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defGeometry2D.hpp
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#ifndef DEF_GEOMETRY2D_HPP
#define DEF_GEOMETRY2D_HPP
#pragma region Documentation
/***
* - Constants
* - EPSILON - is used for comparing floating point values
* - PI - is just the Pi number stolen from the Internet (just kidding... I calculated it myself)
* - Functions
* - utils::equal - checks if difference between 2 values is less than or equals to the EPSILON constant
* (values must have *-* and *<=* operators implemented)
* - Structs
* - vec2d<T> - a struct for storing *x* and *y* components of type T
* - Methods:
* - vec2d::clamp - clamps each component to the *start* and *end*
* - vec2d::lerp - lineally interpolates each component between *start* and *end*
* - vec2d::dist - calculates distance between *this* and *v* points
* - vec2d::dot - calculates dot product of *this* and *v* vectors
* - vec2d::cross - calculates cross product of *this* and *v* vectors
* - vec2d::angle - calculates angle between *this* and *v* using dot product
* - vec2d::length - calculates a length of the vector
* - vec2d::mag - calculates a length of the vector
* - vec2d::mag2 - calculates a square root out of the vec2d::mag value
* - vec2d::man - calculates Manhattan distance between *this* and *v* points
* - vec2d::max - performs std::max function on each component of *this* with the *v* components
* - vec2d::min - performs std::min function on each component of *this* with the *v* components
* - vec2d::swap - swaps components of *this* and *v* vectors
* - vec2d::norm - returns *v* / *v.length()*
* - vec2d::abs - performs std::abs on each component of the vector
* - vec2d::perp - returns a perpendicular vector to the *this* vector
* - vec2d::floor - performs std::floor on each component of the vector
* - vec2d::ceil - performs std::ceil on each component of the vector
* - vec2d::round - performs std::round on each component of the vector
* - vec2d::cart - treats *x* as a radius and *y* as an angle and returns a vector where *x* and *y* are points in the cartesian space
* - vec2d::polar - returns a vector where "x" component is a length of the *this* vector and "y" is the angle between (length, 0) and (x, y) points
* - vec2d::str - returns *x* and *y* components as a string: "(x, y)"
***/
#pragma endregion
#include <vector>
#include <string>
#include <cmath>
#include <algorithm>
#include <cstdint>
#ifndef DGE_IGNORE_VEC2D
#define DGE_IGNORE_VEC2D
#endif
namespace def
{
constexpr double EPSILON = 0.1;
constexpr double PI = 3.141592653589793;
namespace utils
{
template <class T1, class T2>
constexpr auto equal(T1 lhs, T2 rhs);
}
template <class T>
struct vec2d
{
static_assert(std::is_arithmetic<T>::value, "vec2d<T> must be numeric");
constexpr vec2d() = default;
constexpr vec2d(const T& x, const T& y);
constexpr vec2d(const vec2d&) = default;
constexpr vec2d& operator=(const vec2d&) = default;
T x = 0, y = 0;
constexpr vec2d clamp(const vec2d& start, const vec2d& end) const;
constexpr vec2d lerp(const vec2d& v, const double t) const;
constexpr auto dist(const vec2d& v) const;
constexpr auto dot(const vec2d& v) const;
constexpr auto cross(const vec2d& v) const;
constexpr auto angle(const vec2d& v) const;
constexpr auto length() const;
constexpr auto mag() const;
constexpr auto mag2() const;
constexpr auto man(const vec2d& v) const;
constexpr vec2d max(const vec2d& v) const;
constexpr vec2d min(const vec2d& v) const;
constexpr void swap(vec2d& v);
constexpr vec2d norm() const;
constexpr vec2d abs() const;
constexpr vec2d perp() const;
constexpr vec2d floor() const;
constexpr vec2d ceil() const;
constexpr vec2d round() const;
constexpr vec2d cart() const;
constexpr vec2d polar() const;
std::string str() const;
template <class F>
constexpr operator vec2d<F>() const
{
return { static_cast<F>(this->x), static_cast<F>(this->y) };
}
};
typedef vec2d<int> vi2d;
typedef vec2d<float> vf2d;
typedef vec2d<double> vd2d;
template <class T1, class T2>
constexpr vec2d<T1>& operator+=(vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr vec2d<T1>& operator-=(vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr vec2d<T1>& operator*=(vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr vec2d<T1>& operator/=(vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr vec2d<T1>& operator%=(vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr vec2d<T1>& operator+=(vec2d<T1>& v1, const T2& v2);
template <class T1, class T2>
constexpr vec2d<T1>& operator-=(vec2d<T1>& v1, const T2& v2);
template <class T1, class T2>
constexpr vec2d<T1>& operator*=(vec2d<T1>& v1, const T2& v2);
template <class T1, class T2>
constexpr vec2d<T1>& operator/=(vec2d<T1>& v1, const T2& v2);
template <class T1, class T2>
constexpr vec2d<T1>& operator%=(vec2d<T1>& v1, const T2& v2);
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator+(const vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator-(const vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator*(const vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator/(const vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator%(const vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator+(const vec2d<T1>& v1, const T2& v2);
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator-(const vec2d<T1>& v1, const T2& v2);
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator*(const vec2d<T1>& v1, const T2& v2);
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator/(const vec2d<T1>& v1, const T2& v2);
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator+(const T1& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator-(const T1& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator*(const T1& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator/(const T1& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator%(const T1& v1, const vec2d<T2>& v2);
template <class T>
constexpr vec2d<T> operator-(const vec2d<T>& v);
template <class T1, class T2>
constexpr bool operator==(const vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr bool operator<=(const vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr bool operator>=(const vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr bool operator<(const vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr bool operator>(const vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T1, class T2>
constexpr bool operator!=(const vec2d<T1>& v1, const vec2d<T2>& v2);
template <class T>
struct circle
{
constexpr circle() = default;
constexpr circle(const vec2d<T>& pos, float radius);
constexpr T area() const;
constexpr T circumference() const;
vec2d<T> pos;
float radius = 0.0f;
};
template <class T>
struct line
{
constexpr line() = default;
constexpr line(const vec2d<T>& start, const vec2d<T>& end);
constexpr vec2d<T> vector() const;
template <class T1>
constexpr T dist(const vec2d<T1>& v) const;
vec2d<T> start, end;
};
enum side : uint8_t
{
SIDE_LEFT,
SIDE_TOP,
SIDE_RIGHT,
SIDE_BOTTOM,
SIDE_NONE
};
template <class T>
