课程首页地址：http://blog.csdn.net/sxhelijian/article/details/7910565，本周题目链接：http://blog.csdn.net/sxhelijian/article/details/8953304
【项目5（选做）】类的组合与继承
（1）先建立一个Point(点)类，包含数据成员x,y(坐标点)；
（2）以Point为基类，派生出一个Circle(圆)类，增加数据成员(半径)，基类的成员表示圆心；
（3）编写上述两类中的构造、析构函数及必要的输入输出函数
（4）定义友元函数int locate，判断点p在圆c上、圆c内或圆c外，返回值<0圆内，==0圆上，>0 圆外；
（5）重载关系运算符（6种）运算符，使之能够按圆的面积比较两个圆的大小；
（6）给定一点p，求出该点与圆心相连成的直线与圆的两个交点并输出
下面给出用于测试的main()函数，涉及到的类请自行定义
int main( ){
Circle c1(3,2,4),c2(4,5,5); //c2应该大于c1
Point p1(1,1),p2(3,-2),p3(7,3); //分别位于c1内、上、外
cout<<"圆c1: "<<c1;
cout<<"点p1: "<<p1;
cout<<"点p1在圆c1之"<<((locate(p1, c1)>0)?"外":((locate(p1, c1)<0)?"内":"上"))<<endl;
cout<<"点p2: "<<p2;
cout<<"点p2在圆c1之"<<((locate(p2, c1)>0)?"外":((locate(p2, c1)<0)?"内":"上"))<<endl;
cout<<"点p3: "<<p3;
cout<<"点p3在圆c1之"<<((locate(p3, c1)>0)?"外":((locate(p3, c1)<0)?"内":"上"))<<endl;
cout<<endl;
cout<<"圆c1: "<<c1;
if(c1>c2) cout<<"大于"<<endl;
if(c1<c2) cout<<"小于"<<endl;
if(c1>=c2) cout<<"大于等于"<<endl;
if(c1<=c2) cout<<"小于等于"<<endl;
if(c1==c2) cout<<"等于"<<endl;
if(c1!=c2) cout<<"不等于"<<endl;
cout<<"圆c2: "<<c1;
cout<<endl;
Point p4,p5;
crossover_point1(p1,c1, p4, p5);
cout<<"点p1: "<<p1;
cout<<"与圆c1: "<<c1;
cout<<"的圆心相连，与圆交于两点，分别是："<<endl;
cout<<"交点: "<<p4;
cout<<"交点: "<<p5;
cout<<endl;
return 0;
}
针对4楼的疑问，加一张图，是（6）求解方式的说明。
参考解答：
#include <iostream>#include<Cmath>using namespace std;class Point{public: Point(double x=0,double y=0); //构造函数 double distance(const Point &p) const; //求距离 double getx() const {return x;} double gety() const {return y;} void setx(double x1){x=x1;} void sety(double y1){y=y1;} friend ostream & operator<<(ostream &,const Point &);//重载运算符“<<”protected: //受保护成员 double x,y;};//Point的构造函数Point::Point(double a,double b):x(a),y(b){}double Point::distance(const Point &p) const //求距离{ double dx = x-p.x; double dy = y-p.y; return sqrt(dx*dx+dy*dy);}ostream & operator<<(ostream &output,const Point &p){ output<<"["<<p.x<<","<<p.y<<"]"<<endl; return output;}class Circle:public Point //circle是Point类的公用派生类{public: Circle(double x=0,double y=0,double r=0); //构造函数 double area ( ) const; //计算圆面积 friend ostream &operator<<(ostream &,const Circle &);//重载运算符“<<” friend int locate(const Point &p, const Circle &c); //判断点p在圆上、圆内或圆外，返回值：<0圆内，==0圆上，>0 圆外 //重载关系运算符（种）运算符，使之能够按圆的面积比较两个圆的大小； bool operator>(const Circle &); bool operator<(const Circle &); bool operator>=(const Circle &); bool operator<=(const Circle &); bool operator==(const Circle &); bool operator!=(const Circle &); //给定一点p，求出该点与圆c的圆心相连成的直线与圆的两个交点p1和p2(为了带回计算结果，p1和p2需要声明为引用) friend void crossover_point(Point &p,Circle &c, Point &p1,Point &p2 ) ;protected: double radius;};//定义构造函数，对圆心坐标和半径初始化Circle::Circle(double a,double b,double r):Point(a,b),radius(r){ }//计算圆面积double Circle::area( ) const{ return 3.14159*radius*radius;}//重载运算符“<<”，使之按规定的形式输出圆的信息ostream &operator<<(ostream &output,const Circle &c){ output<<"Center=["<<c.x<<", "<<c.y<<"], r="<<c.radius<<endl; return