UVA 478 Points in Figures: Rectangles…(判定点在多边形内)

UVA 478 Points in Figures: Rectangles…(判定点在多边形内)

题意:

       有n(n<=10)个图形,可能是三角形或矩形或圆.现在给你多个点,然后要你判断每个点分别在哪些图形内? 如果正好在图形边上,不算.

分析:

       对于三角形,直接判断指定点与三角形三边的叉积是否同时大于0或同时小与0即可(也可以用点在多边形内的模板判断).

       对于矩形,只要给定点的x和y坐标属于(x1,x2)与(y1,y2)这两个开区间即可.

       对于圆,只要给定点到圆心的距离小于半径即可说该点在圆内.

       程序中对于每个点依次用3种类别的所有图形去匹配该点,因为图形数目很少,所以只要该点在图形i内,那么标记数组的in[i]=true即可.

AC代码:

#include<cstdio>#include<cmath>#include<algorithm>#include<cstring>#include<vector>using namespace std;const int maxn=10+5;const double eps=1e-10;int dcmp(double x){    if(fabs(x)<eps) return 0;    return x<0?-1:1;}struct Point{    double x,y;    Point(){}    Point(double x,double y):x(x),y(y){}};typedef Point Vector;Vector operator-(Point A,Point B){    return Vector(A.x-B.x,A.y-B.y);}double Cross(Vector A,Vector B){    return A.x*B.y-A.y*B.x;}struct Rectangle{    int id;    double x1,y1,x2,y2;//注意这里y1表示最小y坐标,y2表示最大y坐标,与输入不同    Rectangle(int id,double x1,double y1,double x2,double y2):id(id),x1(x1),y1(y1),x2(x2),y2(y2){}    bool InRectangle(Point p)    {        return p.x<x2&&p.x>x1&&p.y>y1&&p.y<y2;    }};struct Triangle{    int id;    Point a1,a2,a3;    Triangle(int id,Point a1,Point a2,Point a3):id(id),a1(a1),a2(a2),a3(a3){}    bool InTriangle(Point p)    {        int v1=dcmp(Cross(a1-a2,p-a2));        int v2=dcmp(Cross(a2-a3,p-a3));        int v3=dcmp(Cross(a3-a1,p-a1));        return (v1<0&&v2<0&&v3<0) || (v1>0&&v2>0&&v3>0);    }};struct Circle{    int id;    double x,y;    double r;    Circle(int id,double x,double y,double r):id(id),x(x),y(y),r(r){}    bool InCircle(Point p)    {        double dist2= (p.x-x)*(p.x-x)+(p.y-y)*(p.y-y);        return dist2<r*r;    }};vector<Rectangle> R;//保存所有矩形vector<Triangle> T; //保存所有三角形vector<Circle> C;   //保存所有圆int main(){    char type;    int n=0;    while(scanf(" %c",&type)==1 && type!='*')    {        if(type=='r')        {            double x1,y1,x2,y2;            scanf("%lf%lf%lf%lf",&x1,&y2,&x2,&y1);            R.push_back(Rectangle(++n,x1,y1,x2,y2));        }        else if(type=='t')        {            Point p1,p2,p3;            scanf("%lf%lf%lf%lf%lf%lf",&p1.x,&p1.y,&p2.x,&p2.y,&p3.x,&p3.y);            T.push_back(Triangle(++n,p1,p2,p3));        }        else if(type=='c')        {            double x,y,r;            scanf("%lf%lf%lf",&x,&y,&r);            C.push_back(Circle(++n,x,y,r));        }    }    int num=1;    Point p;    while(scanf("%lf%lf",&p.x,&p.y)==2)    {        if(dcmp(p.x-9999.9)==0 && dcmp(p.y-9999.9)==0 ) break;        bool in[maxn];        memset(in,0,sizeof(in));        bool flag=false;//flag==true表示该点至少在一个图形内        for(int i=0;i<R.size();++i)            if(R[i].InRectangle(p)) in[R[i].id]=flag=true;        for(int i=0;i<T.size();++i)            if(T[i].InTriangle(p)) in[T[i].id]=flag=true;        for(int i=0;i<C.size();++i)            if(C[i].InCircle(p)) in[C[i].id]=flag=true;        if(!flag) printf("Point %d is not contained in any figure\n",num);        else        {            for(int i=1;i<=n;++i)if(in[i])                printf("Point %d is contained in figure %d\n",num,i);        }        ++num;    }    return 0;}