struct rect
{
constexpr rect() = default;
constexpr rect(const vec2d<T>& pos, const vec2d<T>& size);
constexpr T area() const;
constexpr T perimeter() const;
constexpr line<T> left() const;
constexpr line<T> top() const;
constexpr line<T> right() const;
constexpr line<T> bottom() const;
constexpr vec2d<T> top_left() const;
constexpr vec2d<T> top_right() const;
constexpr vec2d<T> bottom_left() const;
constexpr vec2d<T> bottom_right() const;
constexpr line<T> side(uint32_t i) const;
vec2d<T> pos;
vec2d<T> size;
static constexpr uint8_t SIDES = 4;
};
// point contains point
// rectangle contains point
// rectangle contains rectangle
// rectangle contains line
// rectangle contains circle
// line contains point
// line contains line
// circle contains point
// circle contains circle
// circle contains line
// circle contains rectangle
// point intersects point
// point intersects circle
// point intersects rectangle
// point intersects line
// rectangle intersects point
// rectangle intersects line
// rectangle intersects rectangle
// rectangle intersects circle
// line intersects point
// line intersects line
// line intersects rectangle
// line intersects circle
// circle intersects point
// circle intersects line
// circle intersects rectangle
// circle intersects circle
// Checks if p1 and p2 have the same coordinates
template <class T1, class T2>
constexpr bool contains(const vec2d<T1>& p1, const vec2d<T2>& p2);
// Checks if r contains p
template <class T1, class T2>
constexpr bool contains(const rect<T1>& r, const vec2d<T2>& p);
// Checks if r1 contains r2
template <class T1, class T2>
constexpr bool contains(const rect<T1>& r1, const rect<T2>& r2);
// Checks if r contains l
template <class T1, class T2>
constexpr bool contains(const rect<T1>& r, const line<T2>& l);
// Checks if r contains с
template <class T1, class T2>
constexpr bool contains(const rect<T1>& r, const circle<T2>& c);
// Checks if l1 contains l2
template <class T1, class T2>
constexpr bool contains(const line<T1>& l1, const line<T2>& l2);
// Checks if l contains p
template <class T1, class T2>
constexpr bool contains(const line<T1>& l, const vec2d<T2>& p);
// Checks if c contains p
template <class T1, class T2>
constexpr bool contains(const circle<T1>& c, const vec2d<T2>& p);
// Checks if c contains l
template <class T1, class T2>
constexpr bool contains(const circle<T1>& c, const line<T2>& l);
// Checks if c contains r
template <class T1, class T2>
constexpr bool contains(const circle<T1>& c, const rect<T2>& r);
// Checks if c1 contains c2
template <class T1, class T2>
constexpr bool contains(const circle<T1>& c1, const circle<T2>& c2);
// Checks if p1 and p2 have the same coordinates
template <class T1, class T2>
constexpr bool intersects(const vec2d<T1>& p1, const vec2d<T2>& p2, std::vector<vec2d<T2>>& intersections);
// Checks if p intersects l
template <class T1, class T2>
constexpr bool intersects(const vec2d<T1>& p, const line<T2>& l, std::vector<vec2d<T2>>& intersections);
// Checks if p intersects r
template <class T1, class T2>
constexpr bool intersects(const vec2d<T1>& p, const rect<T2>& r, std::vector<vec2d<T2>>& intersections, side* s = nullptr);
// Checks if p intersects circle
template <class T1, class T2>
constexpr bool intersects(const vec2d<T1>& p, const circle<T2>& c, std::vector<vec2d<T2>>& intersections);
// Checks if c intersects p
template <class T1, class T2>
constexpr bool intersects(const circle<T1>& c, const vec2d<T2>& p, std::vector<vec2d<T2>>& intersections);
