计算几何入门一：点，线段，直线，向量

素颜马尾好姑娘i 2022-06-10 01:37 319阅读 0赞

知识都是高中或大一高数知识，自行回顾，模板已给出！！！

涉及点，直线，线段，向量，交点坐标的求法以下模板都可以直接复制粘贴使用  
模板如下：

#include <iostream>
    #include<cmath>
    #include<algorithm>
    using namespace std;
    #define EPS 1e-10
    #define equals(a,b) (fabs((a)-(b))<EPS)
    struct Point {
        double x,y;
        Point(double x=0,double y=0):x(x),y(y){}
    };
    typedef Point Vector;
    
    struct Segment {
        Point p1,p2;
    };
    typedef Segment Line;
    //重载运算符
    Vector operator +(Vector a,Vector b) {
        return Vector(a.x+b.x,a.y+b.y);
    }
    Vector operator -(Point a,Point b){
        return Vector(a.x-b.x,a.y-b.y);
    }
    Vector operator *(Vector a,double k){
        return Vector(k*a.x,k*a.y);
    }
    //向量的模
    double morn(Vector a){
        return sqrt(a.x*a.x+a.y*a.y);
    }
    //向量的内积（点积）
    double dot(Vector a,Vector b){
        return a.x*b.x+a.y*b.y;
    }
    //向量的外积（叉乘）
    double Cross(Vector a,Vector b){
        return a.x*b.y-b.x*a.y;
    }
    //判断向量是否平行
    bool IsParallel(Vector a,Vector b){
        return equals(Cross(a,b),0.0);
    }
    //点到直线投影
    Point project(Segment s,Point p){
        Vector base=s.p1-s.p2;
        double r=dot(p-s.p1,base)/morn(base);
        return s.p1+base*r;
    }
    //点关于直线的对称点
    Point reflect(Segment s,Point p){
        return p+(project(s,p)-p)*2.0;
    }
    //点到直线距离
    double getDisLP(Line l,Point p){
        return morn(Cross(l.p2-l.p1,p-l.p1)/morn(l.p2-l.p1));
    }
    //点到线段的距离
    double getDisSP(Segment s,Point p){
        if(dot(s.p2-s.p1,p-s.p1)<0.0)return morn(p-s.p1);
        if(dot(s.p1-s.p2,p-s.p2)<0.0)return morn(p-s.p2);
        return getDisLP(s,p);
    }
    //向量与点的位置
    int ccw(Point p0,Point p1,Point p2){
        Vector a=p1-p0;
        Vector b=p2-p0;
        if(Cross(a,b)>EPS) return 1;
        if(Cross(a,b)<-EPS) return -1;
        if(dot(a,b)<-EPS) return 2;
        if(morn(a)<morn(b)) return -2;
        return 0;
    }
    //线段相交
    bool intersect(Point p1,Point p2,Point q1,Point q2){
        bool ret;
        ret=(ccw(p1,p2,q1)*ccw(p1,p2,q2)<=0&&ccw(q1,q2,p1)*ccw(q1,q2,p2)<=0);
        return ret;
    }
    //线段交点
    Point getCrossPoint(Segment s1,Segment s2){
        Vector base=s2.p2-s2.p1;
        double d1=morn(Cross(base,s1.p1-s2.p1));
        double s2=morn(Cross(base,s1.p2-s2.p1));
        double t=d1/(d1+d2);
        return s1.p1+(s1.p2-s1.p1)*t;
    }
    int main() {
    
        return 0;
    }