w(static_cast<T>(vector.w)) {}
template<class T>
constexpr Rect<T>::Rect()
: x(0), y(0), w(0), h(0) {}
template<class T>
constexpr Rect<T>::Rect(T x, T y, T w, T h)
: x(x), y(y), w(w), h(h) {}
template<class T>
template<class X, class Y, class W, class H>
constexpr Rect<T>::Rect(X x, Y y, W w, H h)
: x(static_cast<T>(x)), y(static_cast<T>(y)), w(static_cast<T>(w)), h(static_cast<T>(h)) {}
template<class T>
template<class K>
constexpr Rect<T>::Rect(const Rect<K>& rect)
: x(static_cast<T>(rect.x)), y(static_cast<T>(rect.y)), w(static_cast<T>(rect.w)), h(static_cast<T>(rect.h)) {}
template<class T>
constexpr Rect<T> Rect<T>::operator+(const Vec2<T>& rhs) const {
return Rect(x + rhs.x, y + rhs.y, w, h);
}
template<class T>
constexpr Rect<T> Rect<T>::operator-(const Vec2<T>& rhs) const {
return Rect(x - rhs.x, y - rhs.y, w, h);
}
template<class T>
constexpr Rect<T>& Rect<T>::operator+=(const Vec2<T>& rhs) {
x += rhs.x;
y += rhs.y;
return *this;
}
template<class T>
constexpr Rect<T>& Rect<T>::operator-=(const Vec2<T>& rhs) {
x -= rhs.x;
y -= rhs.y;
return *this;
}
template<class T>
constexpr bool Rect<T>::operator==(const Rect& rhs) const {
return Calc::abs(x - rhs.x) < epsilon && Calc::abs(y - rhs.y) < epsilon && Calc::abs(w - rhs.w) < epsilon && Calc::abs(h - rhs.h) < epsilon;
}
template<class T>
constexpr bool Rect<T>::operator!=(const Rect& rhs) const {
return !(*this == rhs);
}
template<class T>
constexpr T Rect<T>::left() const { return x; }
template<class T>
constexpr T Rect<T>::right() const { return x + w; }
template<class T>
constexpr T Rect<T>::top() const { return y; }
template<class T>
constexpr T Rect<T>::bottom() const { return y + h; }
template<class T>
constexpr Vec2<T> Rect<T>::center() const { return Vec2<T>(x + w / 2, y + h / 2); }
template<class T>
constexpr T Rect<T>::center_x() const { return x + w / 2; }
template<class T>
constexpr T Rect<T>::center_y() const { return y + h / 2; }
template<class T>
constexpr Vec2<T> Rect<T>::top_left() const { return Vec2<T>(x, y); }
template<class T>
constexpr Vec2<T> Rect<T>::top_right() const { return Vec2<T>(x + w, y); }
template<class T>
constexpr Vec2<T> Rect<T>::bottom_right() const { return Vec2<T>(x + w, y + h); }
template<class T>
constexpr Vec2<T> Rect<T>::bottom_left() const { return Vec2<T>(x, y + h); }
template<class T>
constexpr Vec2<T> Rect<T>::center_left() const { return Vec2<T>(x, y + h / 2); }
template<class T>
constexpr Vec2<T> Rect<T>::center_right() const { return Vec2<T>(x + w, y + h / 2); }
template<class T>
constexpr Vec2<T> Rect<T>::middle_top() const { return Vec2<T>(x + w / 2, y); }
template<class T>
constexpr Vec2<T> Rect<T>::middle_bottom() const { return Vec2<T>(x + w / 2, y + h); }
template<class T>
constexpr Line<T> Rect<T>::left_line() const { return Line<T>(left(), top(), left(), bottom()); }
template<class T>
constexpr Line<T> Rect<T>::right_line() const { return Line<T>(right(), top(), right(), bottom()); }
template<class T>
constexpr Line<T> Rect<T>::top_line() const { return Line<T>(left(), top(), right(), top()); }
template<class T>
constexpr Line<T> Rect<T>::bottom_line() const { return Line<T>(left(), bottom(), right(), bottom()); }
template<class T>
constexpr bool Rect<T>::contains(const Vec2<T>& pt) const {
return pt.x >= x && pt.x < x + w && pt.y >= y && pt.y < y + h;
}
template<class T>
constexpr bool Rect<T>::contains(const Rect& rect) const {
return rect.x >= x && rect.x + rect.w < x + w && rect.y >= y && rect.y + rect.h < y + h;
}
template<class T>
constexpr bool Rect<T>::overlaps(const Rect& rect) const {
return x + w >= rect.x && y + h >= rect.y && x < rect.x + rect.w && y < rect.y + rect.h;
}
template<class T>
constexpr Rect<T> Rect<T>::overlap_rect(const Rect& against) const {
Rect result;
if (x + w >= against.x && x < against.x + against.w)
{
result.x = Calc::max(x, against.x);
result.w = Calc::min(x + w, against.x + against.w) - result.x;
}
if (y + h >= against.y && y < against.y + against.h)
{
result.y = Calc::max(y, against.y);
result.h = Calc::min(y + h, against.y + against.h) - result.y;
}
return result;
}
template<class T>
constexpr bool Rect<T>::intersects(const Line<T>& line) const {
return line.intersects(*this);
}
template<class T>
constexpr bool Rect<T>::intersects(const Line<T>& line, Vec2<T>* out_intersection_point) const {
return line.intersects(*this, out_intersection_point);
}
template<class T>
constexpr bool Rect<T>::intersects(const Vec2<T>& line_from, const Vec2<T>& line_to) const {
return intersects(Line<T>(line_from, line_to));
}
template<class T>
constexpr bool Rect<T>::intersects(const Vec2<T>& line_from, const Vec2<T>& line_to, Vec2<T>* out_intersection_point) const {
return intersects(Line<T>(line_from, line_to), out_intersection_point);
}
template<class T>
constexpr Vec2<T> Rect<T>::intersection_point(const Line<T>& line) const {
Vec2<T> ret;
if (line.intersects(*this, &ret))
return ret;
return Vec2<T>::zero;
}
template<class T>
constexpr Vec2<T> Rect<T>::intersection_point(const Vec2<T>& line_from, const Vec2<T>& line_to) const {
Vec2<T> ret;
if (Line<T>(line_from, line_to).intersects(*this, &ret))
return ret;
return Vec2<T>::zero;
}
template<class T>
constexpr Rect<T> Rect<T>::scale(T s) const {
return Rect<T>(x * s, y * s, w * s, h * s);
}
template<class T>
constexpr Rect<T> Rect<T>::scale(T sx, T sy) const {
return Rect<T>(x * sx, y * sy, w * sx, h * sy);
}
template<class T>
constexpr Rect<T> Rect<T>::inflate(T amount) const {
return Rect(x - amount, y - amount, w + amount * 2, h + amount * 2);
}
template<class T>
constexpr Rect<T> Rect<T>::inflate(T amount_x, T amount_y) const {
return Rect(x - amount_x, y - amount_y, w + amount_x * 2, h + amount_y * 2);
}
template<class T>
constexpr u8 Rect<T>::get_sector(const Vec2<T>& pt) const
{
u8 result = 0;
if (pt.x < left())
result |= 0b0001;
else if (pt.x >= right())
result |= 0b0010;
if (pt.y < top())
result |= 0b0100;
else if (pt.y >= bottom())
result |= 0b1000;
return result;
}
template<class T>
constexpr Rect<T> Rect<T>::transform(const Rect& rect, const Mat3x2<T>& matrix) {
return Rect<T>(
(rect.x * matrix.m11) + (rect.y * matrix.m21) + matrix.m31,
(rect.x * matrix.m12) + (rect.y * matrix.m22) + matrix.m32,
(rect.w * matrix.m11) + (rect.h * matrix.m21),
(rect.w * matrix.m12) + (rect.h * matrix.m22));
}
template<class T>
constexpr Rect<T> Rect<T>::from_points(const Vec2<T>& from, const Vec2<T>& to) {
auto min = Vec2<T>::min(from, to);
auto max = Vec2<T>::max(from, to);
return Rect<T>(min.x, min.y, max.x - min.x, max.y - min.y);
}
template<class T>