// Checks if r intersects p
template <class T1, class T2>
constexpr bool intersects(const rect<T1>& r, const vec2d<T2>& p, std::vector<vec2d<T2>>& intersections, side* s = nullptr);
// Checks if r1 intersects r2
template <class T1, class T2>
constexpr bool intersects(const rect<T1>& r1, const rect<T2>& r2, std::vector<vec2d<T2>>& intersections, std::vector<side>* s = nullptr);
// Checks if r intersects c
template <class T1, class T2>
constexpr bool intersects(const rect<T1>& r, const circle<T2>& c, std::vector<vec2d<T2>>& intersections, std::vector<side>* s = nullptr);
// Checks if l1 intersects l2
template <class T1, class T2>
constexpr bool intersects(const line<T1>& l1, const line<T2>& l2, std::vector<vec2d<T2>>& intersections);
// Checks if l intersects r
template <class T1, class T2>
constexpr bool intersects(const line<T1>& l, const rect<T2>& r, std::vector<vec2d<T2>>& intersections, std::vector<side>* s = nullptr);
// Checks if l intersects c
template <class T1, class T2>
constexpr bool intersects(const line<T1>& l, const circle<T2>& c, std::vector<vec2d<T2>>& intersections);
// Checks if r intersects l
template <class T1, class T2>
constexpr bool intersects(const rect<T1>& r, const line<T2>& l, std::vector<vec2d<T2>>& intersections, std::vector<side>* s = nullptr);
// Checks if l intersects p
template <class T1, class T2>
constexpr bool intersects(const line<T1>& l, const vec2d<T2>& p, std::vector<vec2d<T2>>& intersections);
// Checks if c1 intersects c2
template <class T1, class T2>
constexpr bool intersects(const circle<T1>& c1, const circle<T2>& c2, std::vector<vec2d<T2>>& intersections);
// Checks if c intersects l
template <class T1, class T2>
constexpr bool intersects(const circle<T1>& c, const line<T2>& l, std::vector<vec2d<T2>>& intersections);
// Checks if c intersects r
template <class T1, class T2>
constexpr bool intersects(const circle<T1>& c, const rect<T2>& r, std::vector<vec2d<T2>>& intersections, std::vector<side>* s = nullptr);
#define DEF_GEOMETRY2D_IMPL
#ifdef DEF_GEOMETRY2D_IMPL
#undef DEF_GEOMETRY2D_IMPL
template <class T>
constexpr vec2d<T>::vec2d(const T& x, const T& y) : x(x), y(y)
{
}
template <class T1, class T2>
constexpr vec2d<T1>& operator+=(vec2d<T1>& v1, const vec2d<T2>& v2)
{
v1.x += v2.x;
v1.y += v2.y;
return v1;
}
template <class T1, class T2>
constexpr vec2d<T1>& operator-=(vec2d<T1>& v1, const vec2d<T2>& v2)
{
v1.x -= v2.x;
v1.y -= v2.y;
return v1;
}
template <class T1, class T2>
constexpr vec2d<T1>& operator*=(vec2d<T1>& v1, const vec2d<T2>& v2)
{
v1.x *= v2.x;
v1.y *= v2.y;
return v1;
}
template <class T1, class T2>
constexpr vec2d<T1>& operator/=(vec2d<T1>& v1, const vec2d<T2>& v2)
{
v1.x /= v2.x;
v1.y /= v2.y;
return v1;
}
template <class T1, class T2>
constexpr vec2d<T1>& operator%=(vec2d<T1>& v1, const vec2d<T2>& v2)
{
v1.x %= v2.x;
v1.y %= v2.y;
return v1;
}
template <class T1, class T2>
constexpr vec2d<T1>& operator+=(vec2d<T1>& v1, const T2& v2)
{
v1.x += v2;
v1.y += v2;
return v1;
}
template <class T1, class T2>
constexpr vec2d<T1>& operator-=(vec2d<T1>& v1, const T2& v2)
{
v1.x -= v2;
v1.y -= v2;
return v1;
}
template <class T1, class T2>
constexpr vec2d<T1>& operator*=(vec2d<T1>& v1, const T2& v2)
{
v1.x *= v2;
v1.y *= v2;
return v1;
}
template <class T1, class T2>
constexpr vec2d<T1>& operator/=(vec2d<T1>& v1, const T2& v2)
{
v1.x /= v2;
v1.y /= v2;
return v1;
}
template <class T1, class T2>
constexpr vec2d<T1>& operator%=(vec2d<T1>& v1, const T2& v2)
{
v1.x %= v2;
v1.y %= v2;
return v1;
}
