UVA11275 3D Triangles（三维几何）
https://www.luogu.com.cn/problem/UVA11275
三维入门入门，贴个板子。
1 #define IO std::ios::sync_with_stdio(0) 2 #include <bits/stdc++.h> 3 using namespace std; 4 const double eps=1e-6; 5 6 int dcmp(double x){ 7 if(fabs(x)<eps)return 0; 8 return x<0?-1:1; 9 } 10 struct Point3{ 11 double x,y,z; 12 Point3(double x=0,double y=0,double z=0):x(x),y(y),z(z){} 13 }; 14 15 typedef Point3 Vector3; 16 17 Vector3 operator +(Vector3 A,Vector3 B){ 18 return Vector3(A.x+B.x,A.y+B.y,A.z+B.z); 19 } 20 Vector3 operator -(Point3 A,Point3 B){ 21 return Vector3(A.x-B.x,A.y-B.y,A.z-B.z); 22 } 23 Vector3 operator *(Vector3 A,double p){ 24 return Vector3(A.x*p,A.y*p,A.z*p); 25 } 26 Vector3 operator /(Vector3 A,double p){ 27 return Vector3(A.x/p,A.y/p,A.z/p); 28 } 29 bool operator ==(const Point3 &a,const Point3 &b){ 30 return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0&&dcmp(a.z-b.z)==0; 31 } 32 double Dot(Vector3 A,Vector3 B){ 33 return A.x*B.x+A.y*B.y+A.z*B.z; 34 } 35 double Length(Vector3 A){ 36 return sqrt(Dot(A,A)); 37 } 38 double Angle(Vector3 A,Vector3 B){ 39 return acos(Dot(A,B)/Length(A)/Length(B)); 40 } 41 double popldis(Point3 p,Point3 p0,Vector3 n){ 42 return fabs(Dot(p-p0,n)); 43 } 44 Point3 pty(Point3 p,Point3 p0,Vector3 n){ 45 return p-n*Dot(p-p0,n); 46 } 47 Point3 lineplane(Point3 p1,Point3 p2,Point3 p0,Vector3 n){ 48 Vector3 v=p2-p1; 49 double t=(Dot(n,p0-p1)/Dot(n,p2-p1)); 50 return p1+v*t; 51 } 52 Vector3 Cross(Vector3 A,Vector3 B){ 53 return Vector3(A.y*B.z-A.z*B.y,A.z*B.x-A.x*B.z,A.x*B.y-A.y*B.x); 54 } 55 double Area2(Point3 A,Point3 B,Point3 C){ 56 return Length(Cross(B-A,C-A)); 57 } 58 bool PointTri(Point3 p,Point3 p0, Point3 p1,Point3 p2){ 59 double a1=Area2(p,p0,p1); 60 double a2=Area2(p,p1,p2); 61 double a3=Area2(p,p2,p0); 62 return dcmp(a1+a2+a3-Area2(p0,p1,p2))==0; 63 } 64 bool segtri(Point3 p0,Point3 p1,Point3 p2,Point3 A,Point3 B,Point3 &P){ 65 Vector3 n=Cross(p1-p0,p2-p0); 66 if(dcmp(Dot(n,B-A))==0)return false; 67 else{ 68 double t=Dot(n,p0-A)/Dot(n,B-A); 69 if(dcmp(t)<0||dcmp(t-1)>0)return false; 70 P=A+(B-A)*t; 71 return PointTri(P,p0,p1,p2); 72 } 73 } 74 double ptoline(Point3 P,Point3 A,Point3 B){ 75 Vector3 v1=B-A,v2=P-A; 76 return Length(Cross(v1,v2))/Length(v1); 77 } 78 double ptoseg(Point3 P,Point3 A,Point3 B){ 79 if(A==B)return Length(P-A); 80 Vector3 v1=B-A,v2=P-A,v3=P-B; 81 if(dcmp(Dot(v1,v2))<0)return Length(v2); 82 else if(dcmp(Dot(v1,v3))>0)return Length(v3); 83 else return Length(Cross(v1,v2))/Length(v1); 84 } 85 double Volume6(Point3 A,Point3 B,Point3 C,Point3 D){ 86 return Dot(D-A,Cross(B-A,C-A)); 87 } 88 void readp(Point3 &p){ 89 scanf("%lf%lf%lf",&p.x,&p.y,&p.z); 90 } 91 92 Point3 p[10]; 93 int T; 94 int main(){ 95 scanf("%d",&T); 96 while(T--){ 97 for(int i=0;i<6;i++){ 98 readp(p[i]); 99 } 100 int f=0; 101 if(segtri(p[0],p[1],p[2],p[3],p[4],p[6]))f=1; 102 if(segtri(p[0],p[1],p[2],p[3],p[5],p[6]))f=1; 103 if(segtri(p[0],p[1],p[2],p[4],p[5],p[6]))f=1; 104 if(segtri(p[3],p[4],p[5],p[0],p[1],p[6]))f=1; 105 if(segtri(p[3],p[4],p[5],p[0],p[2],p[6]))f=1; 106 if(segtri(p[3],p[4],p[5],p[1],p[2],p[6]))f=1; 107 printf("%d\n",f); 108 } 109 }
