基于C++的计算不同图形面积

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要求

  1. 定义抽象基类Shape，由它派生出5个派生类：Circle、Square、Rectangle、Trapezoid、Triangle。用虚函数分别计算多个不同类图形的面积，并求它们的面积和。
  2. 要求用基类指针数组，使它的每一个元素指向一个派生类的对象，使用一个循环完成对多个图像的面积计算与求和。
  3. 图型的数据在定义对象时给定
  4. 定义顶点Point类，并在5个派生类中使用
  5. 圆以圆心坐标，半径的方式给定，其余以顶点坐标的方式给定
  6. 各个派生类的构造函数中应判断给定顶点组合是否满足图形属性

知识点

  1. 类的继承与派生
  2. 虚函数的使用

代码

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#include <iostream>
#include <math.h>
#include <stdlib.h>
#define pi 3.1415926
#define eps 1e-6
using namespace std;
//点类
class Point
{
public:
    double x,y;
    Point(){};
    Point(double x,double y):x(x),y(y){};
    Point &operator=(const Point &p){
        x=p.x;
        y=p.y;
        return *this;
    }
};
//基类
class Shape
{
public:
    Point *p;
    virtual double Area()=0;//求面积
    bool check_angle90(Point a,Point b,Point c){//判断是否垂直
        return fabs((a.x-c.x)*(b.x-c.x)+(b.y-c.y)*(a.y-c.y))<=eps;
    }
    bool check_Parallel(Point a,Point b,Point c,Point d){//判断是否平行
        return fabs((a.x-b.x)*(c.y-d.y)-(a.y-b.y)*(c.x-d.x))<=eps;
    }
    double dis2(Point a,Point b){//求两点间距离
        return pow(a.x-b.x,2)+pow(a.y-b.y,2);
    }
    void Swap(Point &x,Point &y){//交换两点
        Point temp;
        temp=x;
        x=y;
        y=temp;
    }
};
//派生类：圆形
class Circle: public Shape
{
public:
    double r;
    Circle(Point point,double radius){
        if(r<=0){
            cout<<"Wrong parameter"<<endl;
        }
        p=new Point(point);
        r=radius;
    }
    ~Circle(){
        delete p;
    }
    double Area(){
        return r*r*pi;
    }
};
//派生类：矩阵
class Rectangle: public Shape
{
public:
    double width,height;
    bool check(Point point[],bool isSquare){//判断是否是矩形或者正方形
        int k=0;
        while(k<3){//找到一个直角
            if(check_angle90(point[0],point[1],point[2]))break;
            Swap(point[k],point[3]);
            k++;
        }
        if(k==3)return false;
        Swap(point[1],point[2]);
        double edge2[4];
        for(int i=0;i<4;i++){
            edge2[i]=dis2(point[i],point[(i+1)%4]);
        }

        //矩形两对边相等，正方形四边相等
        if(isSquare)return fabs(edge2[0]-edge2[2])<=eps&&fabs(edge2[1]-edge2[3])<=eps&&fabs(edge2[0]-edge2[1])<=eps;
        else return fabs(edge2[0]-edge2[2])<=eps&&fabs(edge2[1]-edge2[3])<=eps;
    }
    double Area(){
        return width*height;
    }
    Rectangle(){};
    Rectangle(Point point[]){
        if(!check(point,0)){
            cout<<"Wrong parameter"<<endl;
            return;
        }
        p=new Point[4];
        for(int i=0;i<4;i++){
            p[i]=point[i];
        }
        width=sqrt(dis2(point[0],point[1]));
        height=sqrt(dis2(point[0],point[3]));
    }
    ~Rectangle(){
        delete[] p;
    }
};
//派生类：正方形
class Square: public Rectangle
{
public:
    double edge;
    Square(Point point[]){
        if(!check(point,1)){
            cout<<"Wrong parameter"<<endl;
            return;
        }
        p=new Point[4];
        for(int i=0;i<4;i++){
            p[i]=point[i];
        }
        edge=sqrt(dis2(point[0],point[1]));
    }
    ~Square(){
        delete[] p;
    }
    double Area(){
        return edge*edge;
    }
};
//派生类：三角形
class Triangle: public Shape
{
public:
    double edge[3];
    bool check(Point point[]){//三角形只要判断是否有零边
        for(int i=0;i<3;i++){
            edge[i]=sqrt(dis2(point[i],point[(i+1)%3]));
        }
        return edge[0]>eps&&edge[1]>eps&&edge[2]>eps;
    }
    double Area(){//海伦公式
        double aver=(edge[0]+edge[1]+edge[2])/2;
        return sqrt(aver*(aver-edge[0])*(aver-edge[1])*(aver-edge[2]));
    }
    Triangle(Point point[]){
        if(!check(point)){
            cout<<"Wrong parameter"<<endl;
        }
        p=new Point[3];
        for(int i=0;i<3;i++){
            p[i]=point[i];
        }
    }
    ~Triangle(){
        delete[] p;
    }
};

class Trapezoid: public Shape
{
public:
     bool check(Point point[]){
        int i=0;
        while(i<3){//找平行的一对边，为上下底
            if(check_Parallel(point[0],point[1],point[2],point[3]))break;
            Swap(point[i],point[3]);
            i++;
        }
        if(i==3)return false;
        //找高，且高不为零
        double y0=point[0].y-point[1].y,x0=point[0].x-point[1].x;
        if(fabs(x0)<=eps)height=fabs(point[0].x-point[2].x);
        else {
            double k=y0/x0;
            double b1=point[0].y-k*point[0].x;
            double b2=point[2].y-k*point[2].x;
            height=fabs(b1-b2)/sqrt(1+k*k);
        }
        return height>eps;
    }
    double Area(){
        return (topline+baseline)*height/2;
    }
    double height,topline,baseline;
    Trapezoid(Point point[]){
        if(!check(point)){
            cout<<"Wrong parameter"<<endl;
        }
        p=new Point[4];
        for(int i=0;i<4;i++){
            p[i]=point[i];
        }
        topline=sqrt(dis2(point[0],point[1]));
        baseline=sqrt(dis2(point[2],point[3]));
    }
    ~Trapezoid(){
        delete[] p;
    }
};
int main()
{
    Shape *p[5];
    //圆心和半径
    Point circlePoint(0.0,0.0);
    double radius=5.5;
    //长方形
    Point rectVertex[4]={{0.0,0.0},{1.0,0.0},{1.0,2.0},{0.0,2.0}};
    //正方形
    Point squVertex[4]={{0.0,0.0},{4.8,3.6},{1.2,8.4},{-3.6,4.8}};
    //三角形
    Point triVertex[3]={{0.0,0.0},{4.6,8.9},{-4.3,4.2}};
    //梯形
    Point traVertex[4]={{0.0,0.0},{5.0,0.0},{1.0,7.0},{9.0,7.0}};
    //Circle cir()
    Circle cir(circlePoint,radius);
    Rectangle rect(rectVertex);
    Square squ(squVertex);
    Triangle tri(triVertex);
    Trapezoid tra(traVertex);

    //调用各种派生类
    p[0]=&cir;
    p[1]=&rect;
    p[2]=&squ;
    p[3]=&tri;
    p[4]=&tra;

    double sumArea=0;
    for(int i=0;i<4;i++){
        sumArea+=p[i]->Area();
    }
    cout << sumArea << endl;
    return 0;
}

运行结果

运行结果

结语

本次实验的重点在于类之间的继承和组合，以及对于纯虚函数的应用和类的成员函数的重复利用。
花在这份代码的时间其实大部分在构思如何判断形状。