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator+(const vec2d<T1>& v1, const vec2d<T2>& v2)
{
return vec2d(v1.x + v2.x, v1.y + v2.y);
}
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator-(const vec2d<T1>& v1, const vec2d<T2>& v2)
{
return vec2d(v1.x - v2.x, v1.y - v2.y);
}
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator*(const vec2d<T1>& v1, const vec2d<T2>& v2)
{
return vec2d(v1.x * v2.x, v1.y * v2.y);
}
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator/(const vec2d<T1>& v1, const vec2d<T2>& v2)
{
return vec2d(v1.x / v2.x, v1.y / v2.y);
}
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator%(const vec2d<T1>& v1, const vec2d<T2>& v2)
{
return vec2d(v1.x % v2.x, v1.y % v2.y);
}
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator+(const vec2d<T1>& v1, const T2& v2)
{
return vec2d(v1.x + v2, v1.y + v2);
}
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator-(const vec2d<T1>& v1, const T2& v2)
{
return vec2d(v1.x - v2, v1.y - v2);
}
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator*(const vec2d<T1>& v1, const T2& v2)
{
return vec2d(v1.x * v2, v1.y * v2);
}
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator/(const vec2d<T1>& v1, const T2& v2)
{
return vec2d(v1.x / v2, v1.y / v2);
}
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator+(const T1& v1, const vec2d<T2>& v2)
{
return vec2d(v1 + v2.x, v1 + v2.y);
}
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator-(const T1& v1, const vec2d<T2>& v2)
{
return vec2d(v1 - v2.x, v1 - v2.y);
}
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator*(const T1& v1, const vec2d<T2>& v2)
{
return vec2d(v1 * v2.x, v1 * v2.y);
}
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator/(const T1& v1, const vec2d<T2>& v2)
{
return vec2d(v1 / v2.x, v1 / v2.y);
}
template <class T1, class T2>
constexpr vec2d<decltype(T1(1) + T2(1))> operator%(const T1& v1, const vec2d<T2>& v2)
{
return vec2d(v1 % v2.x, v1 % v2.y);
}
template <class T>
constexpr vec2d<T> operator-(const vec2d<T>& v)
{
return vec2d(-v.x, -v.y);
}
template <class T1, class T2>
constexpr bool operator==(const vec2d<T1>& v1, const vec2d<T2>& v2)
{
return v1.x == v2.x && v1.y == v2.y;
}
template <class T1, class T2>
constexpr bool operator<=(const vec2d<T1>& v1, const vec2d<T2>& v2)
{
return v1.x <= v2.x && v1.y <= v2.y;
}
template <class T1, class T2>
constexpr bool operator>=(const vec2d<T1>& v1, const vec2d<T2>& v2)
{
return v1.x >= v2.x && v1.y >= v2.y;
}
template <class T1, class T2>
constexpr bool operator<(const vec2d<T1>& v1, const vec2d<T2>& v2)
{
return v1.x < v2.x && v1.y < v2.y;
}
template <class T1, class T2>
constexpr bool operator>(const vec2d<T1>& v1, const vec2d<T2>& v2)
{
return v1.x > v2.x && v1.y > v2.y;
}
template <class T1, class T2>
constexpr bool operator!=(const vec2d<T1>& v1, const vec2d<T2>& v2)
{
return v1.x != v2.x || v1.y != v2.y;
}
template <class T>
constexpr vec2d<T> vec2d<T>::clamp(const vec2d& start, const vec2d& end) const
{
return { std::clamp(x, start.x, end.x), std::clamp(y, start.y, end.y) };
}
template <class T>
constexpr vec2d<T> vec2d<T>::lerp(const vec2d& v, const double t) const
{
return { (T)std::lerp(x, v.x, t), (T)std::lerp(y, v.y, t) };
}
template <class T>
constexpr auto vec2d<T>::dist(const vec2d<T>& v) const
{
return (*this - v).length();
}
template <class T>
constexpr auto vec2d<T>::dot(const vec2d& v) const
{
return x * v.x + y * v.y;
}
template <class T>
constexpr auto vec2d<T>::cross(const vec2d& v) const
{
return x * v.y - y * v.x;
}
template<typename T>
