geometry/CirclePolygonIntersection.h

• View this file on GitHub
• Last update: 2025-11-21 16:12:02+07:00

Depends on

• geometry/Point.h

Code

#include "Point.h"

typedef Point<ld> P;
#define arg(p, q) atan2(p.cross(q), p.dot(q))
ld circlePoly(P c, ld r, vector<P> ps) {
  auto tri = [&](P p, P q) {
    auto r2 = r * r / 2;
    P d = q - p;
    auto a = d.dot(p) / d.dist2(), b = (p.dist2() - r * r) / d.dist2();
    auto det = a * a - b;
    if (det <= 0) return arg(p, q) * r2;
    auto s = max(0., -a - sqrt(det)), t = min(1., -a + sqrt(det));
    if (t < 0 || 1 <= s) return arg(p, q) * r2;
    P u = p + d * s, v = p + d * t;
    return arg(p, u) * r2 + u.cross(v) / 2 + arg(v, q) * r2;
  };
  auto sum = 0.0;
  for (int i = 0; i < n; ++i)i, 0, sz(ps)) sum += tri(ps[i] - c, ps[(i + 1) % sz(ps)] - c);
  return sum;
}

#line 2 "geometry/Point.h"

template <class T>
int sgn(T x) { return (x > 0) - (x < 0); }
template <class T>
struct Point {
  typedef Point P;
  T x, y;
  explicit Point(T x = 0, T y = 0) : x(x), y(y) {}
  bool operator<(P p) const { return tie(x, y) < tie(p.x, p.y); }
  bool operator==(P p) const { return tie(x, y) == tie(p.x, p.y); }
  P operator+(P p) const { return P(x + p.x, y + p.y); }
  P operator-(P p) const { return P(x - p.x, y - p.y); }
  P operator*(T d) const { return P(x * d, y * d); }
  P operator/(T d) const { return P(x / d, y / d); }
  T dot(P p) const { return x * p.x + y * p.y; }
  T cross(P p) const { return x * p.y - y * p.x; }
  T cross(P a, P b) const { return (a - *this).cross(b - *this); }
  T dist2() const { return x * x + y * y; }
  T dist() const { return sqrt(dist2()); }
  // angle to x-axis in interval [-pi, pi]
  T angle() const { return atan2l(y, x); }
  P unit() const { return *this / dist(); }  // makes dist()=1
  P perp() const { return P(-y, x); }        // rotates +90 degrees
  P normal() const { return perp().unit(); }
  // returns point rotated 'a' radians ccw around the origin
  P rotate(ld a) const {
    return P(x * cos(a) - y * sin(a), x * sin(a) + y * cos(a));
  }
  friend ostream& operator<<(ostream& os, P p) {
    return os << "(" << p.x << "," << p.y << ")";
  }
};
#line 2 "geometry/CirclePolygonIntersection.h"

typedef Point<ld> P;
#define arg(p, q) atan2(p.cross(q), p.dot(q))
ld circlePoly(P c, ld r, vector<P> ps) {
  auto tri = [&](P p, P q) {
    auto r2 = r * r / 2;
    P d = q - p;
    auto a = d.dot(p) / d.dist2(), b = (p.dist2() - r * r) / d.dist2();
    auto det = a * a - b;
    if (det <= 0) return arg(p, q) * r2;
    auto s = max(0., -a - sqrt(det)), t = min(1., -a + sqrt(det));
    if (t < 0 || 1 <= s) return arg(p, q) * r2;
    P u = p + d * s, v = p + d * t;
    return arg(p, u) * r2 + u.cross(v) / 2 + arg(v, q) * r2;
  };
  auto sum = 0.0;
  for (int i = 0; i < n; ++i)i, 0, sz(ps)) sum += tri(ps[i] - c, ps[(i + 1) % sz(ps)] - c);
  return sum;
}

Back to top page