计算几何模板
#include <cstdio> #include <cmath> #include <vector> #include <cstring> #include <algorithm> #define point Vector #define ll long long #define setIO(s) freopen(s".in","r",stdin) using namespace std; const double eps = 1e-8; struct Vector { double x, y; Vector(double X = 0.0, double Y = 0.0){ x = X, y = Y; } }; struct Line { point s, e; Line() {}; Line(point i, point j) { s = i, e = j; } }; int dcmp(double x) { if(fabs(x) < eps) return 0; return x < 0 ? -1 : 1; } bool operator < (const point &a, const point & b) { if(dcmp(a.x - b.x) == 0) return a.y < b.y; else return a.x < b.x; } bool operator == (const point &a, const point & b) { if(dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0) return true; return false; } Vector operator + (Vector a, Vector b) { return Vector(a.x + b.x, a.y + b.y); } Vector operator - (Vector a, Vector b) { return Vector(a.x - b.x, a.y - b.y); } Vector operator * (Vector a, double p) { return Vector(a.x * p, a.y * p); } Vector operator / (Vector a, double p) { return Vector(a.x / p, a.y / p); } double dot(Vector a, Vector b) { return a.x * b.x + a.y * b.y; } double len(point a) { return sqrt(dot(a, a)); } double sqr(double x) { return x * x; } double dis(point a, point b) { return sqrt(sqr(a.x - b.x) + sqr(a.y - b.y)); } // b 在 a 的逆时针为正,夹角为 a 转到 b 的有向角度(sin) double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; } // 求点积再除以模长. double Angle(Vector a, Vector b) { return acos(dot(a, b) / len(a) / len(b)); } // 求法向量. Vector normal(Vector a) { double u = len(a); return Vector(-a.y / u, a.x / u); } // 看 tmp 是否在 ab 上 int Onsegment(point tmp, point a, point b) { if(dcmp(cross(a - tmp, b - tmp)) == 0 && dcmp(dot(a - tmp, b - tmp)) <= 0) return 1; return 0; } // 前面是线段上,后面是不在线段上相交. int Line_Intersect(point a, point b, point c, point d) { double x1 = cross(b - a, c - a), y1 = cross(b - a, d - a); double x2 = cross(d - c, a - c), y2 = cross(d - c, b - c); if(!dcmp(x1) || !dcmp(x2) || !dcmp(y1) || !dcmp(y2)) { bool f1 = Onsegment(a, c, d); bool f2 = Onsegment(b, c, d); bool f3 = Onsegment(c, a, b); bool f4 = Onsegment(d, a, b); bool f = (f1 | f2 | f3 | f4); return f; } if(dcmp(x1) * dcmp(y1) < 0 && dcmp(x2) * dcmp(y2) < 0) return 1; return 0; } // l1 为直线,l2 为线段, 看是否相交 int seg_inter_line(Line l1, Line l2) { if(dcmp(cross(l1.e - l2.s, l1.s - l2.s)) * dcmp(cross(l1.e - l2.e, l1.s - l2.e)) <= 0) return 1; return 0; } // 看直线 l1 和 l2 的位置情况. int judge_Line(Line l1, Line l2) { if(dcmp(cross(l1.e - l1.s, l2.e - l2.s)) == 0) { // 0 : 共线,-1:平行. if(seg_inter_line(l1, l2) == 1) return 0; else return -1; } return 1; } // 求直线 l1 与 l2 的交点 point Get_Line(Line l1, Line l2) { Vector v1 = l1.e - l1.s, v2 = l2.e - l2.s; double t = cross(l2.s - l1.s, v2) / cross(v1, v2); return l1.s + v1 * t; } // 判断点 p 是否在多边形内. // -1: 在边界. // 0 : 在外部 // 1 : 在内部 int ispoly(point p, point poly[], int len) { int cnt = 0; Line ray, side; ray.s = p; ray.e = point(-1000000000.0, p.y); for(int i = 0; i < len; ++ i) { side = Line(poly[i], poly[(i + 1) % len]); // 在边界 if(Onsegment(p, side.e, side.s)) return -1; // 平行线不用考虑 if(dcmp(side.s.y - side.e.y) == 0) continue; if(Onsegment(side.s, ray.s, ray.e)) { // 凸包点在射线上. if(dcmp(side.s.y - side.e.y) > 0) ++ cnt; } else if(Onsegment(side.e, ray.s, ray.e)) { if(dcmp(side.e.y - side.s.y) > 0) ++ cnt; } else if(Line_Intersect(side.e, side.s, ray.s, ray.e) == 1) ++ cnt; } if(cnt & 1) return 1; return 0; }