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[3];
    Point3() {}
    Point3(double *_x) { for (int i = 0; i < 3; i++) x[i] = _x[i];}
} ;
typedef Point3 Vec3;

Vec3 operator + (Vec3 a, Vec3 b) {
    Vec3 ret;
    for (int i = 0; i < 3; i++) ret.x[i] = a.x[i] + b.x[i];
    return ret;
}
Vec3 operator - (Vec3 a, Vec3 b) {
    Vec3 ret;
    for (int i = 0; i < 3; i++) ret.x[i] = a.x[i] - b.x[i];
    return ret;
}
Vec3 operator * (Vec3 a, double p) {
    Vec3 ret;
    for (int i = 0; i < 3; i++) ret.x[i] = a.x[i] * p;
    return ret;
}
Vec3 operator / (Vec3 a, double p) {
    Vec3 ret;
    for (int i = 0; i < 3; i++) ret.x[i] = a.x[i] / p;
    return ret;
}

const double EPS = 1e-8;
inline int sgn(double x) { return (x > EPS) - (x < -EPS);}

bool operator < (Point3 a, Point3 b) {
    for (int i = 0; i < 3; 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 = 0; i < 3; 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 = 0; i < 3; 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 = 0; i < 3; i++) ret.x[i] = a.x[(i + 1) % 3] * b.x[(i + 2) % 3] - b.x[(i + 1) % 3] * a.x[(i + 2) % 3];
    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)) == 0;}
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) == 0) {
        if (ptInPlane(s, p0, n)) return 2;
        return 0;
    }
    x = s + (t - s) * (res1 / res2);
    return 1;
}

bool ptInTri(Point3 p, Point3 *tri) {
    double area = triArea(tri[0], tri[1], tri[2]);
    double sum = 0.0;
    for (int i = 0; i < 3; i++) sum += triArea(p, tri[i], tri[(i + 1) % 3]);
    return sgn(sum - area) == 0;
}

bool triSegIntersect(Point3 *tri, Point3 s, Point3 t) {
    Vec3 n = crossDet(tri[0], tri[1], tri[2]);
    if (sgn(dotDet(n, t - s)) == 0) return false;
    else {
        double k = dotDet(n, tri[0] - s) / dotDet(n, t - s);
        if (sgn(k) < 0 || sgn(k - 1) > 0) return false;
        Point3 x = s + (t - s) * k;
        return ptInTri(x, tri);
    }
}

Point3 tri[2][3];

bool check() {
    for (int i = 0; i < 2; i++) {
        for (int j = 0; j < 3; j++) {
            if (triSegIntersect(tri[i], tri[i ^ 1][j], tri[i ^ 1][(j + 1) % 3])) return true;
        }
    }
    return false;
}

int main() {
//    freopen("in", "r", stdin);
    int n;
    cin >> n;
    while (n--) {
        for (int i = 0; i < 2; i++) {
            for (int j = 0; j < 3; j++) {
                for (int k = 0; k < 3; k++) {
                    cin >> tri[i][j].x[k];
                }
            }
        }
        cout << check() << endl;
    }
    return 0;
}

——written by Lyon