Computational Geometry的常用代码

今天偷懒了，一直没写博客。

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为了保持“每天一篇”的更新，发一点上课用的东西：我们ICPC自己的Library，用来做Computation Geometry题目的。

主要包含：基本的点、线、圆、三角形、多边形的关系，以及两个很有用的算法：线切割多边形; Convex Hall -- 找出n个点所形成的最外围的凸多边形。

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代码见下：（本来想直接上传的，但要压缩一遍才行太麻烦了）

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#include <iostream>#include <sstream>#include <vector>#include <string>#include <cstdio>#include <cstring>#include <algorithm>#include <queue>#include <set>#include <stack>#include <map>#include <list>#include <cmath>#define EPS 1e-100#define PI  3.1415926535897932384626433832795028841971693993#define DEG_to_RAD(X)   (X * PI / 180)#define RAD_to_DEG(X)   (X / PI * 180)#define CIR_INSIDE  0#define CIR_BORDER  1#define CIR_OUTSIDE 2#define TRI_NONE    0#define TRI_ACUTE   1#define TRI_RIGHT   2#define TRI_OBTUSE  3using namespace std;typedef pair<int,int>   ii;typedef vector<int>     vi;typedef vector<ii>      vii;typedef vector<vi>     vvi;typedef vector<vii>    vvii;typedef map<int,int>    mii;struct Point_i{    int x; int y;    Point_i(int _x, int _y){ x = _x; y = _y;}};struct Point{    double x,y;    Point(){ }    Point(double _x, double _y){        x = _x; y = _y;    }    bool operator < (const Point other) const{        if(fabs(x - other.x) > EPS) return x < other.x;        return y < other.y;    }    bool operator == (const Point other) const{        return (fabs(x - other.x) < EPS && (fabs(y - other.y) < EPS));    }   struct Point* operator = (const Point *other){       x = other->x; y = other->y;       return this;    }};struct Circle{    Point c;    double r;    Circle(Point _c, double _r){        c = _c; r = _r;    }    Circle* operator = (const Circle *oth){        c = oth->c; r = oth->r;        return this;    }};bool areSame(Point_i p1, Point_i p2){    return p1.x == p2.x && p1.y == p2.y;}bool areSame(Point p1, Point p2){    return fabs(p1.x - p2.x) < EPS && fabs(p1.y - p2.y) < EPS;}double dist(Point p1, Point p2){    return hypot(p1.x - p2.x, p1.y - p2.y);}Point rotate(Point p, double theta){    double rad = DEG_to_RAD(theta);    return Point(p.x * cos(rad) - p.y * sin(rad),                 p.x * sin(rad) + p.y * cos(rad));}// ax + by + c = 0struct Line{    double a,b,c;    const bool operator<(Line x) const{        if(abs(a - x.a) > EPS)  return a < x.a;        if(abs(b - x.b) > EPS)  return b < x.b;        if(abs(c - x.c) > EPS)  return c < x.c;        return false;   // when it's equal    }};void PointsToLine(Point p1, Point p2, Line *l){    if(p1.x == p2.x){        l->a = 1.0; l->b = 0.0; l->c = -p1.x;    } else{        l->a = -(double)(p1.y - p2.y) / (p1.x - p2.x);        l->b = 1.0;        l->c = -(double)(l->a * p1.x) - (l->b * p1.y);    }}bool areParallel(Line l1, Line l2){    return (fabs(l1.a - l2.a) < EPS) && (fabs(l1.b-l2.b) < EPS);}bool areSame(Line l1, Line l2){    return areParallel(l1,l2) && (fabs(l1.c - l2.c) < EPS);}bool areIntersect(Line l1, Line l2,Point *p){    if(areSame(l1,l2))   return false;    if(areParallel(l1,l2)) return false;    p->x = (l2.b * l1.c - l1.b * l2.c) / (l2.a * l1.b - l1.a * l2.b);    if(fabs(l1.b) > EPS){        p->y = -(l1.a * p->x + l1.c) / l1.b;    } else{        p->y = -(l2.a * p->x + l2.c) / l2.b;    }    return true;}// returs the distance from p to the Line defined by// two Points A and B ( A and B must bedifferent)// the closest Point is stored in the 4th parameter (by reference)double distToLine(Point p, Point A,Point B, Point *c){    double scale = (double)        ((p.x - A.x) * (B.x - A.x) + (p.y - A.y) * (B.y - A.y)) /        ((B.x - A.x) * (B.x - A.x) + (B.y - A.y) * (B.y - A.y));    c->x = A.x + scale * (B.x - A.x);    c->y = A.y + scale * (B.y - A.y);    return dist(p, *c);}double distToLineSegment(Point p, Point A,Point B, Point *c){    if( (B.x - A.x) * (p.x - A.x) + (B.y - A.y) * (p.y - A.y) < EPS){        c->x =  A.x; c->y = A.y;        return dist(p,A);    }    if( (A.x - B.x) * (p.x - B.x) + (A.y - B.y) * (p.y - B.y) < EPS){        c->x = B.x; c->y = B.y;        return dist(p,B);    }    return distToLine(p,A,B,c);}// The cross product of pq,prdouble crossProduct(Point p, Point q, Point r){    return (r.x - q.x) * (p.y - q.y) - (r.y - q.y) * (p.x - q.x);}// returns true if Point r is on the same Line as the Line pqbool colinear(Point p, Point q,Point r){    return fabs(crossProduct(p,q,r)) < EPS;}bool ccw(Point p, Point q, Point r){    return crossProduct(p,q,r) > 0;}struct vec{    double x, y;    vec(double _x, double _y){ x = _x, y = _y;}};vec toVector(Point p1, Point p2){    return vec(p2.x - p1.x, p2.y - p1.y);}vec scaleVector(vec v, double s){    return vec(v.x * s, v.y * s);}Point translate(Point p, vec v){    return Point(p.x + v.x, p.y + v.y);}bool Point_sort_x(Point a, Point b){    if( fabs(a.x - b.x) < EPS)  return a.y < b.y;    return (a.x < b.x);}        /* Circles */// int versionint inCircle(Point_i p, Point_i c, int r){    int dx = p.x - c.x, dy = p.y - c.y;    int Euc = dx * dx + dy * dy, rSq= r * r;    return Euc < rSq ? CIR_INSIDE : Euc == rSq ? CIR_BORDER : CIR_OUTSIDE;}// float versionint inCircle(Point p, Point c, int r){    double dx = p.x - c.x, dy = p.y - c.y;    double Euc = dx * dx + dy * dy, rSq= r * r;    return (Euc - rSq < EPS) ? CIR_BORDER : Euc < rSq ? CIR_INSIDE : CIR_OUTSIDE;}bool circle2PtsRad(Point p1, Point p2, double r, Point *c){    double d2 = (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y);    double det = r * r / d2 - 0.25;    if(det < 0) return false;    double h = sqrt(det);    c->x = (p1.x + p2.x) * 0.5 + (p1.y - p2.y) * h;    c->y = (p1.y + p2.y) * 0.5 + (p2.x - p1.x) * h;    return true;}double gcDistance(double pLat, double pLong,                  double qLat, double qLong, double radius) {    pLat *= PI / 180; pLong *= PI / 180;    qLat *= PI / 180; qLong *= PI / 180;    return radius * acos(cos(pLat)*cos(pLong)*cos(qLat)*cos(qLong) +                         cos(pLat)*sin(pLong)*cos(qLat)*sin(qLong) +                         sin(pLat)*sin(qLat));}        /* Triangle */// Find the trigangle type based on the arr of points givenint findTriangleType(Point arr[]){    double res = crossProduct(arr[0],arr[1],arr[2]);    if(fabs(res) < EPS)  return TRI_RIGHT;    else if(res < 0) return TRI_OBTUSE;    res = crossProduct(arr[1],arr[0],arr[2]);    if(res < EPS){        swap(arr[0],arr[1]);        if(fabs(res) < EPS)    return TRI_RIGHT;        return TRI_OBTUSE;    }    res = crossProduct(arr[2],arr[0],arr[1]);    if(res < EPS){        swap(arr[0],arr[1]);        if(fabs(res) < EPS)  return TRI_RIGHT;        return TRI_OBTUSE;    }    return TRI_ACUTE;}double perimeter(double ab, double bc, double ca) {    return ab + bc + ca; }double perimeter(Point a, Point b, Point c) {    return dist(a, b) + dist(b, c) + dist(c, a); }double area(double ab, double bc, double ca) {    // Heron's formula, split sqrt(a * b) into sqrt(a) * sqrt(b); in implementation    double s = 0.5 * perimeter(ab, bc, ca);    return sqrt(s) * sqrt(s - ab) * sqrt(s - bc) * sqrt(s - ca); }double area(Point a, Point b, Point c) {    return area(dist(a, b), dist(b, c), dist(c, a)); }double rInCircle(double ab, double bc, double ca) {    return area(ab, bc, ca) / (0.5 * perimeter(ab, bc, ca)); }double rInCircle(Point a, Point b, Point c) {    return rInCircle(dist(a, b), dist(b, c), dist(c, a)); }double rCircumCircle(double ab, double bc, double ca) {    return ab * bc * ca / (4.0 * area(ab, bc, ca)); }double rCircumCircle(Point a, Point b, Point c) {    return rCircumCircle(dist(a, b), dist(b, c), dist(c, a)); }bool canFormTriangle(double a, double b, double c) {    return (a + b > c) && (a + c > b) && (b + c > a); }        /* Polygon */double perimeter(vector<Point> P){    double result = 0.0;    for(int i=0;i<P.size()-1;i++){        result += dist(P[i],P[i+1]);    }    return result;}double polygonArea(vector<Point> P){    double result = 0, x1, y1, x2, y2;    for(int i=0;i<P.size()-1;i++){        x1 = P[i].x; x2 = P[i+1].x;        y1 = P[i].y; y2 = P[i+1].y;        result += (x1 * y2 - x2 * y1);    }    return fabs(result) / 2.0;}bool isConvex(vector<Point> P){    int sz = (int) P.size();    if(sz < 3)  return false;    bool isLeft = ccw(P[0], P[1], P[2]);    for(int i=1; i<(int)P.size();i++){        if(ccw(P[i],P[(i+1)%sz],P[(i+2)%sz]) != isLeft) return false;    }    return true;}double angle(Point a, Point b, Point c){    double ux = b.x - a.x, uy = b.y - a.y;    double vx = c.x - a.x, vy = c.y - a.y;    return acos( (ux * vx + uy*vy) / sqrt((ux*ux + uy*uy) * ( vx*vx + vy*vy)));}bool inPolygon(Point p, vector<Point> P){    if(P.size() == 0) return false;    double sum = 0;    for(int i=0;i<P.size() -1; i++){        if(crossProduct(p,P[i],P[i+1]) < 0)    sum -= angle(p,P[i],P[i+1]);        else    sum += angle(p,P[i],P[i+1]);    }    return (fabs(sum - 2*PI) < EPS || fabs(sum + 2*PI) < EPS);}Point lineIntersectSeg(Point p, Point q, Point A, Point B){    double a = B.y - A.y;    double b = A.x - B.x;    double c = B.x * A.y - A.x * B.y;    double u = fabs(a*p.x + b*p.y + c);    double v = fabs(a*q.x + b*q.y + c);    return Point((p.x*v + q.x*u) / (u+v), (p.y*v + q.y*u) / (u+v));}// cuts polygon Q along the line formed by point a -> point b// (note: the last point must be the same as the first point)vector<Point> cutPolygon(Point a, Point b, vector<Point> Q) {    vector<Point> P;    for (int i = 0; i < (int)Q.size(); i++) {        double left1 = crossProduct(a, b, Q[i]), left2 = 0.0;        if (i != (int)Q.size() - 1) left2 = crossProduct(a, b, Q[i + 1]);        if (left1 > -EPS) P.push_back(Q[i]);        if (left1 * left2 < -EPS)            P.push_back(lineIntersectSeg(Q[i], Q[i + 1], a, b));    }    if (P.empty()) return P;    if (fabs(P.back().x - P.front().x) > EPS ||        fabs(P.back().y - P.front().y) > EPS)        P.push_back(P.front());    return P; }Point pivot(0, 0);bool angle_cmp(Point a, Point b) { // angle-sorting function    if (colinear(pivot, a, b))        return dist(pivot, a) < dist(pivot, b); // which one is closer?    double d1x = a.x - pivot.x, d1y = a.y - pivot.y;    double d2x = b.x - pivot.x, d2y = b.y - pivot.y;    return (atan2(d1y, d1x) - atan2(d2y, d2x)) < 0; }vector<Point> CH(vector<Point> P) {    int i, N = (int)P.size();    if (N <= 3) return P; // special case, the CH is P itself        // first, find P0 = point with lowest Y and if tie: rightmost X    int P0 = 0;    for (i = 1; i < N; i++)        if (P[i].y  < P[P0].y ||            (P[i].y == P[P0].y && P[i].x > P[P0].x))            P0 = i;    // swap selected vertex with P[0]    Point temp = P[0]; P[0] = P[P0]; P[P0] = temp;        // second, sort points by angle w.r.t. P0, skipping P[0]    pivot = P[0]; // use this global variable as reference    sort(++P.begin(), P.end(), angle_cmp);        // third, the ccw tests    Point prev(0, 0), now(0, 0);    stack<Point> S; S.push(P[N - 1]); S.push(P[0]); // initial    i = 1; // and start checking the rest    while (i < N) { // note: N must be >= 3 for this method to work        now = S.top();        S.pop(); prev = S.top(); S.push(now); // get 2nd from top        if (ccw(prev, now, P[i])) S.push(P[i++]); // left turn, ACC        else S.pop(); // otherwise, pop until we have a left turn    }        vector<Point> ConvexHull; // from stack back to vector    while (!S.empty()) { ConvexHull.push_back(S.top()); S.pop(); }    return ConvexHull; } // return the resultint main(){        return 0;}

哦，对了。我把自己做UVA题目的情况放到了网上，开源的：http://code.google.com/p/songyy-uva-problems/。

有兴趣的话可以去看看：）