简单三维几何，判断俩个三角形是否相交

简单三维几何，多贴些三维几何的基本的东西，一些基本函数，和定义，

判断俩个三角形是否相交，如果相交，那么必然有一个三角形的一条边经过另一个三角形的内部、边上或者顶点，

代码：

#include<iostream>#include<cstdio>#include<cstring>#include<cstdlib>#include<cctype>#include<cmath>#include<string>#include<map>#include<set>#include<vector>#include<queue>#include<stack>using namespace std;const double eps=1e-6;int dcmp(double x){    return fabs(x)<eps?0:(x>0?1:-1);}struct Point3{    double x,y,z;    Point3(double x,double y,double z):x(x),y(y),z(z){}    Point3() {}    void in()    {        cin>>x>>y>>z;    }};typedef Point3 Vector3;Vector3 operator +(Vector3 A,Vector3 B){    return Vector3(A.x+B.x,A.y+B.y,A.z+B.z);}Vector3 operator -(Vector3 A,Vector3 B){    return Vector3(A.x-B.x,A.y-B.y,A.z-B.z);}Vector3 operator * (Vector3 A,double p){    return Vector3(A.x*p,A.y*p,A.z*p);}Vector3 operator / (Vector3 A,double p){    return Vector3(A.x/p,A.y/p,A.z/p);}bool operator == (Vector3 A,Vector3 B){    return !dcmp(A.x-B.x)&&!dcmp(A.y-B.y)&&!dcmp(A.z-B.z);}double Dot(Vector3 A,Vector3 B){    return A.x*B.x+A.y*B.y+A.z*B.z;}double Length(Vector3 A){    return sqrt(Dot(A,A));}double Angle(Vector3 A,Vector3 B){    return acos(Dot(A,B)/Length(A)/Length(B));}double DistanceToPlane(Point3 p,Point3 p0,Vector3 n){    return fabs(Dot(p-p0,n)/Length(n));}Point3 GetPlaneProjection(Point3 p,Point3 p0,Vector3 n){    double d=Dot(p-p0,n)/Length(n);    return p+n*d;}Point3 LinePlaneIntersection(Point3 p1,Point3 p2,Point3 p3,Point3 p0,Vector3 n){    Vector3 v=p2-p1;    double t=(Dot(n,p0-p1)/Dot(n,p2-p1));    return p1+v*t;}Vector3 Cross(Vector3 A,Vector3 B){    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);}double  Area2(Point3 A,Point3 B,Point3 C){    return Length(Cross(B-A,C-A));}bool PointInTri(Point3 P,Point3 P0,Point3 P1,Point3 P2){    double area1=Area2(P,P0,P1);    double area2=Area2(P,P1,P2);    double area3=Area2(P,P2,P0);    return dcmp(area1+area2+area3-Area2(P0,P1,P2))==0;}bool TriSegIntersection(Point3 P0,Point3 P1,Point3 P2,Point3 A,Point3 B,Point3 &P){    Vector3 n=Cross(P1-P0,P2-P0);    if(dcmp(Dot(n,B-A)==0)) return false;    else    {        double t=Dot(n,P0-A)/Dot(n,B-A);        if(dcmp(t)<0||dcmp(t-1)>0) return false;        P=A+(B-A)*t;        return PointInTri(P,P0,P1,P2);    }}double DistaceToLine(Point3 P,Point3 A,Point3 B){    Vector3 v1=B-A,v2=P-A;    return Length(Cross(v1,v2)/Length(v1));}double DistaceToSegment(Point3 P,Point3 A,Point3 B){    if(A==B) return Length(P-A);    Vector3 v1=B-A,v2=P-A,v3=P-B;    if(dcmp(Dot(v1,v2))<0) return Length(v2);    else if(dcmp(Dot(v1,v3))>0) return Length(v3);    else return Length(Cross(v1,v2))/Length(v1);}double Volume6(Point3 A,Point3 B,Point3 C,Point3 D){    return Dot(D-A,Cross(B-A,C-A));}struct Face{    int v[3];    Vector3 normal(Point3 *P)const    {        return Cross(P[v[1]]-P[v[0]],P[v[2]]-P[v[0]]);    }    int cansee(Point3 *P,int i) const    {        return Dot(P[i]-P[v[0]],normal(P))>0?1:0;    }};vector<Face> CH3D(Point3 *P,int n){    int vis[100][100];    memset(vis,0,sizeof(vis));    vector<Face> cur;    cur.push_back((Face) {{0,1,2}});    cur.push_back((Face) {{2,1,0}});    for(int i=3;i<n;i++)    {        vector<Face> next;        for(int j=0;j<cur.size();j++)        {            Face &f=cur[j];            int res=f.cansee(P,i);            if(!res) next.push_back(f);            for(int k=0;k<3;k++) vis[f.v[k]][f.v[(k+1)%3]]=res;        }        for(int j=0;j<cur.size();j++)            for(int k=0;k<3;k++)            {                int a=cur[j].v[k],b=cur[j].v[(k+1)%3];                if(vis[a][b]!=vis[b][a]&&vis[a][b])                next.push_back((Face) {{a,b,i}});            }            cur=next;    }    return cur;}double rand01() {return rand()/(double)RAND_MAX;}double randeps() {return (rand01()-0.5)*eps;}Point3 add_noise(Point3 p){    return Point3(p.x+randeps(),p.y+randeps(),p.z+randeps());}bool TriTriIntersection(Point3 *T1,Point3 *T2){    Point3 P;    for(int i=0;i<3;i++)    {        if(TriSegIntersection(T1[0],T1[1],T1[2],T2[i],T2[(i+1)%3],P))            return true;        if(TriSegIntersection(T2[0],T2[1],T2[2],T1[i],T1[(i+1)%3],P))            return true;    }    return false;}int main(){    int t;    cin>>t;    while(t--)    {        Point3 T1[3],T2[3];        for(int i=0;i<3;i++)            T1[i].in();        for(int i=0;i<3;i++)            T2[i].in();        printf("%d\n",TriTriIntersection(T1,T2)?1:0);    }    return 0;}