POJ 1584 A Round Peg in a Ground Hole（点到直线距离，圆与多边形相交，多边形是否为凸）...

题意：给出一个多边形和一个圆，问是否是凸多边形，若是则再问圆是否在凸多边形内部。

分3步：

1、判断是否是凸多边形

2、判断点是否在多边形内部

3、判断点到各边的距离是否大于等于半径

上代码：

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std;#define maxn 2000
#define eps 10E-8struct Point
{double x, y;Point operator-(const Point &a) const{Point ret;ret.x = x - a.x;ret.y = y - a.y;return ret;}
} point[maxn], peg;double pegr;
int n;int dblcmp(double a)
{if (fabs(a) < eps)return 0;return a >0?1 : -1;
}double xmult(const Point &a, const Point &b)
{return a.x * b.y - b.x * a.y;
}void input()
{scanf("%lf%lf%lf", &pegr, &peg.x, &peg.y);for (int i =0; i < n; i++)scanf("%lf%lf", &point[i].x, &point[i].y);int t =0;int i =0;while (i < n && t ==0){t = dblcmp(xmult(point[(i +1)%n] - point[i], point[(i +2)%n] - point[i]));i++;}if (t <0)reverse(point, point + n);
}bool convex()
{for (int i =0; i < n; i++)if (dblcmp(xmult(point[(i +1)%n] - point[i], point[(i +2)%n] - point[(i +1)%n]))    <0)return false;return true;
}bool inconvex()
{for (int i =0; i < n; i++)if (dblcmp(xmult(point[(i +1)%n] - point[i], peg - point[(i +1)%n])) <=0)return false;return true;
}double dist(const Point &a, const Point &b)
{Point p;p = a - b;return sqrt(p.x * p.x + p.y * p.y);
}bool ok()
{for (int i =0; i < n; i++)if (dblcmp(abs(xmult(peg - point[i], point[(i +1)%n] - point[i]))/dist(point[i], point[(i +1)%n]) - pegr) <0)return false;return true;
}int main()
{while (scanf("%d", &n) != EOF){if (n<3)break;input();if (!convex())printf("HOLE IS ILL-FORMED\n");else if (!inconvex()||!ok())printf("PEG WILL NOT FIT\n");elseprintf("PEG WILL FIT\n");}return 0;
}