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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 proj(vec p) const {
// calculate orthogonal projection of point p on the line
// TODO
return vec(0, 0);
}
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 {
//TODO
return 1;
}
};
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 {
// TODO
return 1;
}
};
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 :*/
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