uva 11275 3D Triangles (3D-Geometry)

uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=2250

　　判断两个空间中的三角形是否有公共点。

代码如下：

 #include <cstdio>
 #include <cstring>
 #include <cmath>
 #include <vector>
 #include <iostream>
 #include <algorithm>

 using namespace std;

 struct Point3 {
     double x[];
     Point3() {}
     Point3(double *_x) { for (int i = ; i < ; i++) x[i] = _x[i];}
 } ;
 typedef Point3 Vec3;

 Vec3 operator + (Vec3 a, Vec3 b) {
     Vec3 ret;
     for (int i = ; i < ; i++) ret.x[i] = a.x[i] + b.x[i];
     return ret;
 }
 Vec3 operator - (Vec3 a, Vec3 b) {
     Vec3 ret;
     for (int i = ; i < ; i++) ret.x[i] = a.x[i] - b.x[i];
     return ret;
 }
 Vec3 operator * (Vec3 a, double p) {
     Vec3 ret;
     for (int i = ; i < ; i++) ret.x[i] = a.x[i] * p;
     return ret;
 }
 Vec3 operator / (Vec3 a, double p) {
     Vec3 ret;
     for (int i = ; i < ; i++) ret.x[i] = a.x[i] / p;
     return ret;
 }

 const double EPS = 1e-;
 inline int sgn(double x) { return (x > EPS) - (x < -EPS);}

 bool operator < (Point3 a, Point3 b) {
     for (int i = ; i < ; i++) {
         if (sgn(a.x[i] - b.x[i])) return a.x[i] < b.x[i];
     }
     return true;
 }
 bool operator == (Point3 a, Point3 b) {
     for (int i = ; i < ; i++) {
         if (sgn(a.x[i] - b.x[i])) return false;
     }
     return true;
 }

 double dotDet(Vec3 a, Vec3 b) {
     double ret = 0.0;
     for (int i = ; i < ; i++) ret += a.x[i] * b.x[i];
     return ret;
 }
 inline double dotDet(Point3 o, Point3 a, Point3 b) { return dotDet(a - o, b - o);}
 inline Vec3 crossDet(Vec3 a, Vec3 b) {
     Vec3 ret;
     for (int i = ; i < ; i++) ret.x[i] = a.x[(i + ) % ] * b.x[(i + ) % ] - b.x[(i + ) % ] * a.x[(i + ) % ];
     return ret;
 }
 inline Vec3 crossDet(Point3 o, Point3 a, Point3 b) { return crossDet(a - o, b - o);}
 inline double vecLen(Vec3 x) { return sqrt(dotDet(x, x));}
 inline double angle(Vec3 a, Vec3 b) { return acos(dotDet(a, b) / vecLen(a) / vecLen(b));}
 inline double ptDis(Point3 a, Point3 b) { return vecLen(a - b);}
 inline double triArea(Point3 a, Point3 b, Point3 c) { return vecLen(crossDet(a, b, c));}
 inline Vec3 vecUnit(Vec3 x) { return x / vecLen(x);}

 struct Plane {
     Point3 p;
     Vec3 n;
     Plane() {}
     Plane(Point3 p, Vec3 n) : p(p), n(n) {}
     Plane(Point3 a, Point3 b, Point3 c) { p = a; n = crossDet(b - a, c - a);}
 } ;
 inline double pt2Plane(Point3 p, Point3 p0, Vec3 n) { return dotDet(p - p0, n) / vecLen(n);}
 inline double pt2Plane(Point3 p, Plane P) { return pt2Plane(p, P.p, P.n);}
 inline Point3 ptOnPlane(Point3 p, Point3 p0, Vec3 n) { return p + n * pt2Plane(p, p0, n);}
 inline Point3 ptOnPlane(Point3 p, Plane P) { return ptOnPlane(p, P.p, P.n);}
 inline bool ptInPlane(Point3 p, Point3 p0, Vec3 n) { return sgn(dotDet(p - p0, n)) == ;}
 inline bool ptInPlane(Point3 p, Plane P) { return ptInPlane(p, P.p, P.n);}

 int linePlaneIntersect(Point3 s, Point3 t, Point3 p0, Vec3 n, Point3 &x) {
     double res1 = dotDet(n, p0 - s);
     double res2 = dotDet(n, t - s);
     if (sgn(res2) == ) {
         if (ptInPlane(s, p0, n)) return ;
         return ;
     }
     x = s + (t - s) * (res1 / res2);
     return ;
 }

 bool ptInTri(Point3 p, Point3 *tri) {
     double area = triArea(tri[], tri[], tri[]);
     double sum = 0.0;
     for (int i = ; i < ; i++) sum += triArea(p, tri[i], tri[(i + ) % ]);
     return sgn(sum - area) == ;
 }

 bool triSegIntersect(Point3 *tri, Point3 s, Point3 t) {
     Vec3 n = crossDet(tri[], tri[], tri[]);
     if (sgn(dotDet(n, t - s)) == ) return false;
     else {
         double k = dotDet(n, tri[] - s) / dotDet(n, t - s);
         if (sgn(k) <  || sgn(k - ) > ) return false;
         Point3 x = s + (t - s) * k;
         return ptInTri(x, tri);
     }
 }

 Point3 tri[][];

 bool check() {
     for (int i = ; i < ; i++) {
         for (int j = ; j < ; j++) {
             if (triSegIntersect(tri[i], tri[i ^ ][j], tri[i ^ ][(j + ) % ])) return true;
         }
     }
     return false;
 }

 int main() {
 //    freopen("in", "r", stdin);
     int n;
     cin >> n;
     while (n--) {
         for (int i = ; i < ; i++) {
             for (int j = ; j < ; j++) {
                 for (int k = ; k < ; k++) {
                     cin >> tri[i][j].x[k];
                 }
             }
         }
         cout << check() << endl;
     }
     return ;
 }

——written by Lyon