constexpr auto vec2d<T>::angle(const vec2d& v) const
{
return acos(dot(v) / (length() + v.length()));
}
template <class T>
constexpr auto vec2d<T>::length() const
{
return mag();
}
template <class T>
constexpr auto vec2d<T>::mag() const
{
return static_cast<T>(std::sqrt(x * x + y * y));
}
template <class T>
constexpr auto vec2d<T>::mag2() const
{
return static_cast<T>(x * x + y * y);
}
template <class T>
constexpr auto vec2d<T>::man(const vec2d& v) const
{
return std::abs(x - v.x) + std::abs(y - v.y);
}
template <class T>
constexpr vec2d<T> vec2d<T>::max(const vec2d& v) const
{
return vec2d(std::max(x, v.x), std::max(y, v.y));
}
template <class T>
constexpr vec2d<T> vec2d<T>::min(const vec2d& v) const
{
return vec2d(std::min(x, v.x), std::min(y, v.y));
}
template <class T>
constexpr void vec2d<T>::swap(vec2d& v)
{
std::swap(x, v.x);
std::swap(y, v.y);
}
template <class T>
constexpr vec2d<T> vec2d<T>::norm() const
{
auto n = (T)1 / mag();
return vec2d(x * n, y * n);
}
template <class T>
constexpr vec2d<T> vec2d<T>::abs() const
{
return vec2d(std::abs(x), std::abs(y));
}
template <class T>
constexpr vec2d<T> vec2d<T>::perp() const
{
return vec2d(-y, x);
}
template <class T>
constexpr vec2d<T> vec2d<T>::floor() const
{
return vec2d(std::floor(x), std::floor(y));
}
template <class T>
constexpr vec2d<T> vec2d<T>::ceil() const
{
return vec2d(std::ceil(x), std::ceil(y));
}
template <class T>
constexpr vec2d<T> vec2d<T>::round() const
{
return vec2d(std::round(x), std::round(y));
}
template <class T>
constexpr vec2d<T> vec2d<T>::cart() const
{
return vec2d(cos(y) * x, sin(y) * x);
}
template <class T>
constexpr vec2d<T> vec2d<T>::polar() const
{
return vec2d(mag(), atan2(y, x));
}
template <class T>
std::string vec2d<T>::str() const
{
return "(" + std::to_string(x) + ", " + std::to_string(y) + ")";
}
template <class T1, class T2>
constexpr auto utils::equal(T1 lhs, T2 rhs)
{
return abs(lhs - rhs) <= EPSILON;
}
template <class T>
constexpr rect<T>::rect(const vec2d<T>& p, const vec2d<T>& s)
{
pos = p;
size = s;
}
template <class T>
constexpr T rect<T>::area() const
{
return size.x * size.y;
}
template <class T>
constexpr T rect<T>::perimeter() const
{
return 2 * (size.x + size.y);
}
template <class T>
constexpr line<T> rect<T>::left() const
{
return { pos, { pos.x, pos.y + size.y } };
}
template <class T>
constexpr line<T> rect<T>::top() const
{
return { pos, { pos.x + size.x, pos.y } };
}
template <class T>
constexpr line<T> rect<T>::right() const
{
return { { pos.x + size.x, pos.y }, bottom_right() };
}
template <class T>
constexpr line<T> rect<T>::bottom() const
{
return { { pos.x, pos.y + size.y }, bottom_right() };
}
template<class T>
constexpr vec2d<T> rect<T>::top_left() const
{
return pos;
}
template<class T>
constexpr vec2d<T> rect<T>::top_right() const
{
return { pos.x + size.x, pos.y };
}
template<class T>
constexpr vec2d<T> rect<T>::bottom_left() const
{
return { pos.x, pos.y + size.y };;
}
template<class T>
constexpr vec2d<T> rect<T>::bottom_right() const
{
return pos + size;
}
template<class T>
constexpr line<T> rect<T>::side(uint32_t i) const
{
switch (i)
{
case SIDE_LEFT: return left();
case SIDE_TOP: return top();
case SIDE_RIGHT: return right();
case SIDE_BOTTOM: return bottom();
}
return {};
}
template <class T>
constexpr circle<T>::circle(const vec2d<T>& p, float r)
{
pos = p;
radius = r;
}
template <class T>
constexpr T circle<T>::area() const
{
return PI * double(radius * radius);
}
template <class T>
constexpr T circle<T>::circumference() const