output;}//判断点p在圆内、圆c内或圆c外int locate(const Point &p, const Circle &c){ const Point cp(c.x,c.y); //圆心 double d = cp.distance(p); if (abs(d - c.radius) < 1e-7) return 0; //相等 else if (d < c.radius) return -1; //圆内 else return 1; //圆外}//重载关系运算符（种）运算符，使之能够按圆的面积比较两个圆的大小；bool Circle::operator>(const Circle &c){ return (this->radius - c.radius) > 1e-7;}bool Circle::operator<(const Circle &c){ return (c.radius - this->radius) > 1e-7;}bool Circle::operator>=(const Circle &c){ return !(*this < c);}bool Circle::operator<=(const Circle &c){ return !(*this > c);}bool Circle::operator==(const Circle &c){ return abs(this->radius - c.radius) < 1e-7;}bool Circle::operator!=(const Circle &c){ return abs(this->radius - c.radius) > 1e-7;}//给定一点p，求出该点与圆c的圆心相连成的直线与圆的两个交点p1和p2(为了带回计算结果，p1和p2需要声明为引用)void crossover_point(Point &p, Circle &c, Point &p1,Point &p2 ){ p1.setx (c.getx() + sqrt(c.radius*c.radius/(1+((c.gety()-p.gety())/(c.getx()-p.getx()))*((c.gety()-p.gety())/(c.getx()-p.getx()))))); p2.setx (c.getx() - sqrt(c.radius*c.radius/(1+((c.gety()-p.gety())/(c.getx()-p.getx()))*((c.gety()-p.gety())/(c.getx()-p.getx()))))); p1.sety (p.gety() + (p1.getx() -p.getx())*(c.gety()-p.gety())/(c.getx()-p.getx())); p2.sety (p.gety() + (p2.getx() -p.getx())*(c.gety()-p.gety())/(c.getx()-p.getx()));}int main( ){ Circle c1(3,2,4),c2(4,5,5); //c2应该大于c1 Point p1(1,1),p2(3,-2),p3(7,3); //分别位于c1内、上、外 cout<<"圆c1: "<<c1; cout<<"点p1: "<<p1; cout<<"点p1在圆c1之"<<((locate(p1, c1)>0)?"外":((locate(p1, c1)<0)?"内":"上"))<<endl; cout<<"点p2: "<<p2; cout<<"点p2在圆c1之"<<((locate(p2, c1)>0)?"外":((locate(p2, c1)<0)?"内":"上"))<<endl; cout<<"点p3: "<<p3; cout<<"点p3在圆c1之"<<((locate(p3, c1)>0)?"外":((locate(p3, c1)<0)?"内":"上"))<<endl; cout<<endl; cout<<"圆c1: "<<c1; if(c1>c2) cout<<"大于"<<endl; if(c1<c2) cout<<"小于"<<endl; if(c1>=c2) cout<<"大于等于"<<endl; if(c1<=c2) cout<<"小于等于"<<endl; if(c1==c2) cout<<"等于"<<endl; if(c1!=c2) cout<<"不等于"<<endl; cout<<"圆c2: "<<c2; cout<<endl; Point p4,p5; crossover_point(p1,c1, p4, p5); cout<<"点p1: "<<p1; cout<<"与圆c1: "<<c1; cout<<"的圆心相连，与圆交于两点，分别是："<<endl; cout<<"交点: "<<p4; cout<<"交点: "<<p5; cout<<endl; return 0;}
再一种解法：
#include <iostream>#include<Cmath>using namespace std;class Point{public: Point(double x=0,double y=0); //构造函数 double distance(const Point &p) const; //求距离 double getx() const{return x;} double gety() const{return y;} void setx(double x1){x=x1;} void sety(double y1){y=y1;} friend ostream & operator<<(ostream &,const Point &);//重载运算符“<<”protected: //受保护成员 double x,y;};//Point的构造函数Point::Point(double a,double b):x(a),y(b){}double Point::distance(const Point &p) const //求距离{ double dx = x-p.x; double dy = y-p.y; return sqrt(dx*dx+dy*dy);}ostream & operator<<(ostream &output,const Point &p){ output<<"["<<p.x<<","<<p.y<<"]"<<endl; return output;}struct Two_points //专为crossover_point()函数返回值定义的结构体{ Point p1; Point p2;};class Circle:public Point //circle是Point类的公用派生类{public: Circle(double x=0,double y=0,double r=0); //构造函数 double area ( ) const; //计算圆面积 friend ostream &operator<<(ostream &,const Circle &);//重载运算符“<<” friend int locate(const Point &p, const Circle &c); //判断点p在圆上、圆内或圆外，返回值：<0圆内，==0圆上，>0 圆外 //重载关系运算符（种）运算符，使之能够按圆的面积比较两个圆的大小； bool operator>(const Circle &); bool operator<(const Circle &); bool operator>=(const Circle &); bool operator<=(const Circle &); bool operator==(const Circle &); bool operator!