Write the Cube class without using gpt:

Instructions

Follow the instructions below for each class.

Point.java

This class represents a point in $3$ dimensional Cartesian space.

Fields

Field Name

Type

Access Modifier

Description

x

double

private

The x coordinate in Cartesian space

y

double

private

The y coordinate in Cartesian space

z

double

private

The z coordinate in Cartesian space

Constructor

Access Modifier

Constructor Name

Input Parameters

Description

public

Point

double x$,$

double y$,$

double z

Construct a newly allocated Point object and instantiate the fields to their respective parameters.

public

Point

None

Construct a newly allocated Point object and instantiate all fields set to $0\mathrm{.}0.$

Methods

Method Name

Return Type

Access Modifier

Input Parameters

Description

getX

double

public

none

Returns the x value of this Point.

getY

double

public

none

Returns the y value of this Point.

getZ

double

public

none

Returns the z value of this Point.

setX

void

public

double x

Sets the x value of this Point

setY

void

public

double y

Sets the y value of this Point

setZ

void

public

double z

Sets the z value of this Point

compareTo

boolean

public

Point point

Compares this Point to point. Return true if the Points are equal. For this assignment double variables are considered equal if they are within $+/-0\mathrm{.}0001$ precision of each other, see note at the end. Otherwise return false.

toString

String

public

None

Returns the String representation of this Point.

For Example, given the following fields:

x $=1\mathrm{.}000$

y $=2\mathrm{.}000$

z $=0\mathrm{.}000$

The result of calling toString$()$ would be:

$($x$1\mathrm{.}000,$ y$2\mathrm{.}000,$ z$0\mathrm{.}000)$

Note the returned String should be formatted to EXACTLY $3$ decimal places.

UnitVector.java

This class represents a Unit Vector in $3$ dimensional Cartesian space. A unit vector is a direction with magnitude $1.$

Fields

Field Name

Type

Access Modifier

Description

i

double

private

the i component of a vector in $3$D space

j

double

private

The j component of a vector in $3$D space

k

double

private

The z component of a vector in $3$D space

Constructors:

Access Modifier

Constructor Name

Input Parameters

Description

public

UnitVector

double i$,$

double j$,$

double k

Construct a newly allocated UnitVector object and instantiate the fields to the specified parameters.

Confirm that the magnitude of the UnitVector is equal to $1\mathrm{.}000.$ For this assignment double variables are considered equal if they are within $+/-0\mathrm{.}0001$ precision of each other, see note at the end.

Magnitude$=\backslash$sqrt$\{$i$^\{2\}+$j$^\{2\}+$k$^\{2\}\}$

If the value is not equal to $1\mathrm{.}000$ then scale the vector by its magnitude with the following series of equations:

i$=\backslash$frac$\{$i$\}\{$Magnitude$\}$

j$=\backslash$frac$\{$j$\}\{$Magnitude$\}$

k$=\backslash$frac$\{$k$\}\{$Magnitude$\}$

Note: in the case where the magnitude is equal to $0$ all fields should be initialized to $0\mathrm{.}000.$

public

UnitVector

Point start,

Point end

Construct a newly allocated UnitVector object from the two given points using the following equation:

i $=$ end.x $-$ start.x

j $=$ end.y $-$ start.y

k $=$ end.z $-$ start.z

Confirm that the magnitude of the UnitVector is equal to $1\mathrm{.}000.$ For this assignment double variables are considered equal if they are within $+/-0\mathrm{.}0001$ precision of each other, see note at the end.

Magnitude$=\backslash$sqrt$\{$i$^\{2\}+$j$^\{2\}+$k$^\{2\}\}$

If the value is not equal to $1\mathrm{.}000$ then scale the vector by its magnitude with the following series of equations:

i$=\backslash$frac$\{$i$\}\{$Magnitude$\}$

j$=\backslash$frac$\{$j$\}\{$Magnitude$\}$

k$=\backslash$frac$\{$k$\}\{$Magnitude$\}$

Note: in the case where the magnitude is equal to $0$ all fields should be initialized to $0\mathrm{.}000.$

public

UnitVector

none

Construct a newly allocated UnitVector object with all fields instantiated to $0\mathrm{.}000.($An invalid vector$)$

Methods:

Method Name

Return Type

Access Modifier

Input

Parameters

Description

getI

note: $\text{'}$I$\text{'}$ is a capital $\text{'}$i$\text{'}$

double

public

None

Returns the i value of this UnitVector

getJ

double

public

None

Returns the j value of this UnitVector

getK

double

public

None

Returns the k value of this UnitVector

flipVector

void

public

None

Changes the direction of this UnitVector to be the inverse.

i $=-$i$,$ j $=-$j$,$ and k $=-$k

compareTo

boolean

public

UnitVector vector

Compares this UnitVector to vector. Return true if the UnitVectors are equal. For this assignment double variables are considered equal if they are within $+/-0\mathrm{.}0001$ precision of each other, see note at the end. Otherwise return false.

crossProduct

UnitVector

public

UnitVector b

Returns a newly allocated UnitVector object with fields set by the following equations:

i$=$this.j$*$b$.$k$-$this.k$*$b$.$j

j$=$this.k$*$b$.$i$-$this.i$*$b$.$k

k$=$this.i$*$b$.$j$-$this.j$*$b$.$i

Confirm that the magnitude of the UnitVector is equal to $1\mathrm{.}000.$ For this assignment double variables are considered equal if they are within $+/-0\mathrm{.}0001$ precision of each other, see note at the end.

Magnitude$=\backslash$sqrt$\{$i$^\{2\}+$j$^\{2\}+$k$^\{2\}\}$

If the value is not equal to $1\mathrm{.}000$ then scale the vector by its magnitude with the following series of equations: