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#pragma once

#include <math.h>

#define EPSILON 1e-6
#define abs(x) ((x)<0?-(x):(x))

struct vec {
    double x, y;

    vec(double xx, double yy) : x(xx), y(yy) {}

    double norm() const {
        return sqrt(x*x + y*y);
    }
    double sqnorm() const {
        return x*x + y*y;
    }

    double angle() const {
        double xx = x / norm();
        double a = acos(x);
        return (y > 0 ? a : -a);
    }

    vec normalize() const {
        double n = norm();
        return vec(x / n, y / n);
    }

    bool is_nil() const {
        return sqnorm() < EPSILON;
    }

    static vec from_polar(double r, double theta) {
        return vec(r * cos(theta), r * sin(theta));
    }

    static double dot(vec a, vec b) {       // dot product (produit scalaire)
        return a.x * b.x + a.y * b.y;
    }
    static double cross(vec a, vec b) {     // cross product (déterminant 2x2)
        return a.x * b.y - a.y * b.x;
    }
    static double angle(vec a, vec b) {     // oriented angle between two vectors
        if (a.is_nil() || b.is_nil()) return 0;
        float cos = dot(a.normalize(), b.normalize());
        if (cos <= -1) return M_PI;
        float uangle = acos(cos);
        if (cross(a, b) > 0) {
            return uangle;
        } else {
            return -uangle;
        }
    }
};

inline vec operator+(const vec& a, const vec& b) { return vec(a.x+b.x, a.y+b.y); }
inline vec operator-(const vec& a, const vec& b) { return vec(a.x-b.x, a.y-b.y); }
inline vec operator-(const vec& a) { return vec(-a.x, -a.y); }
inline vec operator*(double a, const vec& v) { return vec(a*v.x, a*v.y); }
inline vec operator*(const vec& v, double a) { return vec(a*v.x, a*v.y); }
inline vec operator/(const vec& v, double a) { return vec(v.x/a, v.y/a); }

struct line {
    // Line defined by ax + by + c = 0
    double a, b, c;

    line(double aa, double bb, double cc) : a(aa), b(bb), c(cc) {}
    line(vec p1, vec p2) {
        a = p1.x-p2.x ;
        b = p1.y-p2.y ;
        c = p1.x*(p2.x-p1.x)+p1.y*(p2.y-p1.y);
    }

    bool on_line(vec p) const {
        return a * p.x + b * p.y + c < EPSILON;
    }

    double dist(vec p) const {
        // calculate distance from p to the line
        return abs(a*p.x + b*p.y + c) / sqrt(a*a + b*b);
    }
    vec dir() const {
        // calculate a directional vector oh the line
        return vec(-b,a);
    }

    vec proj(vec p) const {
        // calculate orthogonal projection of point p on the line
        return p-(a*p.x+b*p.y+c)/(a*a+b*b)*vec(a,b);
    }

    double angle() const {
        return vec(-b, a).angle();
    }

};

struct segment {
    vec a, b;

    segment(vec pa, vec pb) : a(pa), b(pb) {}

    bool on_segment(vec p) const {
        // TODO

        // does point intersect segment?
        return false;
    }

    double dist(vec p) const {
        double scal = vec::dot(b-a, p-a);
        double sqn = (b-a).sqnorm();
        if (scal > sqn) return (p-b).norm();
        if (scal < 0) return (p-a).norm();
        return line(a,b).dist(p);
    }
};

struct circle {
    vec c;
    double r;

    circle(double x, double y, double rr) : c(x, y), r(rr) {}
    circle(vec cc, double rr) : c(cc), r(rr) {}

    bool on_circle(vec p) const {
        return ((p - c).norm() - r < EPSILON);
    }

    double dist(vec p) const {
        // distance à un cercle
        double d = (c-p).norm() ;
        if (d > r) return (d - r);
        return 0;
    }
};

struct circpoint {
    circle c;
    double theta;

    circpoint(circle cc, double th) : c(cc), theta(th) {}
    circpoint(vec cc, double rr, double th) : c(cc, rr), theta(th) {}

    vec pos() const {
        return c.c + vec(c.r * cos(theta), c.r * sin(theta));
    }
};

struct circarc {
    circle c;
    double theta1, theta2;

    circarc(circle cc, double tha, double thb) : c(cc), theta1(tha), theta2(thb) {}

    double dist(vec p) const {
        // TODO
        return 1;
    }
};

/* vim: set ts=4 sw=4 tw=0 noet :*/