$($Geometry: find the bounding rectangle$)$ IN C$++$

A bounding rectangle is the minimum rectangle that encloses a set of points in a two$-$dimensional plane, as shown in Figure $11\mathrm{.}9$d$.$ Write a function that returns a bounding rectangle for a set of points in a two$-$dimensional plane, as follows:

const int SIZE $=2$;

Rectangle$2$D getRectangle$($const double points$[][$SIZE$],$ int numberOfPoints$)$;

Write another function that returns a pointer to the bounding rectangle as follows:

Rectangle$2$D$*$ getRectanglePointer$($const double points$[][$SIZE$],$ int numberOfPoints$)$;

The Rectangle$2$D class is defined in Programming Exercise $11\mathrm{.}9.$ When you create a new submission, you'll notice a template code that includes an implementation of the Rectangle$2$D class. Your task is to fill in the missing parts.

THE CODE:

$//$ This exercise uses the Rectangle$2$D class in Exercise $11\mathrm{.}9.$

#ifndef RECTANGLE$2$D$\_$H

#define RECTANGLE$2$D$\_$H

class Rectangle$2$D

$\{$

public:

Rectangle$2$D$()$;

Rectangle$2$D$($double x$,$ double y$,$ double width, double height$)$;

double getX$()$ const;

double getY$()$ const;

double getWidth$()$ const;

double getHeight$()$ const;

$//$ The rest in Exercise $11\mathrm{.}9$ are not used in this exercise. They can be omitted

private:

double x$,$ y; $//$ Center of the rectangle

double width, height;

$\}$;

#endif

Rectangle$2$D::Rectangle$2$D$()$

$\{$

x $=$ y $=0$;

width $=$ height $=1$;

$\}$

Rectangle$2$D::Rectangle$2$D$($double x$,$ double y$,$ double width, double height$)$

$\{$

this$->$x $=$ x;

this$->$y $=$ y;

this$->$width $=$ width;

this$->$height $=$ height;

$\}$

double Rectangle$2$D::getX$()$ const

$\{$

return x;

$\}$

double Rectangle$2$D::getY$()$ const

$\{$

return y;

$\}$

double Rectangle$2$D::getWidth$()$ const

$\{$

return width;

$\}$

double Rectangle$2$D::getHeight$()$ const

$\{$

return height;

$\}$

$//$ MyRectangle$2$D getRectangle$($const double points$[][$SIZE$],$ int numberOfPoints$)$;

const int SIZE $=2$;

double minX$($const double points$[][$SIZE$],$ int numberOfPoints$)$

$\{$

$//$ Return the code to return the minimum y$-$coordinate in points

$\}$

double maxX$($const double points$[][$SIZE$],$ int numberOfPoints$)$

$\{$

$//$ Return the code to return the maximum x$-$coordinate in points

$\}$

double minY$($const double points$[][$SIZE$],$ int numberOfPoints$)$

$\{$

$//$ Return the code to return the minimum y$-$coordinate in points

$\}$

double maxY$($const double points$[][$SIZE$],$ int numberOfPoints$)$

$\{$

$//$ Return the code to return the maximum y$-$coordinate in points

$\}$

Rectangle$2$D$*$ getRectanglePointer$($const double points$[][$SIZE$],$ int numberOfPoints$)$

$\{$

$//$ Write your code to return a point to a Rectangle$2$D object that is the minimum bounding rectangle for the points

$//$ Hint: invoke minX, minY, maxX, and maxY to find the minimum x$,$ y and maximum x$,$ y for the bounding rectangle.

$\}$

Rectangle$2$D getRectangle$($const double points$[][$SIZE$],$ int numberOfPoints$)$

$\{$

$//$ Write your code to return a Rectangle$2$D object that is the minimum bounding rectangle for the points

$//$ Hint: invoke minX, minY, maxX, and maxY to find the minimum x$,$ y and maximum x$,$ y for the bounding rectangle.

$\}$

#include

using namespace std;

int main$()$

$\{$

double points$[5][2]$;

cout $<<$ "Enter five points: $"$;

$//$ Write your code to read five points

Rectangle$2$D boundingRectangle $=$ getRectangle$($points$,5)$;

cout $<<$ "The bounding rectangle's center $("<<$ boundingRectangle.getX$()<<","<<$

boundingRectangle.getY$()<<"),$ width $"<<$ boundingRectangle.getWidth$()<<$

$",$ height $"<<$ boundingRectangle.getHeight$()<<$ endl;

Rectangle$2$D$*$ boundingRectangleP $=$ getRectanglePointer$($points$,5)$;

cout $<<$ "The bounding rectangle's center $("<<$ boundingRectangleP$->$getX$()<<","<<$

boundingRectangleP$->$getY$()<<"),$ width $"<<$ boundingRectangleP$->$getWidth$()<<$

$",$ height $"<<$ boundingRectangleP$->$getHeight$()<<$ endl;

return $0$;

$\}$