计算几何初步——共面判断(FZU1393)

先判断第三点是否与前2点共线，是的话，这4点肯定共面。

反之则以这3点确定一个平面方程，以此判断第四点是否在同一个面上。

#include<iostream>
#include<iostream>
#define EPS 1e-8
using namespace std;

struct point {
    double x, y, z;
    point (){}
    point (double _x, double _y, double _z):x(_x),y(_y),z(_z){}    
}data[4];

bool equal_0(point &p)
{
    if (p.x+p.y+p.z > EPS || p.x+p.y+p.z < -EPS)return false;
    return true;     
}

point cross(point &p, point &q)
{
    point temp(p.y*q.z-p.z*q.y,p.z*q.x-p.x*q.z,p.x*q.y-p.y*q.x);
    return temp; 
}

bool on_line(point &p1, point &p2, point &temp)
{
    point direction1(p2.x-p1.x,p2.y-p1.y,p2.z-p1.z);
    point direction2(temp.x-p1.x,temp.y-p1.y,temp.z-p1.z);
    point direction3 = cross(direction1,direction2);
    if (equal_0(direction3)) {
        return true;    
    }
    return false;    
}

bool is_interface(point &k, point &a, point &p)
{
    if (k.x*(p.x - a.x) + k.y*(p.y - a.y) + k.z*(p.z - a.z) <= EPS &&
            k.x*(p.x - a.x) + k.y*(p.y - a.y) + k.z*(p.z - a.z) >= -EPS)
        return true;
    return false;    
}

int main()
{
    int T;
    scanf("%d",&T);
    while (T--) {
        for (int i(0); i<4; ++i) {
            scanf("%lf%lf%lf",&data[i].x,&data[i].y,&data[i].z);    
        }
        if (on_line(data[0],data[1],data[2])) {
            cout<<"Yes"<<endl;    
        }    else {
            point direction1(data[1].x - data[0].x,data[1].y - data[0].y,data[1].z - data[0].z);
            point direction2(data[2].x - data[0].x,data[2].y - data[0].y,data[2].z - data[0].z);
            point direction = cross(direction1,direction2);
            if (is_interface(direction,data[0],data[3])) {
                cout<<"Yes"<<endl;    
            }    else {
                cout<<"No"<<endl;    
            }
        }
    }
    return 0;    
}