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#pragma once
#include <stdlib.h>
#include <math.h>
#include <algorithm>
#include <assert.h>
#define EPSILON 1e-6
#define abs(x) ((x)<0?-(x):(x))
inline double frand(double a, double b) {
double r = ((double)rand()) / ((double)RAND_MAX);
return r * (b - a) + a;
}
inline double canon_angle(double ref, double move_it){
while (ref>move_it) move_it += 2*M_PI;
while (move_it >= ref + 2*M_PI) move_it -= 2*M_PI;
return move_it ;
}
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;
}
bool is_nil() const {
return sqnorm() < EPSILON;
}
double angle() const {
if (is_nil()) return 0;
double xx = x / norm();
double a = acos(xx);
return (y >= 0 ? a : -a + 2*M_PI);
}
vec normalize() const {
double n = norm();
return vec(x / n, y / n);
}
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 + 2*M_PI;
}
}
};
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); }
inline bool operator==(const vec& v, const vec& w) { return (v-w).is_nil(); }
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;
}
vec at_angle(double theta) const {
return c + vec(r * cos(theta), r * sin(theta));
}
bool intersects(vec p) const {
return (c - p).norm() <= r;
}
};
struct circarc {
// represents the arc from theta1 to theta2 moving in the direct way on the circle
// canonical representation : theta2 > theta1
circle c;
double theta1, theta2;
circarc(circle cc, double tha, double thb) : c(cc), theta1(tha), theta2(thb) {
while (theta1 < 0) theta1 += 2*M_PI;
while (theta1 > 2*M_PI) theta1 -= 2*M_PI;
while (theta2 < theta1) theta2 += 2*M_PI;
while (theta2 > theta1 + 2*M_PI) theta2 -= 2*M_PI;
}
bool is_in_pie(vec p) const{
double theta = (p - c.c).angle();
if (theta > theta1 && theta2 > theta) return true ;
if (theta + 2*M_PI > theta1 && theta2 > theta + 2*M_PI) return true ;
return false ;
}
double dist(vec p) const {
if (is_in_pie(p)) return abs((p-c.c).norm()-c.r);
return std::min((p - c.at_angle(theta1)).norm(), (p - c.at_angle(theta2)).norm());
}
};
struct angular_sector {
// attention, les circarc doivent avoir le même centre et les mêmes angles
circarc inner, outer;
angular_sector(circarc i, circarc o) : inner(i), outer(o) {
assert(i.c.c == o.c.c);
assert(i.theta1 == o.theta1);
assert(i.theta2 == o.theta2);
}
bool is_in_sector(vec p) const{
if(inner.is_in_pie(p) && (p-inner.c.c).norm() <=outer.c.r && inner.c.r <=(p-inner.c.c).norm())return true;
return false;
}
double dist(vec p) const{
if (is_in_sector(p)) return 0;
return std::min(std::min(std::min(inner.dist(p),outer.dist(p)),
segment(vec::from_polar(inner.c.r,inner.theta1)+inner.c.c,
vec::from_polar(outer.c.r,inner.theta2)+inner.c.c).dist(p)),
segment(vec::from_polar(inner.c.r,inner.theta2)+inner.c.c,
vec::from_polar(outer.c.r,inner.theta2)+inner.c.c).dist(p)) ;
}
};
/* vim: set ts=4 sw=4 tw=0 noet :*/
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