三维计算几何模版

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网上找了一个三维计算几何模版，完善了一下，使它能使用了...
#include <cstdio>#include <cstring>#include <algorithm>using namespace std;/***********基础*************/const double EPS=0.000001;typedef struct Point_3D {    double x, y, z;    Point_3D(double xx = 0, double yy = 0, double zz = 0): x(xx), y(yy), z(zz) {}    bool operator == (const Point_3D& A) const {        return x==A.x && y==A.y && z==A.z;    }}Vector_3D;Point_3D read_Point_3D() {    double x,y,z;    scanf("%lf%lf%lf",&x,&y,&z);    return Point_3D(x,y,z);}Vector_3D operator + (const Vector_3D & A, const Vector_3D & B) {    return Vector_3D(A.x + B.x, A.y + B.y, A.z + B.z);}Vector_3D operator - (const Point_3D & A, const Point_3D & B) {    return Vector_3D(A.x - B.x, A.y - B.y, A.z - B.z);}Vector_3D operator * (const Vector_3D & A, double p) {    return Vector_3D(A.x * p, A.y * p, A.z * p);}Vector_3D operator / (const Vector_3D & A, double p) {    return Vector_3D(A.x / p, A.y / p, A.z / p);}double Dot(const Vector_3D & A, const Vector_3D & B) {    return A.x * B.x + A.y * B.y + A.z * B.z;}double Length(const Vector_3D & A) {    return sqrt(Dot(A, A));}double Angle(const Vector_3D & A, const Vector_3D & B) {    return acos(Dot(A, B) / Length(A) / Length(B));}Vector_3D Cross(const Vector_3D & A, const Vector_3D & B) {    return Vector_3D(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(const Point_3D & A, const Point_3D & B, const Point_3D & C) {    return Length(Cross(B - A, C - A));}double Volume6(const Point_3D & A, const Point_3D & B, const Point_3D & C, const Point_3D & D) {    return Dot(D - A, Cross(B - A, C - A));}// 四面体的重心Point_3D Centroid(const Point_3D & A, const Point_3D & B, const Point_3D & C, const Point_3D & D) {    return (A + B + C + D) / 4.0;}/************点线面*************/// 点p到平面p0-n的距离。n必须为单位向量double DistanceToPlane(const Point_3D & p, const Point_3D & p0, const Vector_3D & n){    return fabs(Dot(p - p0, n)); // 如果不取绝对值，得到的是有向距离}// 点p在平面p0-n上的投影。n必须为单位向量Point_3D GetPlaneProjection(const Point_3D & p, const Point_3D & p0, const Vector_3D & n){    return p - n * Dot(p - p0, n);}//直线p1-p2 与平面p0-n的交点Point_3D LinePlaneIntersection(Point_3D p1, Point_3D p2, Point_3D p0, Vector_3D n){    Vector_3D v= p2 - p1;    double t = (Dot(n, p0 - p1) / Dot(n, p2 - p1)); //分母为0，直线与平面平行或在平面上    return p1 + v * t; //如果是线段 判断t是否在0~1之间}// 点P到直线AB的距离double DistanceToLine(const Point_3D & P, const Point_3D & A, const Point_3D & B){    Vector_3D v1 = B - A, v2 = P - A;    return Length(Cross(v1, v2)) / Length(v1);}//点到线段的距离double DistanceToSeg(Point_3D p, Point_3D a, Point_3D b){    if(a == b)    {        return Length(p - a);    }    Vector_3D v1 = b - a, v2 = p - a, v3 = p - b;    if(Dot(v1, v2) + EPS < 0)    {        return Length(v2);    }    else    {        if(Dot(v1, v3) - EPS > 0)        {            return Length(v3);        }        else        {            return Length(Cross(v1, v2)) / Length(v1);        }    }}//求异面直线 p1+s*u与p2+t*v的公垂线对应的s 如果平行|重合，返回falsebool LineDistance3D(Point_3D p1, Vector_3D u, Point_3D p2, Vector_3D v, double & s){    double b = Dot(u, u) * Dot(v, v) - Dot(u, v) * Dot(u, v);    if(abs(b) <= EPS)    {        return false;    }    double a = Dot(u, v) * Dot(v, p1 - p2) - Dot(v, v) * Dot(u, p1 - p2);    s = a / b;    return true;}// p1和p2是否在线段a-b的同侧bool SameSide(const Point_3D & p1, const Point_3D & p2, const Point_3D & a, const Point_3D & b){    return Dot(Cross(b - a, p1 - a), Cross(b - a, p2 - a)) - EPS >= 0;}// 点P在三角形P0, P1, P2中bool PointInTri(const Point_3D & P, const Point_3D & P0, const Point_3D & P1, const Point_3D & P2){    return SameSide(P, P0, P1, P2) && SameSide(P, P1, P0, P2) && SameSide(P, P2, P0, P1);}// 三角形P0P1P2是否和线段AB相交bool TriSegIntersection(const Point_3D & P0, const Point_3D & P1, const Point_3D & P2, const Point_3D & A, const Point_3D & B, Point_3D & P){    Vector_3D n = Cross(P1 - P0, P2 - P0);    if(abs(Dot(n, B - A)) <= EPS)    {        return false;    // 线段A-B和平面P0P1P2平行或共面    }    else   // 平面A和直线P1-P2有惟一交点    {        double t = Dot(n, P0 - A) / Dot(n, B - A);        if(t + EPS < 0 || t - 1 - EPS > 0)        {            return false;    // 不在线段AB上        }        P = A + (B - A) * t; // 交点        return PointInTri(P, P0, P1, P2);    }}//空间两三角形是否相交bool TriTriIntersection(Point_3D * T1, Point_3D * T2){    Point_3D 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;}//空间两直线上最近点对 返回最近距离 点对保存在ans1 ans2中double SegSegDistance(Point_3D a1, Point_3D b1, Point_3D a2, Point_3D b2, Point_3D& ans1, Point_3D& ans2){    Vector_3D v1 = (a1 - b1), v2 = (a2 - b2);    Vector_3D N = Cross(v1, v2);    Vector_3D ab = (a1 - a2);    double ans = Dot(N, ab) / Length(N);    Point_3D p1 = a1, p2 = a2;    Vector_3D d1 = b1 - a1, d2 = b2 - a2;    double t1, t2;    t1 = Dot((Cross(p2 - p1, d2)), Cross(d1, d2));    t2 = Dot((Cross(p2 - p1, d1)), Cross(d1, d2));    double dd = Length((Cross(d1, d2)));    t1 /= dd * dd;    t2 /= dd * dd;    ans1 = (a1 + (b1 - a1) * t1);    ans2 = (a2 + (b2 - a2) * t2);    return fabs(ans);}// 判断P是否在三角形A, B, C中，并且到三条边的距离都至少为mindist。保证P, A, B, C共面bool InsideWithMinDistance(const Point_3D & P, const Point_3D & A, const Point_3D & B, const Point_3D & C, double mindist){    if(!PointInTri(P, A, B, C))    {        return false;    }    if(DistanceToLine(P, A, B) < mindist)    {        return false;    }    if(DistanceToLine(P, B, C) < mindist)    {        return false;    }    if(DistanceToLine(P, C, A) < mindist)    {        return false;    }    return true;}// 判断P是否在凸四边形ABCD（顺时针或逆时针）中，并且到四条边的距离都至少为mindist。保证P, A, B, C, D共面bool InsideWithMinDistance(const Point_3D & P, const Point_3D & A, const Point_3D & B, const Point_3D & C, const Point_3D & D, double mindist){    if(!PointInTri(P, A, B, C))    {        return false;    }    if(!PointInTri(P, C, D, A))    {        return false;    }    if(DistanceToLine(P, A, B) < mindist)    {        return false;    }    if(DistanceToLine(P, B, C) < mindist)    {        return false;    }    if(DistanceToLine(P, C, D) < mindist)    {        return false;    }    if(DistanceToLine(P, D, A) < mindist)    {        return false;    }    return true;}/*************凸包相关问题*******************///加干扰double rand01(){    return rand() / (double)RAND_MAX;}double randeps(){    return (rand01() - 0.5) * EPS;}Point_3D add_noise(const Point_3D & p){    return Point_3D(p.x + randeps(), p.y + randeps(), p.z + randeps());}struct Face{    int v[3];    Face(int a, int b, int c)    {        v[0] = a;        v[1] = b;        v[2] = c;    }    Vector_3D Normal(const vector<Point_3D> & P) const    {        return Cross(P[v[1]] - P[v[0]], P[v[2]] - P[v[0]]);    }    // f是否能看见P[i]    int CanSee(const vector<Point_3D> & P, int i) const    {        return Dot(P[i] - P[v[0]], Normal(P)) > 0;    }};// 增量法求三维凸包// 注意：没有考虑各种特殊情况（如四点共面）。实践中，请在调用前对输入点进行微小扰动vector<Face> CH3D(const vector<Point_3D> & P){    int n = P.size();    vector<vector<int> > vis(n);    for(int i = 0; i < n; i++)    {        vis[i].resize(n);    }    vector<Face> cur;    cur.push_back(Face(0, 1, 2)); // 由于已经进行扰动，前三个点不共线    cur.push_back(Face(2, 1, 0));    for(int i = 3; i < n; i++)    {        vector<Face> next;        // 计算每条边的“左面”的可见性        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]) // (a,b)是分界线，左边对P[i]可见                {                    next.push_back(Face(a, b, i));                }            }        cur = next;    }    return cur;}struct ConvexPolyhedron{    int n;    vector<Point_3D> P, P2;    vector<Face> faces;    bool read()    {        if(scanf("%d", &n) != 1)        {            return false;        }        P.resize(n);        P2.resize(n);        for(int i = 0; i < n; i++)        {            P[i] = read_Point_3D();            P2[i] = add_noise(P[i]);        }        faces = CH3D(P2);        return true;    }    //三维凸包重心    Point_3D centroid()    {        Point_3D C = P[0];        double totv = 0;        Point_3D tot(0, 0, 0);        for(int i = 0; i < faces.size(); i++)        {            Point_3D p1 = P[faces[i].v[0]], p2 = P[faces[i].v[1]], p3 = P[faces[i].v[2]];            double v = -Volume6(p1, p2, p3, C);            totv += v;            tot = tot + Centroid(p1, p2, p3, C) * v;        }        return tot / totv;    }    //凸包重心到表面最近距离    double mindist(Point_3D C)    {        double ans = 1e30;        for(int i = 0; i < faces.size(); i++)        {            Point_3D p1 = P[faces[i].v[0]], p2 = P[faces[i].v[1]], p3 = P[faces[i].v[2]];            ans = min(ans, fabs(-Volume6(p1, p2, p3, C) / Area2(p1, p2, p3)));        }        return ans;    }};int main() {        return 0;}
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