constexpr Quad<T>::Quad()
: a(), b(), c(), d() {}
template<class T>
constexpr Quad<T>::Quad(const Vec2<T>& a, const Vec2<T>& b, const Vec2<T>& c, const Vec2<T>& d)
: a(a), b(b), c(c), d(d) {}
template<class T>
constexpr void Quad<T>::project(const Vec2<T>& axis, T* min, T* max) const {
T dot = Vec2<T>::dot(a, axis);
*min = dot;
*max = dot;
dot = Vec2<T>::dot(b, axis);
*min = dot < *min ? dot : *min;
*max = dot > *max ? dot : *max;
dot = Vec2<T>::dot(c, axis);
*min = dot < *min ? dot : *min;
*max = dot > *max ? dot : *max;
dot = Vec2<T>::dot(d, axis);
*min = dot < *min ? dot : *min;
*max = dot > *max ? dot : *max;
}
template<class T>
constexpr Circle<T>::Circle()
: center(0, 0), radius(0) {}
template<class T>
constexpr Circle<T>::Circle(T x, T y, T radius)
: center(x, y), radius(radius) {}
template<class T>
constexpr Circle<T>::Circle(const Vec2<T>& center, T radius)
: center(center), radius(radius) {}
template<class T>
template<class K>
constexpr Circle<T>::Circle(const Circle<K>& circle)
: center(Vec2<T>(static_cast<T>(circle.center.x), static_cast<T>(circle.center.y))), radius(static_cast<T>(circle.radius)) {}
template<class T>
constexpr void Circle<T>::project(const Vec2<T>& axis, T* min, T* max) const
{
*min = Vec2<T>::dot(center - axis * radius, axis);
*max = Vec2<T>::dot(center + axis * radius, axis);
}
template<class T>
constexpr Line<T>::Line()
: a(0, 0), b(0, 0) {}
template<class T>
constexpr Line<T>::Line(T x0, T y0, T x1, T y1)
: a(x0, y0), b(x1, y1) {}
template<class T>
constexpr Line<T>::Line(const Vec2<T>& a, const Vec2<T>& b)
: a(a), b(b) {}
template<class T>
constexpr Rect<T> Line<T>::bounds() const {
return Rect<T>::from_points(a, b);
}
template<class T>
constexpr Vec2<T> Line<T>::closest_point(const Vec2<T>& pt) const {
auto v = b - a;
auto w = pt - a;
auto t = Vec2<T>::dot(w, v) / (v.x * v.x + v.y * v.y);
if (t < 0) t = 0;
else if (t > 1) t = 1;
return v * t + a;
}
template<class T>
constexpr bool Line<T>::intersects(const Rect<T>& rect, Vec2<T>* out_intersection_point) const
{
u8 ca = rect.get_sector(a);
u8 cb = rect.get_sector(b);
if (ca == cb || (ca & cb) != 0)
return false;
u8 both = ca | cb;
// top
if ((both & 0b0100) != 0 && intersects(rect.top_line(), out_intersection_point))
return true;
// bottom
if ((both & 0b1000) != 0 && intersects(rect.bottom_line(), out_intersection_point))
return true;
// left
if ((both & 0b0001) != 0 && intersects(rect.left_line(), out_intersection_point))
return true;
// right
if ((both & 0b0010) != 0 && intersects(rect.right_line(), out_intersection_point))
return true;
return false;
}
template<class T>
constexpr bool Line<T>::intersects(const Line<T>& line, Vec2<T>* out_intersection_point) const
{
Vec2<T> e = b - a;
Vec2<T> d = line.b - line.a;
T e_dot_d_perp = e.x * d.y - e.y * d.x;
// if e dot d == 0, it means the lines are parallel
// so have infinite intersection points
if (e_dot_d_perp > -epsilon && e_dot_d_perp < epsilon)
return false;
Vec2<T> c = line.a - a;
T t = (c.x * d.y - c.y * d.x) / e_dot_d_perp;
if (t < 0 || t > 1)
return false;
T u = (c.x * e.y - c.y * e.x) / e_dot_d_perp;
if (u < 0 || u > 1)
return false;
if (out_intersection_point)
*out_intersection_point = (e * t) + a;
return true;
}
template<class T>
