二维计算几何模板

最新推荐文章于 2019-08-09 16:23:50 发布

Goodbye_yesterday

最新推荐文章于 2019-08-09 16:23:50 发布

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分类专栏：计算几何

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本文深入探讨了基于向量和点的几何计算方法，包括点的定义、向量操作、距离计算、投影、线段相交判断及多边形面积计算等核心图形算法。通过这些算法，可以解决计算机图形学、地理信息系统、机器人导航等多个领域的复杂问题。

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#include<bits/stdc++.h>
using namespace std;
struct Point//定义点
{
   double x,y;
   Point(double x=0,double y=0):x(x),y(y){ }
}
typedef Point Vector;
Vector operator + (Vector A,Vector B)//重载运算符
{
   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 p)
{
   return Vector(A.x*p,A.y*p);
}
Vector operator /(Vector double p)
{
   return Vector(A.x/p,A.y/p);
}
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;
}
double Length(Vector A)
{
   return sqrt(Dot(A,A));
}
double Angle(Vector A,Vector B)
{
   return acos(Dot(A,B)/Length(A)/Length(B));
}
double Cross(Vector A,Vector B)
{
   return A.x*B.y-A.y*B.x;
}
double Area2(Point A,Point B,Point C)
{
   return Cross(B-A,C-A);
}
Vector Rotate(Vector A,double rad)
{
   return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}
Vector Normal(Vector A)
{
   double L=Length(A);
   return Vector(-A.y/L,A.x/L);
}
Point GetlineIntersection(Point P,Vector v,Point Q,Vector w)
{
   Vector u=P-Q;
   double t=Cross(w,u)/Cross(v,w);
   return P+v*t;
}
double DistanceToLine(Point P,Point A,Point B)
{
   Vector v1=B-A,v2=P-A;
   return fabs(Cross(v1,v2))/Length(v1);
}
double DistanceToSegment(Point P,Point A,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);
   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)//点在直线上的投影
{
   vector v=B-A;
   return A+v*(Dot(v,P-A)/Dot(v,v));
}
bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2)//线段相交
{
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)//
{
   return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dot(a1-p,a2-p))<0;
}
double PolygonArea(Point *p,int n)//多边形的有向面积
{
   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;
}
int main()
{
   return 0;
}