分享程序员开发的那些事...
更新时间：2022-10-12 09:50:50
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;
}