几何的代码实现

布满荆棘的人生 2021-10-26 12:38 248阅读 0赞

## 点的表示 ##

struct  Point{
        double x;double y;
        Point(double x=0,double y=0):x(x),y(y) {}//加这句话是为了重载运算用？？？
    }p1,p2;

重载点运算符

Point operator + (Point p1,Point p2){
        return Point(p1.x+p2.x,p1.y+p2.y);
    }
    Point operator - (Point p1,Point p2){
        return Point(p1.x-p2.x,p1.y-p2.y);
    }
    Point operator * (Point p1,Point p2){
        return Point(p1.x*p2.x,p1.y*p2.y);
    }
    Point operator / (Point p1,Point p2){
        return Point(p1.x/p2.x,p1.y/p2.y);
    }

实现点的运算

#include <iostream> #include <cstdio> #include <cmath> using namespace std; struct Point{ double x;double y; Point(double x=0,double y=0):x(x),y(y) {} }; Point operator + (Point p1,Point p2){ return Point(p1.x+p2.x,p1.y+p2.y); } Point operator - (Point p1,Point p2){ return Point(p1.x-p2.x,p1.y-p2.y); } Point operator * (Point p1,Point p2){ return Point(p1.x*p2.x,p1.y*p2.y); } Point operator / (Point p1,Point p2){ return Point(p1.x/p2.x,p1.y/p2.y); } int main(){ Point p1,p2,p3; p1.x=1.1,p1.y=1.2; p2.x=0.9,p2.y=0.8; p3=p1+p2; printf("相加为%lf %lf\n",p3.x,p3.y); p3=p1-p2; printf("相减为%lf %lf\n",p3.x,p3.y); p3=p1*p2; printf("相乘为%lf %lf\n",p3.x,p3.y); p3=p1/p2; printf("相除为%lf %lf\n",p3.x,p3.y); return 0; }

重载向量运算符

Vector operator + (Vector p1,Vector p2){ return Point(p1.x+p2.x,p1.y+p2.y); } Vector operator - (Point p1,Point p2){ return Point(p1.x-p2.x,p1.y-p2.y); } Vector operator * (Point p1,double p){ return Point(p1.x*p,p1.y*p); } Vector operator / (Point p1,double p){ return Point(p1.x/p,p1.y/p); }

--------------------

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 - (Point A, Point 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 A, double p){ return Vector(A.x/p, A.y/p); }

--------------------

小于运算  
将点集按照x坐标升序排序，若x坐标相同，则按照y坐标排序  
cmp在函数sort();里配合使用

bool operator < (const Point &a,const Point &b){
        if(a.x==b.x)
            return a.y<b.y;
        return a.x<b.x; 
    }

等于运算  
判断两个点是否近似相等

bool operator ==(const Point &a,const Point &b){
        if(dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0)
            return true;
        return false;
    }

点积运算

double Dot(Vector a,Vector b){
        return a.x*b.x+a.y*b.y;
    }

叉乘运算  
可用于求面积

double Cross(Vector a,Vector b){ return a.x*b.y-a.y*b.x; }

取模运算

double Length(Vector a){ return sqrt(Dot(a,a)); }

夹角计算

double Angle(Vector a,Vector b){ return acos(Dot(a,b)/(Length(a)*Length(b))); }

逆时针选择后的向量

Vector Rotate(Vector A, double rad){//rad为弧度 且为逆时针旋转的角 return Vector(A.x*cos(rad)-A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad)); }

判断折线bc是不是向ab的逆时针方向（左边）转向

bool ToLeftTest(Point a, Point b, Point c){ return Cross(b - a, c - b) > 0; }

## 精度问题 ##

定义

static const double PI = acos(-1.0);//π 
    static const double eps = 1e-16;
    static const double inf = 1e100;

x==y  
因为浮点的比较运算有些问题，所以改写成

int dcmp(double a,double b){
        if(fabs(a-b)<eps)
            return 0;//相等
        if(a>b)
            return 1//a大于b
        return -1;//a小于b
    }

输出为-0

double a =-0.00001 printf("%.4f",a);

转载于:https://www.cnblogs.com/Emcikem/p/11354244.html