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。

View Code

 1 #include<iostream>
 2 #include<iostream>
 3 #define EPS 1e-8
 4 using namespace std;
 5 
 6 struct point {
 7     double x, y, z;
 8     point (){}
 9     point (double _x, double _y, double _z):x(_x),y(_y),z(_z){}    
10 }data[4];
11 
12 bool equal_0(point &p)
13 {
14     if (p.x+p.y+p.z > EPS || p.x+p.y+p.z < -EPS)return false;
15     return true;     
16 }
17 
18 point cross(point &p, point &q)
19 {
20     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);
21     return temp; 
22 }
23 
24 bool on_line(point &p1, point &p2, point &temp)
25 {
26     point direction1(p2.x-p1.x,p2.y-p1.y,p2.z-p1.z);
27     point direction2(temp.x-p1.x,temp.y-p1.y,temp.z-p1.z);
28     point direction3 = cross(direction1,direction2);
29     if (equal_0(direction3)) {
30         return true;    
31     }
32     return false;    
33 }
34 
35 bool is_interface(point &k, point &a, point &p)
36 {
37     if (k.x*(p.x - a.x) + k.y*(p.y - a.y) + k.z*(p.z - a.z) <= EPS &&
38             k.x*(p.x - a.x) + k.y*(p.y - a.y) + k.z*(p.z - a.z) >= -EPS)
39         return true;
40     return false;    
41 }
42 
43 int main()
44 {
45     int T;
46     scanf("%d",&T);
47     while (T--) {
48         for (int i(0); i<4; ++i) {
49             scanf("%lf%lf%lf",&data[i].x,&data[i].y,&data[i].z);    
50         }
51         if (on_line(data[0],data[1],data[2])) {
52             cout<<"Yes"<<endl;    
53         }    else {
54             point direction1(data[1].x - data[0].x,data[1].y - data[0].y,data[1].z - data[0].z);
55             point direction2(data[2].x - data[0].x,data[2].y - data[0].y,data[2].z - data[0].z);
56             point direction = cross(direction1,direction2);
57             if (is_interface(direction,data[0],data[3])) {
58                 cout<<"Yes"<<endl;    
59             }    else {
60                 cout<<"No"<<endl;    
61             }
62         }
63     }
64     return 0;    
65 }