poj 1584 A Round Peg in a Ground Hole 点到直线的距离 点是否在多边形内 多边形是否为凸

http://poj.org/problem?id=1584

给一个多边形，和一个圆形的钉子，判断多边形是否为凸多边形，若为凸多边形判断钉子能否被包含在多边形内。

判断是否为凸多边形：相邻的两条边做叉乘i*(i+1)都大于零（假定顶点为逆时针排序，顺时针反之）则为凸多边形。

判断圆心是否在多边形内：设o为圆心，s1,s2为相邻顶点，若叉乘（s1s2）*(s1o)都大于零则圆心在多边形内部。（假定顶点为逆时针排序，顺时针反之）

之后找圆心到多边形边的最短距离，若最短距离小于圆半径必定不会包含在多边形内。

 

 1 #include<stdio.h>

 2 #include<stdlib.h>

 3 #include<string.h>

 4 #include<math.h>

 5 #include<iostream>

 6 #include<algorithm>

 7 #define eps 1e-8

 8 using namespace std;

 9 struct point

10 {

11     double x,y;

12 }p[10000];

13 double multi(point p0,point p1,point p2)

14 {

15     return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);

16 }

17 point inter(point u1,point u2,point v1,point v2)

18 {

19     point ret=u1;

20     double t=((u1.x-v1.x)*(v1.y-v2.y)-(u1.y-v1.y)*(v1.x-v2.x))

21         /((u1.x-u2.x)*(v1.y-v2.y)-(u1.y-u2.y)*(v1.x-v2.x));

22     ret.x+=(u2.x-u1.x)*t;

23     ret.y+=(u2.y-u1.y)*t;

24     return ret;

25 }

26 

27 bool is(point s1,point e1,point s2,point e2)

28 {

29     return  (max(s1.x,e1.x)>=min(s2.x,e2.x))&&

30         (max(s2.x,e2.x)>=min(s1.x,e1.x))&&

31         (max(s1.y,e1.y)>=min(s2.y,e2.y))&&

32         (max(s2.y,e2.y)>=min(s1.y,e1.y))&&

33         (multi(s1,s2,e1)*multi(s1,e1,e2)>=0)&&

34         (multi(s2,s1,e2)*multi(s2,e2,e1)>=0);

35 }

36 point pt(point p,point t1,point t2)

37 {

38     point t=p;

39     t.x+=t1.y-t2.y;

40     t.y+=t2.x-t1.x;

41     return inter(p,t,t1,t2);

42 }

43 double dis(point a,point b)

44 {

45     return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));

46 }

47 void work(point t,int n,double r)

48 {

49     int i;

50     double flag;

51     point a;

52     flag=multi(p[0],p[1],p[2]);//做顶点顺、逆时针标记

53     for(i=1;i<n-1;i++)

54         if(flag*multi(p[i],p[i+1],p[i+2])<-eps)

55         {

56             printf("HOLE IS ILL-FORMED\n");

57             return;

58         } 

59         for(i=0;i<n;i++)

60         {

61             a=pt(t,p[i],p[i+1]);

62             if(multi(p[i],p[i+1],t)*flag<-eps)//圆心不在多边形内部

63             {

64                 printf("PEG WILL NOT FIT\n");

65                 return;

66             }

67             if(dis(a,t)-r<-eps)

68             {

69                 printf("PEG WILL NOT FIT\n");

70                 return;

71             }

72         }

73         printf("PEG WILL FIT\n");

74 }

75 int main()

76 {

77     int i,n;

78     double r;

79     point t;

80     while(scanf("%d",&n),n>=3)

81     {

82         scanf("%lf%lf%lf",&r,&t.x,&t.y);

83         for(i=0;i<n;i++)

84             scanf("%lf%lf",&p[i].x,&p[i].y);

85         p[n]=p[0];

86         work(t,n,r);

87     }

88     return 0;

89 }