计算几何模板

最新推荐文章于 2024-03-31 15:51:24 发布

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本文介绍了两种几何计算中的基本算法：线段相交判断及格雷厄姆扫描法构建凸包。通过C++实现，展示了如何确定两条线段是否相交，并给出了一种构造凸包的有效方法。

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线段相交

#include <iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
typedef double PointType;
struct point
{
    PointType x,y;
};
PointType Direction(point pi,point pj,point pk) //判断向量PiPj在向量PiPk的顺逆时针方向 +顺-逆0共线
{
    return (pj.x-pi.x)*(pk.y-pi.y)-(pk.x-pi.x)*(pj.y-pi.y);
}
bool On_Segment(point pi,point pj,point pk)
{
    if(pk.x>=min(pi.x,pj.x)&&pk.x<=max(pi.x,pj.x)&&pk.y>=min(pi.y,pj.y)&&pk.y<=max(pi.y,pj.y))
    return 1;
    return 0;
}
bool Segment_Intersect(point p1,point p2,point p3,point p4)
{
    PointType d1=Direction(p3,p4,p1),d2=Direction(p3,p4,p2),d3=Direction(p1,p2,p3),d4=Direction(p1,p2,p4);
    if(((d1>0&&d2<0)||(d1<0&&d2>0))&&((d3>0&&d4<0)||(d3<0&&d4>0)))
    return 1;
    if(d1==0&&On_Segment(p3,p4,p1))
    return 1;
    if(d2==0&&On_Segment(p3,p4,p2))
    return 1;
    if(d3==0&&On_Segment(p1,p2,p3))
    return 1;
    if(d4==0&&On_Segment(p1,p2,p4))
    return 1;
    return 0;
}

凸包

#include <iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
typedef double PointType;
struct point
{
    PointType x,y;
    int num;
};
point data[1005],stack[1005],MinA;
int top;
PointType Direction(point pi,point pj,point pk) //判断向量PiPj在向量PiPk的顺逆时针方向 +顺-逆0共线
{
    return (pj.x-pi.x)*(pk.y-pi.y)-(pk.x-pi.x)*(pj.y-pi.y);
}
PointType Dis(point a,point b)
{
    return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
bool cmp(point a,point b)
{
    PointType k=Direction(MinA,a,b);
    if(k>0) return 1;
    if(k<0) return 0;
    return Dis(MinA,a)>Dis(MinA,b);
}
void Graham_Scan(point *a,int numa)
{
    for(int i=0; i<numa; i++)
        if(a[i].y<a[0].y||(a[i].y==a[0].y&&a[i].x<a[0].x))
            swap(a[i],a[0]);
    MinA=a[0],top=0;
    sort(a+1,a+numa,cmp);
    stack[top++]=a[0],stack[top++]=a[1],stack[top++]=a[2];
    for(int i=3; i<numa; i++)
    {
        while(Direction(stack[top-2],stack[top-1],a[i])<0&&top>=2)
            top--;
        stack[top++]=a[i];
    }
}
int main()
{
    int n;
    double r,pi=3.141592654;
    while(~scanf("%d%lf",&n,&r))
    {
        double sum=0;
        for(int i=0; i<n; i++)
            scanf("%lf%lf",&data[i].x,&data[i].y);
        Graham_Scan(data,n);
        for(int i=1; i<top; i++)
            sum+=Dis(stack[i],stack[i-1]);
        sum+=Dis(stack[0],stack[top-1]);
        sum+=pi*r*2;
        printf("%.0fn",sum);
    }
    return 0;
}