计算几何模板 - 全

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#include <cmath>#include <queue>#include <stack>#include <vector>#include <cstdio>#include <string>#include <cctype>#include <climits>#include <cstring>#include <cstdlib>#include <iomanip>#include <iostream>#include <algorithm>using namespace std;#define LL long long#define lson l, m, rt<<1#define rson m+1, r, rt<<1|1#define PI 3.1415926535897932626#define EXIT exit(0);#define DEBUG puts("Here is a BUG");#define CLEAR(name, init) memset(name, init, sizeof(name))const double eps = 1e-6;const int MAXN = (int)1e9 + 5;#define Vector Pointint dcmp(double x){    return fabs(x) < eps ? 0 : (x < 0 ? -1 : 1);}struct Point{    double x, y;    int flag;//点在哪条边上    Point(const Point& rhs): x(rhs.x), y(rhs.y) { }                                 //拷贝构造函数    Point(double x = 0.0, double y = 0.0, int flag = -1): x(x), y(y), flag(flag) {}                           //构造函数     friend istream& operator >> (istream& in, Point& P) { return in >> P.x >> P.y; }     friend ostream& operator << (ostream& out, const Point& P) { return out << P.x << ' ' << P.y; }    friend Vector operator + (const Vector& A, const Vector& B)    {        return Vector(A.x + B.x, A.y + B.y);    }    friend Vector operator - (const Point& A, const Point& B)    {        return Vector(A.x - B.x, A.y - B.y);    }    friend Vector operator * (const Vector& A, const double& p)    {        return Vector(A.x * p, A.y * p);    }    friend Vector operator / (const Vector& A, const double& p)    {        return Vector(A.x / p, A.y / p);    }    friend bool operator == (const Point& A, const Point& B)    {        return dcmp(A.x - B.x) == 0 && dcmp(A.y - B.y) == 0;    }    friend bool operator < (const Point& A, const Point& B)    {        return A.x < B.x || (A.x == B.x && A.y < B.y);    }    void in(void)    {        scanf("%lf%lf", &x, &y);    }    void out(void)    {        printf("%lf %lf", x, y);    }};struct Line{    Point P;                                                                        //直线上一点    Vector dir;                                                                     //方向向量(半平面交中该向量左侧表示相应的半平面)    double ang;                                                                     //极角，即从x正半轴旋转到向量dir所需要的角（弧度）    Line() {}                                                                      //构造函数    Line(const Line& L): P(L.P), dir(L.dir), ang(L.ang) { }    Line(const Point& P, const Vector& dir): P(P), dir(dir)    {        ang = atan2(dir.y, dir.x);    }    bool operator < (const Line& L) const                                           //极角排序    {        return ang < L.ang;    }    Point point(double t)    {        return P + dir * t;    }};typedef vector<Point> Polygon;struct Circle{    Point c;                                                                        //圆心    double r;                                                                       //半径    Circle() { }    Circle(const Circle& rhs): c(rhs.c), r(rhs.r) { }    Circle(const Point& c, const double& r): c(c), r(r) { }    Point point(double ang)    {        return Point(c.x + cos(ang) * r, c.y + sin(ang) * r); //圆心角所对应的    }};double Dot(const Vector& A, const Vector& B){    return A.x * B.x + A.y * B.y; //点积}double Length(const Vector& A){    return sqrt(Dot(A, A) + eps);}double juli(Point A, Point B){    return sqrt((A.x - B.x) * (A.x - B.x) + (A.y - B.y) * (A.y - B.y));}double Angle(const Vector& A, const Vector& B){    return acos(Dot(A, B) / Length(A) / Length(B)); //向量夹角}double Cross(const Vector& A, const Vector& B){    return A.x * B.y - A.y * B.x; //叉积}double Area(const Point& A, const Point& B, const Point& C){    return fabs(Cross(B - A, C - A));}//三边构成三角形的判定bool check_length(double a, double b, double c){    return dcmp(a + b - c) > 0 && dcmp(fabs(a - b) - c) < 0;}bool isTriangle(double a, double b, double c){    return check_length(a, b, c) && check_length(a, c, b) && check_length(b, c, a);}//向量绕起点旋转Vector Rotate(const Vector& A, const double& rad){    return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad));}//向量的单位法线(调用前请确保A 不是零向量)Vector Normal(const Vector& A){    double len = Length(A);    return Vector(-A.y / len, A.x / len);}//两直线交点(用前确保两直线有唯一交点，当且仅当Cross(A.dir, B.dir)非0)Point GetLineIntersection(const Line& A, const Line& B){    Vector u = A.P - B.P;    double t = Cross(B.dir, u) / Cross(A.dir, B.dir);    return A.P + A.dir * t;}//点到直线距离double DistanceToLine(const Point& P, const Line& L){    Vector v1 = L.dir, v2 = P - L.P;    return fabs(Cross(v1, v2)) / Length(v1);}//点到线段距离double DistanceToSegment(const Point& P, const Point& A, const Point& B){    if (A == B) return Length(P - A);    Vector v1 = B - A, v2 = P - A, v3 = P - B;    if (dcmp(Dot(v1, v2)) < 0) return Length(v2);    if (dcmp(Dot(v1, v3)) > 0) return Length(v3);    return fabs(Cross(v1, v2)) / Length(v1);}//点在直线上的投影Point GetLineProjection(const Point& P, const Line& L){    