=(const Circle &); //再给一种解法：给定一点p，求出该点与圆c的圆心相连成的直线与圆的两个交点（返回Two_points型值） Two_points crossover_point(Point &p);protected: double radius;};//定义构造函数，对圆心坐标和半径初始化Circle::Circle(double a,double b,double r):Point(a,b),radius(r){ }//计算圆面积double Circle::area( ) const{ return 3.14159*radius*radius;}//重载运算符“<<”，使之按规定的形式输出圆的信息ostream &operator<<(ostream &output,const Circle &c){ output<<"Center=["<<c.x<<", "<<c.y<<"], r="<<c.radius<<endl; return output;}//判断点p在圆内、圆c内或圆c外int locate(const Point &p, const Circle &c){ const Point cp(c.x,c.y); //圆心 double d = cp.distance(p); if (abs(d - c.radius) < 1e-7) return 0; //相等 else if (d < c.radius) return -1; //圆内 else return 1; //圆外}//重载关系运算符（种）运算符，使之能够按圆的面积比较两个圆的大小；bool Circle::operator>(const Circle &c){ return (this->radius - c.radius) > 1e-7;}bool Circle::operator<(const Circle &c){ return (c.radius - this->radius) > 1e-7;}bool Circle::operator>=(const Circle &c){ return !(*this < c);}bool Circle::operator<=(const Circle &c){ return !(*this > c);}bool Circle::operator==(const Circle &c){ return abs(this->radius - c.radius) < 1e-7;}bool Circle::operator!=(const Circle &c){ return abs(this->radius - c.radius) > 1e-7;}//给定一点p，求出该点与圆的圆心相连成的直线与圆的两个交点（返回Two_points型值）Two_points Circle::crossover_point(Point &p){ Two_points pp; pp.p1.setx ( x + sqrt(radius*radius/(1+((y-p.gety())/(x-p.getx()))*((y-p.gety())/(x-p.getx()))))); pp.p2.setx ( x - sqrt(radius*radius/(1+((y-p.gety())/(x-p.getx()))*((y-p.gety())/(x-p.getx()))))); pp.p1.sety ( p.gety() + (pp.p1.getx() -p.getx())*(y-p.gety())/(x-p.getx())); pp.p2.sety ( p.gety() + (pp.p2.getx() -p.getx())*(y-p.gety())/(x-p.getx())); return pp;}int main( ){ Circle c1(3,2,4),c2(4,5,5); //c2应该大于c1 Point p1(1,1),p2(3,-2),p3(7,3); //分别位于c1内、上、外 cout<<"圆c1: "<<c1; cout<<"点p1: "<<p1; cout<<"点p1在圆c1之"<<((locate(p1, c1)>0)?"外":((locate(p1, c1)<0)?"内":"上"))<<endl; cout<<"点p2: "<<p2; cout<<"点p2在圆c1之"<<((locate(p2, c1)>0)?"外":((locate(p2, c1)<0)?"内":"上"))<<endl; cout<<"点p3: "<<p3; cout<<"点p3在圆c1之"<<((locate(p3, c1)>0)?"外":((locate(p3, c1)<0)?"内":"上"))<<endl; cout<<endl; cout<<"圆c1: "<<c1; if(c1>c2) cout<<"大于"<<endl; if(c1<c2) cout<<"小于"<<endl; if(c1>=c2) cout<<"大于等于"<<endl; if(c1<=c2) cout<<"小于等于"<<endl; if(c1==c2) cout<<"等于"<<endl; if(c1!=c2) cout<<"不等于"<<endl; cout<<"圆c2: "<<c2; cout<<endl; cout<<"用另外一种方法求交点："<<endl; Two_points twoPoint = c1.crossover_point(p1); cout<<"点p1: "<<p1; cout<<"与圆c1: "<<c1; cout<<"的圆心相连，与圆交于两点，分别是："<<endl; cout<<"交点: "<<twoPoint.p1; cout<<"交点: "<<twoPoint.p2; return 0;}