constexpr void Line<T>::project(const Vec2<T>& axis, T* min, T* max) const {
T dot = a.x * axis.x + a.y * axis.y;
*min = dot;
*max = dot;
dot = b.x * axis.x + b.y * axis.y;
*min = dot < *min ? dot : *min;
*max = dot > *max ? dot : *max;
}
template<class T>
constexpr Line<T> Line<T>::operator+(const Vec2<T>& rhs) const {
return Line(a + rhs, b + rhs);
}
template<class T>
constexpr Line<T> Line<T>::operator-(const Vec2<T>& rhs) const {
return Line(a - rhs, b - rhs);
}
template<class T>
constexpr Mat3x2<T>::Mat3x2()
: m11(0), m12(0), m21(0), m22(0), m31(0), m32(0) {}
template<class T>
constexpr Mat3x2<T>::Mat3x2(T m11, T m12, T m21, T m22, T m31, T m32)
: m11(m11), m12(m12), m21(m21), m22(m22), m31(m31), m32(m32) {}
template<class T>
template<class K>
constexpr Mat3x2<T>::Mat3x2(const Mat3x2<K>& m)
: m11(static_cast<T>(m.m11)), m12(static_cast<T>(m.m12))
, m21(static_cast<T>(m.m21)), m22(static_cast<T>(m.m22))
, m31(static_cast<T>(m.m31)), m32(static_cast<T>(m.m32)) {}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::invert() const {
auto det = (m11 * m22) - (m21 * m12);
auto inv_det = 1 / det;
return Mat3x2<T>
(
m22 * inv_det,
-m12 * inv_det,
-m21 * inv_det,
m11 * inv_det,
(m21 * m32 - m31 * m22) * inv_det,
(m31 * m12 - m11 * m32) * inv_det
);
}
template<class T>
T Mat3x2<T>::scaling_factor() const {
return Calc::sqrt(m11 * m11 + m12 * m12);
}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::create_translation(const Vec2<T>& position) {
return Mat3x2(1, 0, 0, 1, position.x, position.y);
}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::create_translation(T x, T y) {
return Mat3x2(1, 0, 0, 1, x, y);
}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::create_scale(T scale) {
return Mat3x2(scale, 0, 0, scale, 0, 0);
}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::create_scale(T x, T y) {
return Mat3x2(x, 0, 0, y, 0, 0);
}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::create_scale(const Vec2<T>& scale) {
return Mat3x2(scale.x, 0, 0, scale.y, 0, 0);
}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::create_scale(T scale, const Vec2<T>& center_point) {
auto tx = center_point.x * (1 - scale);
auto ty = center_point.y * (1 - scale);
Mat3x2<T> result;
result.m11 = scale;
result.m12 = 0;
result.m21 = 0;
result.m22 = scale;
result.m31 = tx;
result.m32 = ty;
return result;
}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::create_scale(const Vec2<T>& scale, const Vec2<T>& center_point) {
auto tx = center_point.x * (1 - scale.x);
auto ty = center_point.y * (1 - scale.y);
Mat3x2<T> result;
result.m11 = scale.x;
result.m12 = 0;
result.m21 = 0;
result.m22 = scale.y;
result.m31 = tx;
result.m32 = ty;
return result;
}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::create_scale(T scale_x, T scale_y, const Vec2<T>& center_point) {
auto tx = center_point.x * (1 - scale_x);
auto ty = center_point.y * (1 - scale_y);
Mat3x2<T> result;
result.m11 = scale_x;
result.m12 = 0;
result.m21 = 0;
result.m22 = scale_y;
result.m31 = tx;
result.m32 = ty;
return result;
}
template<class T>
Mat3x2<T> Mat3x2<T>::create_rotation(T radians) {
auto c = Calc::cos(radians);
auto s = Calc::sin(radians);
return Mat3x2<T>(c, s, -s, c, 0, 0);
}
template<class T>
Mat3x2<T> Mat3x2<T>::create_transform(const Vec2<T>& position, const Vec2<T>& origin, const Vec2<T>& scale, T rotation) {
