URAL 2099 Space Invader题解 （计算几何）

　　啥也不说了，直接看图吧……

代码如下：

#include<stdio.h>
#include<iostream>
#include<math.h>
using namespace std;
#define LL long long
struct point
{
    LL x,y,z;
};
bool fun(point a,point b,point c,point d)
{
    point p1, p2,p3;
    p1.x = a.x-d.x;
    p1.y = a.y-d.y;
    p1.z = a.z-d.z;

    p2.x = a.x-c.x;
    p2.y = a.y-c.y;
    p2.z = a.z-c.z;

    p3.x = b.x-d.x;
    p3.y = b.y-d.y;
    p3.z = b.z-d.z;

    point w1,w2;

    w1.x = p1.y*p2.z-p2.y*p1.z;
    w1.y = p1.z*p2.x-p2.z*p1.x;
    w1.z = p1.x*p2.y-p2.x*p1.y;

    w2.x = p1.y*p3.z-p3.y*p1.z;
    w2.y = p1.z*p3.x-p3.z*p1.x;
    w2.z = p1.x*p3.y-p3.x*p1.y;
    if(w1.x*w2.y==w2.x*w1.y && w1.z*w2.y==w2.z*w1.y)
        return true;
    return false;
}
LL dis(point a,point b)
{
    return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y)+(a.z-b.z)*(a.z-b.z);
}
bool Dis(point a,point b,point c)
{
    if(dis(b,c)>=dis(a,b)+dis(a,c))
        return true;
    return false;
}
bool T(point a,point b,point c,point d)
{
    point p1, p2;
    p1.x = a.x-b.x;
    p1.y=a.y-b.y;
    p1.z=a.z-b.z;
    p2.x=c.x-d.x;
    p2.y=c.y-d.y;
    p2.z=c.z-d.z;
    if(p1.x*p2.x+p1.y*p2.y+p1.z*p2.z == 0){
        return true;
    }
    else return false;
}
int main()
{
//    freopen("J.in.cpp","r",stdin);
    point a, b, c, d;
    scanf("%I64d%I64d%I64d",&a.x,&a.y,&a.z);
    scanf("%I64d%I64d%I64d",&b.x,&b.y,&b.z);
    scanf("%I64d%I64d%I64d",&c.x,&c.y,&c.z);
    scanf("%I64d%I64d%I64d",&d.x,&d.y,&d.z);
    if(T(a,b,c,d) && fun(a,b,c,d) && Dis(b,a,d) && Dis(c,a,d))
    {
        printf("Valid\n");
    }
    else printf("Invalid\n");
    return 0;
}