Represent polygons using ordered arrays of points. Each point is itself an array of

doubles, where the doubles represent the coordinates of the point. A point may have varying

numbers of coordinates, depending on how many dimensions the polygon is in$.$ For example, a

$2$D polygon has points with $2$ coordinates $($x$,$ y$),$ a $3$D polygon has points with $3$ coordinates $($x$,$ y$,$

z$)$ and an n$-$dimensional polygon has points with n coordinates $($x$0,$ x$1,$ x$2,...,$ xn$).$

Below is a triangle, which we can consider $2-$dimensional polygon consisting of $3$ points.

A graph of a line with points Description automatically generated

For this $2$D polygon, we have $3$ points, $\{$A$,$ B$,$ C$\}=\{\{2,1\},\{7,1\},\{7,4\}\}.$

The bounding box for this polygon can be represented as $\{\{2,1\},\{7,4\}\}.$

The total length of the lines connecting the points, which we will refer to as the length of the

polygon, is ~$13\mathrm{.}8$ units.

Make the following changes to the file Asso$1.$java and Polygon.java which are given below:

a$.(1$ Mark$)$ Complete the constructor and setter for the Polygon class. These methods should

both accept an array of points and save it to the corresponding field on the Polygon class.

b$.(3$ Marks$)$ Write the code for the calculateDistance$()$ method. This method will accept two

points as input, with each point being represented by a $1-$dimensional array of doubles. You

can calculate the distance between two points using Euclidean Distance.

c$.(3$ Marks$)$ Complete the calculateLength$()$ method. This method will determine the total

length of the polygon if we were to connect each point to the next point in order. Note that

our polygon is considered to be closed. This means that the last point should connect back

to the first point.

d$.(3$ Marks$)$ Write the calculateBoundingBox$()$ method. This method should return an array of

points that can be used to represent the maximum extents of the polygon. A bounding box

for a shape can be determined using only two points. The first point will represent the

minimum coordinates for the polygon in each dimension, while the second point represents

the maximums.

e$.(3$ Marks$)$ Write the code for the append$()$ method. The append method of a Polygon should

accept another Polygon as input. The method will then combine the Polygons together by

adding all of the points from the input polygon to the array of the second polygon.

f$.(3$ Marks$)$ Complete the checkDimensions$()$ method. This method will accept an array of

points as input. The method will then check that there is at least one point in the array, and

that all of the points in the array exist in the same number of dimensions. $($Eg: one array of

points should not have points that are $2$D as well as points that are $3$D$)$ Return true if the

array passes the check.

g$.(2$ Marks$)$ Finally, we are going to add some validation to our class. If a validation ever fails,

an IllegalArgumentException should be thrown. Here are our validation rules:

a$.$ Anywhere that the points field on the Polygon class may be changed, we must check

that all of the points in the array have the same number of dimensions.

b$.$ If we are to append two polygons together, we must ensure the two polygons are in

the same number of dimensions.

c$.$ To calculate the distance between two points, the points must have the same

number of dimensions.

Asso$1.$java :

import java.util.Arrays;

$/**$

$*$ This is a driver class for Assignment $01$

$*$ It will instantiate and run some operations on Polygon objects

$*/$

public class Ass$01$

$\{$

public static void main$($String$[]$ args$)\{$

$//$ A $2$ dimensional square

System.out.println$("$Square:$")$;

double$[][]$ sqPoints $=\{\{0\mathrm{.}0,1\mathrm{.}0\},\{1\mathrm{.}0,1\mathrm{.}0\},\{1\mathrm{.}0,0\mathrm{.}0\},\{0\mathrm{.}0,0\mathrm{.}0\}\}$;

Polygon square $=$ new Polygon$($sqPoints$)$;

System.out.println$("\backslash$tPoints: $"+$ square$)$;

System.out.println$("\backslash$tLength: $"+$ square.calculateLength$())$;

System.out.println$("\backslash$tBounding Box: $"+$ Arrays.deepToString$($square$.$calculateBoundingBox$()))$;

$//$ A $2$ dimensional triangle

System.out.println$("$Triangle:$")$;

double$[][]$ trPoints $=\{\{-1\mathrm{.}0,0\mathrm{.}0\},\{-2\mathrm{.}0,0\mathrm{.}0\},\{-1\mathrm{.}0,1\mathrm{.}0\}\}$;

Polygon triangle $=$ new Polygon$($trPoints$)$;

System.out.println$("\backslash$tPoints: $"+$ triangle$)$;

System.out.println$("\backslash$tLength: $"+$ triangle.calculateLength$())$;

System.out.println$("\backslash$tBounding Box: $"+$ Arrays.deepToString$($triangle$.$calculateBoundingBox$()))$;

$//$ Combine the square and triangle into $12$D poly

System.out.println$("$Square append Triangle:"$)$;

square.append$($triangle$)$;

System.out.println$("\backslash$tPoints: $"+$ square$)$;

System.out.println$("\backslash$tLength: $"+$ square.calculateLength$())$;

System.out.println$("\backslash$tBounding Box: $"+$ Arrays.deepToString$($square$.$calculateBoundingBox$()))$;