计算几何模板初步

#include <set>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int MAXN = 1005;
const double Pi = acos(-1.0);
const double eps = 1e-6;
const double INF = 1e12;
inline int dcmp(double x) { //正负符号
	if(x <= eps && x >= -eps) return 0;
	return x > 0 ? 1 : -1;
}
inline double sqr(double x) { return x*x; } //平方
struct Vector { //向量
	double x, y;
	inline Vector(double _x=0, double _y=0): x(_x), y(_y){}
	inline Vector operator *(const double &k)const { return Vector(x*k, y*k) ;}
	inline Vector operator +(const Vector &t)const { return Vector(x+t.x, y+t.y); }
	inline Vector operator -(const Vector &t)const { return Vector(x-t.x, y-t.y); }
};
struct Point { //点
    double x, y;
    inline Point(double _x=0, double _y=0): x(_x), y(_y){}
    inline Vector operator -(const Point &t)const {  return Vector(x - t.x, y - t.y); }
    inline Point operator +(const Vector &t)const {  return Point(x + t.x, y + t.y); }
    inline double dist(const Point &t) { return sqrt(sqr(x-t.x) + sqr(y-t.y)); }
    inline double dist(const double &a, const double &b) { return sqrt(sqr(x-a) + sqr(y-b)); }
};
struct Line { //线
	Point p;
	Vector v; //有向
	double ang;
	inline Line(Point _p=Point(0, 0), Vector _v=Vector(0, 0)): p(_p), v(_v), ang(atan2(v.y, v.x)){}
	inline bool operator <(const Line &t)const { return ang < t.ang; }
};
struct Circle { //圆
	Point o; double r;
	inline Circle(Point _o=Point(0, 0), double _r=0): o(_o), r(_r){}
};
inline double Cross(const Vector &a, const Vector &b) { return a.x*b.y - a.y*b.x; } //叉积
inline double Dot(const Vector &a, const Vector &b) { return a.x*b.x + a.y*b.y; } //点积
inline bool Turn_Left(const Point &a, const Point &b, const Point &c) { return dcmp(Cross(b-a, c-a)) > 0; } //三点的上凸或下凸情况
inline bool On_Left(const Line &a, const Point &b) { return dcmp(Cross(a.v, b-a.p)) >= 0; } //点对于线的位置
inline Point GLI(const Point &P, const Vector &v, const Point &Q, const Vector &w) { //直线交点
	Vector u = Q - P;
	double k = Cross(u, w) / Cross(v, w);
	return P + v*k;
}
inline double Angle_C(const double &a, const double &b, const double &c) { //余弦定理
	return acos((sqr(a)+sqr(b)-sqr(c))/(2*a*b));
	//cos C = (a^2+b^2-c^2)/(2ab)
}
inline double Tri_S(const Point &a, const Point &b, const Point &c) { //三角形的面积
	return fabs(Cross(b-a, c-a))/2;
}
inline Point rotate(const double &x, const double &y, const double &degree) { //逆时针旋转degree弧度的坐标
	return Point(x*cos(degree)-y*sin(degree), x*sin(degree)+y*cos(degree));
}
int n, cur; Point O[MAXN], poly[MAXN];
inline bool cmp(const Point &a, const Point &b) { return dcmp(a.x-b.x) ? a.x < b.x : a.y < b.y; }
inline void  Convex_hull() { //凸包
	sort(O + 1, O + n + 1, cmp);
	int tmp;
	poly[++cur] = O[tmp=1];
	for(int i = 2; i <= n; ++i) { //下凸壳
		while(cur > tmp && !Turn_Left(poly[cur-1], poly[cur], O[i])) --cur;
		poly[++cur] = O[i];
	}
	tmp = cur;
	for(int i = n-1; i > 1; --i) { //上凸壳
		while(cur > tmp && !Turn_Left(poly[cur-1], poly[cur], O[i])) --cur;
		poly[++cur] = O[i];
	}
	while(cur > tmp && !Turn_Left(poly[cur-1], poly[cur], O[1])) --cur;
	return;
}

//stO   Orz  -.-  >.<  xp   XD   qwq  QAQ   ToT  QwQ  QuQ  :-)  )-: TnT
inline double calc(double len, double fL, double fM, double fR) {
	return (fL + 4*fM + fR) * len / 6; //辛普森公式
}
inline double f(double x) { /*...*/ } //求值
inline double Simpson(double L, double M, double R, double fL, double fM, double fR, double tmp) { //辛普森
	double M1 = (L + M) / 2, M2 = (M + R) / 2;
	double fM1 = f(M1), fM2 = f(M2);
	double g1 = calc(M-L, fL, fM1, fM), g2 = calc(R-M, fM, fM2, fR);
	if(dcmp(tmp-g1-g2) == 0) return g1 + g2;
	return Simpson(L, M1, M, fL, fM1, fM, g1) + Simpson(M, M2, R, fM, fM2, fR, g2);
}
inline double Farthest_dist() { //旋转卡壳求最远点对
	if(cur == 2) return poly[1].dist(poly[2]);
	for(int i = 0; i < cur; ++i) poly[i] = poly[i+1];
	double res = 0;
	for(int i = 0, j = 2; i < cur; ++i) {
		while(Tri_S(poly[i], poly[(i+1)%cur], poly[j]) < Tri_S(poly[i], poly[(i+1)%cur], poly[(j+1)%cur])) j = (j+1)%cur;
		res = max(res, poly[i].dist(poly[j]));
	}
	for(int i = cur; i >= 1; --i) poly[i] = poly[i-1];
	return res;
}
int main () {}
计算几何模板初步

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