Mat3x2<T> matrix = identity;
if (origin.x != 0 || origin.y != 0)
matrix = create_translation(-origin.x, -origin.y);
if (scale.x != 1 || scale.y != 1)
matrix = matrix * create_scale(scale);
if (rotation != 0)
matrix = matrix * create_rotation(rotation);
if (position.x != 0 || position.y != 0)
matrix = matrix * create_translation(position);
return matrix;
}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::add(const Mat3x2& a, const Mat3x2& b) {
return Mat3x2(
a.m11 + b.m11,
a.m12 + b.m12,
a.m21 + b.m21,
a.m22 + b.m22,
a.m31 + b.m31,
a.m32 + b.m32);
}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::subtract(const Mat3x2& a, const Mat3x2& b) {
return Mat3x2(
a.m11 - b.m11,
a.m12 - b.m12,
a.m21 - b.m21,
a.m22 - b.m22,
a.m31 - b.m31,
a.m32 - b.m32);
}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::multiply(const Mat3x2& a, const Mat3x2& b) {
return Mat3x2(a.m11 * b.m11 + a.m12 * b.m21,
a.m11 * b.m12 + a.m12 * b.m22,
a.m21 * b.m11 + a.m22 * b.m21,
a.m21 * b.m12 + a.m22 * b.m22,
a.m31 * b.m11 + a.m32 * b.m21 + b.m31,
a.m31 * b.m12 + a.m32 * b.m22 + b.m32);
}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::operator *(const Mat3x2& rhs) const {
return multiply(*this, rhs);
}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::operator +(const Mat3x2& rhs) const {
return add(*this, rhs);
}
template<class T>
constexpr Mat3x2<T> Mat3x2<T>::operator -(const Mat3x2& rhs) const {
return subtract(*this, rhs);
}
template<class T>
constexpr Mat3x2<T>& Mat3x2<T>::operator *=(const Mat3x2& rhs) {
*this = multiply(*this, rhs);
return *this;
}
template<class T>
constexpr bool Mat3x2<T>::operator==(const Mat3x2& rhs) {
return
Calc::abs(m11 - rhs.m11) < epsilon &&
Calc::abs(m12 - rhs.m12) < epsilon &&
Calc::abs(m21 - rhs.m21) < epsilon &&
Calc::abs(m22 - rhs.m22) < epsilon &&
Calc::abs(m31 - rhs.m31) < epsilon &&
Calc::abs(m32 - rhs.m32) < epsilon;
}
template<class T>
constexpr bool Mat3x2<T>::operator!=(const Mat3x2& rhs) {
return !(*this == rhs);
}
template<class T>
Mat4x4<T>::Mat4x4() :
m11(0.0f), m12(0.0f), m13(0.0f), m14(0.0f),
m21(0.0f), m22(0.0f), m23(0.0f), m24(0.0f),
m31(0.0f), m32(0.0f), m33(0.0f), m34(0.0f),
m41(0.0f), m42(0.0f), m43(0.0f), m44(0.0f) {}
template<class T>
Mat4x4<T>::Mat4x4(
T m11, T m12, T m13, T m14,
T m21, T m22, T m23, T m24,
T m31, T m32, T m33, T m34,
T m41, T m42, T m43, T m44) :
m11(m11), m12(m12), m13(m13), m14(m14),
m21(m21), m22(m22), m23(m23), m24(m24),
m31(m31), m32(m32), m33(m33), m34(m34),
m41(m41), m42(m42), m43(m43), m44(m44) {}
template<class T>
constexpr Mat4x4<T> Mat4x4<T>::create_ortho(T width, T height, T z_near_plane, T z_far_plane) {
Mat4x4<T> result = identity;
result.m11 = 2 / width;
result.m12 = result.m13 = result.m14 = 0;
result.m22 = -2 / height;
result.m21 = result.m23 = result.m24 = 0;
result.m33 = 1 / (z_near_plane - z_far_plane);
result.m31 = result.m32 = result.m34 = 0;
result.m41 = result.m42 = 0;
result.m43 = z_near_plane / (z_near_plane - z_far_plane);
result.m44 = 1;
return result;
}
template<class T>
constexpr Mat4x4<T> Mat4x4<T>::create_ortho_offcenter(T left, T right, T bottom, T top, T z_near_plane, T z_far_plane) {
Mat4x4<T> result = identity;
result.m11 = 2 / (right - left);
result.m12 = result.m13 = result.m14 = 0;
