平面几何模板

最新推荐文章于 2024-03-31 15:51:24 发布

原创最新推荐文章于 2024-03-31 15:51:24 发布 · 306 阅读

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CC 4.0 BY-SA版权

本文提供了丰富的几何计算方法，包括点、向量操作，如加减乘除、点乘、叉乘等，以及向量旋转、单位法线向量、线段交点计算等实用函数。还介绍了距离计算、投影点求解、线段相交判断和多边形面积计算等功能。

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#include<bits/stdc++.h>
using namespace std;
struct Point{
    double x,y;
    Point(double x=0,double y=0):x(x),y(y){}
};
typedef Point Vector;
Vector operator + (Vector A,Vector B){return Vector(A.x+B.x,A.y+B.y);}
Vector operator - (Vector A,Vector B){return Vector(A.x-B.x,A.y-B.y);}
Vector operator * (Vector A,double B){return Vector(A.x*B,A.y*B);}
Vector operator / (Vector A,double B){return Vector(A.x/B,A.y/B);}
bool operator<(const Point& a,const Point& b){return a.x<b.x||(a.x==b.x&&a.y<b.y);}
const double eps=1e-10;
int dcmp(double x){
    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;}//点乘
double Length(Vector A){return sqrt(Dot(A,A));}//向量长度
double Angle(Vector A,Vector B){return acos(Dot(A,B)/Length(A)/Length(B));}//计算角度
double Cross(Vector A,Vector B){return A.x*B.y-A.y*B.x;}//叉乘
double Area2(Point A,Point B,Point C){return Cross(B-A,C-A);}三角形二倍面积，平行四边形面积
Vector Rotate(Vector A,double rad){//逆时针旋转公式（旋转矩阵）
    return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}
Vector Normal(Vector A){//单位法线向量
    double L=Length(A);
    return Vector(-A.y/L,A.x/L);
}
Point GetLineIntersection(Point P,Vector v,Point Q,Vector w){//点斜式直线交点公式
    Vector u=P-Q;
    double t=Cross(w,u)/Cross(v,w);
    return P+v*t;
}
double DistanceToLine (Point P,Point A,Point B){  //P到A，B两点所在直线的距离
    Vector v1=B-A,v2=P-A;
    return fabs(Cross(v1,v2))/Length(v1);
}
double DistanceToSegment(Point P,Point A,Point B){  //P到A，B两点所在线段的距离
    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){//P在A，B所在直线上的投影点
    Vector v=B-A;
    return A+v*(Dot(v,P-A)/Dot(v,v));
}
bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){//线段相交判定
    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){//点是否在线段上
    return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dot(a1-p,a2-p))<0;
}
double ConvexPolygonArea(Point* p,int n){//计算多边形的面积
    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;
}