{
return 2.0 * PI * (double)radius;
}
template <class T>
constexpr line<T>::line(const vec2d<T>& s, const vec2d<T>& e)
{
start = s;
end = e;
}
template <class T>
constexpr vec2d<T> line<T>::vector() const
{
return end - start;
}
template <class T1, class T2>
constexpr bool contains(const vec2d<T1>& p1, const vec2d<T2>& p2)
{
return utils::equal(p1.x, p2.x) && utils::equal(p1.y, p2.y);
}
template <class T1, class T2>
constexpr bool contains(const circle<T1>& c, const vec2d<T2>& p)
{
auto sqr_radius = c.radius * c.radius;
auto sqr_dist = (c.pos - p).mag2();
return sqr_dist < sqr_radius || utils::equal(sqr_dist, sqr_radius);
}
template <class T1, class T2>
constexpr bool contains(const rect<T1>& r, const vec2d<T2>& p)
{
return p >= r.pos && p <= r.bottom_right();
}
template <class T1, class T2>
constexpr bool contains(const rect<T1>& r1, const rect<T2>& r2)
{
return r1.pos <= r2.pos && r1.bottom_right() >= r2.bottom_right();
}
template <class T1, class T2>
constexpr bool contains(const rect<T1>& r, const line<T2>& l)
{
return l.start >= r.pos && l.end >= r.pos && l.start <= r.bottom_right() && l.end <= r.bottom_right();
}
template<class T1, class T2>
constexpr bool contains(const rect<T1>& r, const circle<T2>& c)
{
rect<T2> rect_circle(c.pos - c.radius, vec2d<T2>(c.radius * 2));
return contains(r, rect_circle);
}
template <class T1, class T2>
constexpr bool contains(const line<T1>& l1, const line<T2>& l2)
{
return (contains(l1.start, l2.start) && contains(l1.end, l2.end)) || (contains(l1.start, l2.end) && contains(l1.end, l2.start));
}
template<class T1, class T2>
constexpr bool contains(const line<T1>& l, const vec2d<T2>& p)
{
vec2d<T1> vec = l.vector();
auto dp = vec.dot(p - l.start) / vec.mag2();
if (dp < 0 || dp > 1)
return false;
vec2d<T2> proj = l.start.lerp(l.end, dp);
// We need to find a proper epsilon value
return p.dist(proj) < EPSILON;
}
template<class T1, class T2>
constexpr bool contains(const circle<T1>& c1, const circle<T2>& c2)
{
return c1.radius >= c1.pos.dist(c2.pos) + c2.radius;
}
template<class T1, class T2>
constexpr bool contains(const circle<T1>& c, const line<T2>& l)
{
return contains(c, l.start) && contains(c, l.end);
}
template<class T1, class T2>
constexpr bool contains(const circle<T1>& c, const rect<T2>& r)
{
auto radius2 = c.radius * c.radius;
auto check_dist = [&](const vec2d<T2>& edge)
{
const auto diff = edge - c.pos;
return diff.dot(diff) <= radius2;
};
return check_dist(r.pos) && check_dist(r.top_right()) && check_dist(r.bottom_left()) && check_dist(r.bottom_right());
}
template<class T1, class T2>
constexpr bool intersects(const vec2d<T1>& p1, const vec2d<T2>& p2, std::vector<vec2d<T2>>& intersections)
{
if (contains(p1, p2))
{
intersections.push_back(p2);
return true;
}
return false;
}
template<class T1, class T2>
constexpr bool intersects(const vec2d<T1>& p, const line<T2>& l, std::vector<vec2d<T2>>& intersections)
{
return intersects(l, p, intersections);
}
template<class T1, class T2>
constexpr bool intersects(const vec2d<T1>& p, const rect<T2>& r, std::vector<vec2d<T2>>& intersections, side* s)
{
return intersects(r, p, intersections, s);
}
template<class T1, class T2>
constexpr bool intersects(const vec2d<T1>& p, const circle<T2>& c, std::vector<vec2d<T2>>& intersections)
{
return intersects(c, p, intersections);
}
template<class T1, class T2>
constexpr bool intersects(const circle<T1>& c, const vec2d<T2>& p, std::vector<vec2d<T2>>& intersections)
{
if (utils::equal((c.pos - p).mag2(), c.radius * c.radius))
{