计算几何模板

基础模板：

 

const double eps = 1e-10;
const double pi = 3.1415926535897 ;
struct Point
{
    double x, y;
    Point(double x = 0, double y = 0):x(x), y(y){}
};
typedef Point Vector;

struct Line//有向直线
{
    Point P;//直线上任意一点
    Vector v;//方向向量（左边就是对应的半平面）
    double ang;//极角，即从x正半轴旋转到向量v所需要的角（弧度）
    Line(Point P, Vector v):P(P), v(v){ang = Angle(v);}
    bool operator < (const Line& L)const
    {
        return ang < L.ang;
    }
};
Vector operator + (Vector A, Vector B){return Vector(A.x+B.x, A.y+B.y);}//向量+向量=向量；点+向量=向量
Vector operator - (Vector A, Vector B){return Vector(A.x-B.x, A.y-B.y);}//点-点=向量
Vector operator * (Vector A, double p){return Vector(A.x*p, A.y*p);}//向量*数=向量
Vector operator / (Vector A, double p){return Vector(A.x/p, A.y/p);}//向量/数=向量
bool operator < (const Point& a, const Point& b)
{
    return a.x < b.x || (a.x == b.x && a.y < b.y);
}
int dcmp(double x)//三态函数,高精度判断
{
    if(fabs(x) < eps)return 0; else return x < 0 ? -1 : 1;
}
bool operator == (const Point& a, const Point& b)
{
    return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0;
}
double Dot(Vector A, Vector B){return A.x*B.x + A.y*B.y;}//点积
double Length(Vector A){return sqrt(Dot(A, A));}//长度
double Angle(Vector A){return atan2(A.y, A.x);}//向量A的极角（弧度）
double Angle(Vector A, Vector B){return acos(Dot(A, B) / Length(A) / Length(B));}//向量A，B夹角
double Cross(Vector A, Vector B){return A.x*B.y - A.y*B.x;}//叉积
double Area2(Point A, Point B, Point C){return Cross(B-A, C-A);}//三角形有向面积的两倍
Vector Rotate(Vector A, double rad)
//向量A逆时针旋转rad(弧度)
{
    return Vector(A.x*cos(rad)-A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad));
}
Vector Normal(Vector A)
//返回A的单位法线，调用前保证A非零
{
    double L = Length(A);
    return Vector(-A.y/L, A.x/L);
}

Point GetlineIntersection(Point P, Vector v, Point Q, Vector w)//(参数式)
//求直线P+tv和Q+tw交点(t为参数)。调用前确保有交点，无交点当且仅当Cross(v, w) = 0;
{
    Vector u = P - Q;
    double t = Cross(w, u) / Cross(v, w);
    return P + v*t;
}
Point GetlineIntersectionB(Point P, Point X, Point Q, Point Y)//(两点式)
//求直线PX和QY交点(t为参数)。调用前确保有交点，无交点当且仅当Cross(v, w) = 0;
{
    Vector v = X - P, w = Y - Q;
    return GetlineIntersection(P, v, Q, w);
}
double DistanceToLine(Point P, Point A, Point B)
//点P到直线AB的距离
{
    Vector v1 = B - A, v2 = P - A;
    return fabs(Cross(v1, v2) / Length(v1));
}
double DistanceToSegment(Point P, Point A, Point B)
//点P到线段AB的距离
{
    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);
    else if(dcmp(Dot(v1, v3)) > 0)return Length(v3);
    else return fabs(Cross(v1, v2)) / Length(v1);
}
Point GetlineProjection(Point P, Point A, Point B)
//点P在直线AB上的投影
{
    Vector v = B - A;
    return A + v *(Dot(v, P-A) / Dot(v,v));
}
bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2)
//判断线段a1a2和b1b2是否规范相交(在端点处相交得用下一个函数特殊判断)
{
    double c1 = Cross(a2-a1, b1-a1), c2 = Cross(a2-a1, b2-a1),
           c3 = Cross(b2-b1, a1-b1), c4 = Cross(b2-b1, a2-b1);
    return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0;
}
bool OnSegment(Point p, Point a1, Point a2)//在线段上返回1，不在返回0
//判断点P是否在线段a1a2上（不包括端点）
{
    return dcmp(Cross(a1-p, a2-p)) == 0 && dcmp(Dot(a1-p, a2-p)) < 0;
}
bool OnSegment2(Point p, Point a1, Point a2)//在线段上返回1，不在返回0
//判断点P是否在线段a1a2上（包括端点）
{
    return OnSegment(p, a1, a2) || p == a1 || p == a2;
}

 

 

 

多边形：

 

//多边形面积
double PolygonArea(Point* p, int n)
{
    double area = 0;
    for(int i = 1; i < n - 1; i++)
        area += Cross(p[i] - p[0], p[i + 1] - p[0]);
    return area / 2;
}

//点在多边形内判定
int isPointInPolygon(Point p, Point * poly, int n)
{
    int wn = 0;
    for(int i = 0; i < n; i++)
    {
        if(OnSegment2(p, poly[i], poly[(i + 1) % n]))return -1;//点在多边形边界上
        int k = dcmp(Cross(poly[(i + 1) % n] - poly[i], p - poly[i]));
        int d1 = dcmp(poly[i].y - p.y);
        int d2 = dcmp(poly[(i + 1) % n].y - p.y);
        if(k > 0 && d1 <= 0 && d2 > 0)wn++;
        if(k < 0 && d2 <= 0 && d1 > 0)wn--;
    }
    if(wn != 0)return 1;//内部
    return 0;//外部
}

//凸包：输入点数组p，个数为n，输出点数组为ch，返回输出点个数
//输入不能有重复点，函数执行完输入点顺序被破坏
//如果不希望凸包的边上存在输入点，把两个<=改成<
int ConvexHull(Point* p, int n, Point * ch)
{
    sort(p, p + n);
    int m = 0;
    for(int i = 0; i < n; i++)
    {
        while(m > 1 && dcmp(Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2])) <= 0)m--;//可将此处的<=改成<，保证凸包的边上没有点
        ch[m++] = p[i];
    }
    int k = m;
    for(int i = n - 2; i >= 0; i--)
    {
        while(m > k && dcmp(Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2])) <= 0)m--;
        ch[m++] = p[i];
    }
    if(n > 1)m--;
    return m;
}

 圆

struct Circle
{
    Point c;//圆心
    double r;//半径
    Circle(){}
    Circle(Point c, double r):c(c), r(r){}
    Point point(double a)//在圆上圆心角为a的点
    {
        return Point(c.x + cos(a) * r, c.y + sin(a) * r);
    }
};