HDU1756--判断点与多边形的相对位置

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1756
题意：判断点是否在给出的多边形内（包括边界）

#include<cstdio>
#include<cstring>
#include<cmath>
#include<iostream>

using namespace std;

const double eps = 1e-8;
//判断double类型（x）与0的大小
int dcmp(double x) { if (fabs(x)<eps) return 0; return (x<0) ? -1 : 1; }
int n, m, i, j, k, temp, cnt;
struct point
{
    double x, y;
    point(double x = 0, double y = 0) :x(x), y(y) {};//定义点的时候直接利用构造函数，很方便
};
point p[105], other, pp;//p[]为构成多边形的点，other为射线上的点

//向量的叉积（传入三个点）
double cross(point A, point B, point C) 
{ 
    return (B.x - A.x) * (C.y - B.y) - (B.y - A.y) * (C.x - B.x); 
}

//向量的点积（传入三个点）
double dot(point A, point B, point C) 
{
    return (A.x - B.x) * (B.x * C.x) + (A.y - B.y) * (B.y - C.y);
}

//判断点p是否在线段a1a2上(叉乘=0；点乘<0)
bool OnSegment(point p, point a1, point a2)
{
    return dcmp(cross(p, a1, a2)) == 0 && dcmp(dot(p, a1, a2)) < 0;
}

//判断规范相交
bool segmentProperIntersection(point a1, point a2, point b1, point b2)
{
    double c1 = cross(a1, a2, b1), c2 = cross(a1, a2, b2);
    double c3 = cross(b1, b2 ,a1), c4 = cross(b1, b2, a2);

    return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;
}

//判断点与多边形的相对位置
int inpolygon(int n)//传入点的个数
{
    int cnt, i = 0;
    while (i < n) {//遍历每一个点
        other.x = rand() + 1000;//随机取一个足够远的点other
        other.y = rand() + 1000;//以pp为起点，other为终点做射线
        for (i = cnt = 0; i < n; i++) {//遍历每条边
            if (dcmp(cross(pp, p[i], p[i + 1])) == 0 &&//如果点pp在边上，返回true
                segmentProperIntersection(pp, other, p[i], p[i + 1]))
                return true;
            else if (dcmp(cross(pp, other, p[i]) == 0))//点p[i]在射线pp_other上，停止本循环，另取other
                break;
            else if (cross(p[i], p[i + 1], pp) * cross(p[i], other, p[i + 1]) > eps &&
                cross(pp, other, p[i]) * cross(pp, p[i + 1], other)>eps)//如果射线与边有交点，则统计交点数
                cnt++;
        }
    }
    return cnt & 1;//如果cnt为奇数，则返回1
}

int main(void)
{

    while (~scanf("%d", &n)) {
        for (i = 0; i < n; i++)//输入多边形
            scanf("%lf%lf", &p[i].x, &p[i].y);
        p[n] = p[0];//方便以后遍历每一条边
        scanf("%d", &m);
        for (j = 0; j < m; j++) {
            temp = 0;
            scanf("%lf%lf", &pp.x, &pp.y);
            if (inpolygon(n)) printf("Yes\n");
            else printf("No\n");
        }
    }

}