计算几何 部分常用函数模板

来自《算法竞赛入门经典-训练指南》 刘汝佳/陈峰 清华大学出版社

#include <iostream>#include <cstdio>#include <cstdlib>#include <cstring>#include <algorithm>#include <cmath>using namespace std;const double eps = 1e-8;int dcmp(double x) //三态函数 处理与double零有关的精度问题 {if(fabs(x) < eps)return 0;return x<0 ? -1 : 1;}#define Vector Point//向量使用点作为表示方法 结构相同 为了代码清晰定义宏加以区别struct Point//点 向量 { double x,y;Point(double x=0,double y=0):x(x),y(y) {}}; //向量运算 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);}bool operator == (const Vector& A, const Vector& B) {return dcmp(A.x-B.x)==0 && dcmp(A.y-B.y)==0;}double Dis(Point A, Point B)//两点距离 {return sqrt((A.x - B.x)*(A.x - B.x) + (A.y - B.y)*(A.y - B.y));}double Dot(Vector A, Vector B){//向量点积 return A.x * B.x + A.y * B.y;}double Length(Vector A){//向量长度 return sqrt(Dot(A,A)); } double Angle(Vector A, Vector B){ //向量夹角 return acos(Dot(A,B) / Length(A) / Length(B));}double Cross(Vector A, Vector B){ //向量叉积return A.x * B.y - A.y * B.x;}double Area2(Point A, Point B, Point C){ // 三角形有向面积两倍return Cross(B-A,C-A);}Vector Rotate(Vector A, double rad){//向量旋转 rad为弧度return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad)); }Vector Normal(Vector A){ //单位法线 (左转90度后的单位向量)//调用需确定A为非零向量double L = Length(A);return Vector(-A.y/L , A.x/L);}//直线向量参数方程 P+tv P为点,v为单位向量 (v长度无用)Point GetLineIntersection(Point P, Vector v, Point Q, Vector w)//获取直线交点 {//调用应保证P,Q有交点 : 即 Cross(v,w)!=0 Vector u = P-Q;double t = Cross(w,u) / Cross(v,w);return P+v*t;} //点到直线距离 使用叉积 即平行四边形的面积除以底 double DisToLine(Point P, Point A, Point B){Vector v1 = B - A, v2 = P - A;return fabs(Cross(v1,v2)) / Length(v1); //不取绝对值是有向距离 } // 直线 struct Line_v //vector form{//P+t*v;  v长度无关 Point P;Vector v;Line_v(Point A,Point B){v = B-A;P = A;}};struct Line_n //normal form{//ax+by+c=0double a,b,c;Line_n(Point x,Point y){a = y.y - x.y;b = x.x - y.x;c = x.x * y.x - x.x * y.y;}};double PolygonArea(Point *p, int n)//多边形有向面积 支持非凸多边形 {double area = 0;for(int i=1; i<n-1; i++)area+=Cross(p[i]-p[0],p[i+1]-p[0]);return area/2;} int main(){return 0;}