#ifndef VEC2D_H_INCLUDED
#define VEC2D_H_INCLUDED

#include <cmath>

class vec2d {
public:
    double x;
    double y;

    vec2d & operator = (const vec2d & other) {
	x = other.x;
	y = other.y;
	return *this;
    }

    vec2d & operator += (const vec2d & other) {
	x += other.x;
	y += other.y;
	return *this;
    }

    vec2d & operator -= (const vec2d & other) {
	x -= other.x;
	y -= other.y;
	return *this;
    }

    vec2d & operator *= (double l) {
	x *= l;
	y *= l;
	return *this;
    }

    vec2d operator + (const vec2d & other) const {
	return vec2d{x + other.x, y + other.y};
    }

    vec2d operator - (const vec2d & other) const {
	return vec2d{x - other.x, y - other.y};
    }

    vec2d operator * (double l) const {
	return vec2d{x*l, y*l};
    }

    vec2d operator / (double a) const {
	return vec2d{x/a, y/a};
    }

    vec2d & rotate (double angle) {
	double sin_a = sin(angle);
	double cos_a = cos(angle);
	double x1 = x;
	double y1 = y;
	x = cos_a*x1 - sin_a*y1;
	y = sin_a*x1 + cos_a*y1;
	return *this;
    }

    static double dot (const vec2d & a, const vec2d & b) {
	return a.x*b.x + a.y*b.y;
    }

    static double cross (const vec2d & a, const vec2d & b) {
	return a.x*b.x + a.y*b.y;
    }
};

static inline vec2d operator * (double l, const vec2d & v) {
    return vec2d{v.x*l, v.y*l};
}

#endif