vec2d.h

#ifndef VEC2D_H_INCLUDED
#define VEC2D_H_INCLUDED

#include "cairo.h"
#include "color.h"

#include <cmath>
#include <iostream>
#include <ostream>

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-() const {
        return vec2d{-x, -y};
    }

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

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

    bool operator==(vec2d& o) const {
        return x == o.x && y == o.y;
    }

    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;
    }

    vec2d orthogonal() {
        return {-y, x};
    }

    void draw(cairo_t* cr, vec2d p, color_t color) const {
        double arrow_lenght_ = 10 * vec2d::norm(*this);
        double arrow_degrees_ = .5;

        // see
        // http://kapo-cpp.blogspot.com/2008/10/drawing-arrows-with-cairo.html
        double angle = atan2(y, x) + M_PI;

        vec2d end = p + (*this) * 30;

        double head_length = fmin(10, arrow_lenght_);
        double x1 = end.x + head_length * cos(angle - arrow_degrees_);
        double y1 = end.y + head_length * sin(angle - arrow_degrees_);
        double x2 = end.x + head_length * cos(angle + arrow_degrees_);
        double y2 = end.y + head_length * sin(angle + arrow_degrees_);

        cairo_set_source_rgb(cr, color.red, color.green, color.blue);

        cairo_move_to(cr, p.x, p.y);
        cairo_line_to(cr, end.x, end.y);
        cairo_stroke(cr);

        cairo_move_to(cr, end.x, end.y);
        cairo_line_to(cr, x1, y1);
        cairo_stroke(cr);

        cairo_move_to(cr, end.x, end.y);
        cairo_line_to(cr, x2, y2);
        cairo_stroke(cr);
    }

    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.y - a.y * b.x;
    }

    static vec2d cross(const double omega, const vec2d& v) {
        return {-omega * v.y, omega * v.x};
    }

    static double norm2(const vec2d& v) {
        return vec2d::dot(v, v);
    }

    static double norm(const vec2d& v) {
        return std::sqrt(dot(v, v));
    }

    static vec2d normalize(const vec2d& v) {
        return v / norm(v);
    }
};

static inline std::ostream& operator<<(std::ostream& os, vec2d& p) {
    return os << '(' << p.x << ", " << p.y << ')';
}

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

#endif