return L.P + L.dir * (Dot(L.dir, P - L.P) / Dot(L.dir, L.dir));}//点在线段上的判定bool isOnSegment(const Point& P, const Point& A, const Point& B){    //若允许点与端点重合，可关闭下面的注释    //if (P == A || P == B) return true;    return dcmp(Cross(A - P, B - P)) == 0 && dcmp(Dot(A - P, B - P)) < 0;}bool specialOnSegment(const Point& P, const Point& A, const Point& B){    //若允许点与端点重合，可关闭下面的注释    if (P == A || P == B) return true;    return dcmp(Cross(A - P, B - P)) == 0 && dcmp(Dot(A - P, B - P)) < 0;}//线段相交判定bool SegmentProperIntersection(const Point& a1, const Point& a2, const Point& b1, const Point& b2){    //若允许在端点处相交，可适当关闭下面的注释    //if (isOnSegment(a1, b1, b2) || isOnSegment(a2, b1, b2) || isOnSegment(b1, a1, a2) || isOnSegment(b2, a1, a2)) return true;    double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1);    double c3 = Cross(b2 - b1, a1 - b1), c4 = Cross(b2 - b1, a2 - b1);    return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0;}//多边形的有向面积double PolygonArea(Polygon po){    int n = po.size();    double area = 0.0;    for (int i = 1; i < n - 1; i++)    {        area += Cross(po[i] - po[0], po[i + 1] - po[0]);    }    return area * 0.5;}//直线和圆的交点int GetLineCircleIntersection(Line& L, const Circle& C){    double t1, t2;    double a = L.dir.x, b = L.P.x - C.c.x, c = L.dir.y, d = L.P.y - C.c.y;    double e = a * a + c * c, f = 2.0 * (a * b + c * d), g = b * b + d * d - C.r * C.r;    double delta = f * f - 4 * e * g;                                                   //判别式    if (dcmp(delta) < 0) return 0;                                                      //相离    if (dcmp(delta) == 0)                                                               //相切    {        t1 = t2 = -f / (2 * e);        sol.push_back(L.point(t1));        return 1;    }    // 相交    t1 = (-f - sqrt(delta)) / (2.0 * e);    sol.push_back(L.point(t1));    t2 = (-f + sqrt(delta)) / (2.0 * e);    sol.push_back(L.point(t2));    return 2;}//凸包(Andrew算法)//如果不希望在凸包的边上有输入点，把两个 <= 改成 <//如果不介意点集被修改，可以改成传递引用Polygon ConvexHull(vector<Point> p){    //预处理，删除重复点    sort(p.begin(), p.end());    p.erase(unique(p.begin(), p.end()), p.end());    int n = p.size(), m = 0;    Polygon res(n + 1);    for (int i = 0; i < n; i++)    {        while (m > 1 && Cross(res[m - 1] - res[m - 2], p[i] - res[m - 2]) <= 0) m--;        res[m++] = p[i];    }    int k = m;    for (int i = n - 2; i >= 0; i--)    {        while (m > k && Cross(res[m - 1] - res[m - 2], p[i] - res[m - 2]) <= 0) m--;        res[m++] = p[i];    }    m -= n > 1;    res.resize(m);    return res;}//点P在有向直线L左边的判定(线上不算)bool isOnLeft(const Line& L, const Point& P){    return Cross(L.dir, P - L.P) > 0;}//半平面交主过程//如果不介意点集被修改，可以改成传递引用Polygon HalfPlaneIntersection(vector<Line> L){    int n = L.size();    int head, rear;                                                                 //双端队列的第一个元素和最后一个元素的下标    vector<Point> p(n);                                                             //p[i]为q[i]和q[i+1]的交点    vector<Line> q(n);                                                              //双端队列    Polygon ans;    sort(L.begin(), L.end());                                                       //按极角排序    q[head = rear = 0] = L[0];                                                      //双端队列初始化为只有一个半平面L[0]    for (int i = 1; i < n; i++)    {        while (head < rear && !isOnLeft(L[i], p[rear - 1])) rear--;        while (head < rear && !isOnLeft(L[i], p[head])) head++;        q[++rear] = L[i];        if (fabs(Cross(q[rear].dir, q[rear - 1].dir)) < eps)                        //两向量平行且同向，取内侧的一个        {            rear--;            if (isOnLeft(q[rear], L[i].P)) q[rear] = L[i];        }        if (head < rear) p[rear - 1] = GetLineIntersection(q[rear - 1], q[rear]);    }    while (head < rear && !isOnLeft(q[head], p[rear - 1])) rear--;                  //删除无用平面    if (rear - head <= 1)         return ans;                                               //空集    p[rear] = GetLineIntersection(q[rear], q[head]);                                //计算首尾两个半平面的交点    for (int i = head; i <= rear; i++)                                              //从deque复制到输出中    {        ans.push_back(p[i]);    }    return ans;}//圆的面积交double calc(double r1, double r2, double d) {    double alpha = acos((r2*r2+d*d-r1*r1)/2/r2/d)*2;    double sector = alpha * r2 * r2 / 2;    double triangle = r2 * r2 * sin(alpha) / 2;    return sector - triangle;}double AreaofCircle(double x1, double y1, double r1, double x2, double y2, double r2){     double d = sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));     if(d <= max(r1, r2) - min(r1, r2) + eps)     return acos(-1.0) * min(r1, r2) * min(r1, r2);       else if (d + eps >= r1 + r2)         return 0.000;     else     return calc(r1, r2, d) + calc(r2, r1, d);       //cout << setprecision(20) << AreaofCircle(x1, y1, r1, x2, y2, r2) << endl ;  }int main(int argc, char const *argv[]){    return 0;}
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