result.m22 = 2 / (top - bottom);
result.m21 = result.m23 = result.m24 = 0;
result.m33 = 1 / (z_near_plane - z_far_plane);
result.m31 = result.m32 = result.m34 = 0;
result.m41 = (left + right) / (left - right);
result.m42 = (top + bottom) / (bottom - top);
result.m43 = z_near_plane / (z_near_plane - z_far_plane);
result.m44 = 1;
return result;
}
template<class T>
Mat4x4<T> Mat4x4<T>::create_perspective(T field_of_view, T ratio, T z_near_plane, T z_far_plane) {
auto scale_x = 1 / Calc::tan(field_of_view * 0.5);
auto scale_y = scale_x / ratio;
Mat4x4 result;
result.m11 = scale_y;
result.m12 = result.m13 = result.m14 = 0;
result.m22 = scale_x;
result.m21 = result.m23 = result.m24 = 0;
result.m31 = result.m32 = 0;
result.m33 = z_far_plane / (z_near_plane - z_far_plane);
result.m34 = -1;
result.m41 = result.m42 = result.m44 = 0;
result.m43 = z_near_plane * z_far_plane / (z_near_plane - z_far_plane);
return result;
}
template<class T>
constexpr Mat4x4<T> Mat4x4<T>::create_translation(T x, T y, T z) {
Mat4x4 result = identity;
result.m41 = x;
result.m42 = y;
result.m43 = z;
return result;
}
template<class T>
constexpr Mat4x4<T> Mat4x4<T>::create_scale(T x, T y, T z) {
Mat4x4 result = identity;
result.m11 = x;
result.m22 = y;
result.m33 = z;
return result;
}
template<class T>
Mat4x4<T> Mat4x4<T>::create_lookat(const Vec3<T>& position, const Vec3<T>& target, const Vec3<T>& up) {
auto zaxis = (position - target).normal();
auto xaxis = Vec3<T>::cross(up, zaxis).normal();
auto yaxis = Vec3<T>::cross(zaxis, xaxis);
Mat4x4 result;
result.m11 = xaxis.x;
result.m12 = yaxis.x;
result.m13 = zaxis.x;
result.m14 = 0.0f;
result.m21 = xaxis.y;
result.m22 = yaxis.y;
result.m23 = zaxis.y;
result.m24 = 0.0f;
result.m31 = xaxis.z;
result.m32 = yaxis.z;
result.m33 = zaxis.z;
result.m34 = 0.0f;
result.m41 = -Vec3<T>::dot(xaxis, position);
result.m42 = -Vec3<T>::dot(yaxis, position);
result.m43 = -Vec3<T>::dot(zaxis, position);
result.m44 = 1.0f;
return result;
}
template<class T>
constexpr Mat4x4<T> Mat4x4<T>::operator*(const Mat4x4& rhs) {
Mat4x4 m;
m.m11 = m11 * rhs.m11 + m12 * rhs.m21 + m13 * rhs.m31 + m14 * rhs.m41;
m.m12 = m11 * rhs.m12 + m12 * rhs.m22 + m13 * rhs.m32 + m14 * rhs.m42;
m.m13 = m11 * rhs.m13 + m12 * rhs.m23 + m13 * rhs.m33 + m14 * rhs.m43;
m.m14 = m11 * rhs.m14 + m12 * rhs.m24 + m13 * rhs.m34 + m14 * rhs.m44;
m.m21 = m21 * rhs.m11 + m22 * rhs.m21 + m23 * rhs.m31 + m24 * rhs.m41;
m.m22 = m21 * rhs.m12 + m22 * rhs.m22 + m23 * rhs.m32 + m24 * rhs.m42;
m.m23 = m21 * rhs.m13 + m22 * rhs.m23 + m23 * rhs.m33 + m24 * rhs.m43;
m.m24 = m21 * rhs.m14 + m22 * rhs.m24 + m23 * rhs.m34 + m24 * rhs.m44;
m.m31 = m31 * rhs.m11 + m32 * rhs.m21 + m33 * rhs.m31 + m34 * rhs.m41;
m.m32 = m31 * rhs.m12 + m32 * rhs.m22 + m33 * rhs.m32 + m34 * rhs.m42;
m.m33 = m31 * rhs.m13 + m32 * rhs.m23 + m33 * rhs.m33 + m34 * rhs.m43;
m.m34 = m31 * rhs.m14 + m32 * rhs.m24 + m33 * rhs.m34 + m34 * rhs.m44;
m.m41 = m41 * rhs.m11 + m42 * rhs.m21 + m43 * rhs.m31 + m44 * rhs.m41;
m.m42 = m41 * rhs.m12 + m42 * rhs.m22 + m43 * rhs.m32 + m44 * rhs.m42;
m.m43 = m41 * rhs.m13 + m42 * rhs.m23 + m43 * rhs.m33 + m44 * rhs.m43;
m.m44 = m41 * rhs.m14 + m42 * rhs.m24 + m43 * rhs.m34 + m44 * rhs.m44;
return m;
}
}
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