code these in java... Face.java

This class represents a single face of a cube in $3$ dimensional Cartesian space. $($A square$)$ A Square is comprised of $2$ Triangles that share $2$ Vertices $($Points$)$ and have identical "Surface Normals" $($their UnitVectors point the same direction$).$

Fields

Field Name

Type

Access Modifier

Description

mesh

Triangle$[]$

private

An array of Triangles that combine to make this Face $($a bounded square$).$

surfaceNormal

UnitVector

private

The the surface normal of this Face.

Constructor

Access Modifier

Constructor Name

Input Parameters

Description

public

Face

Triangle one,

Triangle two,

If triangle one and two share two common vertices and their surface normals are equal. Construct a newly allocated Face object and instantiate the fields to their respective parameters. Triangle one should be index $0$ of mesh.

If the two triangles do not share at least two vertices or the surface normals are not equal then each triangle should be set to Triangle$()$ and the unit vector set to invalid $($all fields $0\mathrm{.}000).$

public

Face

none

Construct a newly allocated Face object and instantiate the fields as follows: each triangle should be set to Triangle$()$ and the unit vector set to invalid $($all fields $0\mathrm{.}000).($The face is invalid$)$

Methods

Method Name

Return Type

Access Modifier

Input Parameters

Description

getMesh

Triangle$[]$

public

None

Returns the Triangle array that makes up the mesh of this Face.

getSurfaceNormal

UnitVector

public

None

Returns the UnitVector representing the surfaceNormal of this Face.

flipSurfaceNormal

void

public

None

Flips the direction of the Surface Normal of this Face, and all of its Triangles.

compareTo

boolean

public

Face face

Compares this Face to face. Return true if the Triangles share the same vertices and normal vectors. 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.

isSimilar

boolean

public

Face face

Compares this Face to face. Returns true if the triangles share the same vertices $($in any order$)$ OR have the same normal vectors. Otherwise return false.

toString

String

public

None

Returns the String representation of this Triangle.

For Example, given the following fields:

Triangle$[0]$:

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

vertexB$=($x$1\mathrm{.}000,$ y$-1\mathrm{.}000,$ z$1\mathrm{.}000)$

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

surfaceNormal $=<0\mathrm{.}000$i$,0\mathrm{.}000$j$,1\mathrm{.}000$k$>$

Triangle$[1]$:

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

vertexB$=($x$0\mathrm{.}000,$ y$-1\mathrm{.}000,$ z$1\mathrm{.}000)$

vertexC$=($x$1\mathrm{.}000,$ y$-1\mathrm{.}000,$ z$1\mathrm{.}000)$

surfaceNormal $=<0\mathrm{.}000$i$,0\mathrm{.}000$j$,1\mathrm{.}000$k$>$

surfaceNormal $=<0\mathrm{.}000$i$,0\mathrm{.}000$j$,1\mathrm{.}000$k$>$

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

$\{$F$[$A$($x$0\mathrm{.}000,$ y$0\mathrm{.}000,$ z$1\mathrm{.}000)$; B$($x$1\mathrm{.}000,$ y$-1\mathrm{.}000,$ z$1\mathrm{.}000)$; C$($x$1\mathrm{.}000,$ y$0\mathrm{.}000,$ z$1\mathrm{.}000)][$A$($x$0\mathrm{.}000,$ y$0\mathrm{.}000,$ z$1\mathrm{.}000)$; B$($x$0\mathrm{.}000,$ y$-1\mathrm{.}000,$ z$1\mathrm{.}000)$; C$($x$1\mathrm{.}000,$ y$-1\mathrm{.}000,$ z$1\mathrm{.}000)]$ N$<0\mathrm{.}000$i$,0\mathrm{.}000$j$,1\mathrm{.}000$k$>\}$

Note: The surface normal for the triangles are not printed, only the one for the face.

Note: This is one continuous string with no new line characters.

If any Triangle is invalid the result of toString$()$ should be:

$\{$InvalidFace$\}$

Cube.java

This class represents a Square in $3$ dimensional Cartesian space. A Cube is comprised of $6$ Faces $($squares$)$ where each face shares an edge $($has $2$ common vertices$)$ with $4$ other faces and faces that do not share an edge have opposite surface normal vectors $($One face has the inverse UnitVector of the other$).$

Fields

Field Name

Type

Access Modifier

Description

mesh

Face$[]$

private

An array of Faces that make up the mesh of the Cube.

Constructor

Access Modifier

Constructor Name

Input Parameters

Description

public

Cube

Face one,

Face two,

Face three,

Face four,

Face five,

Face six

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

Confirm that each face shares exactly one edge with each of $4$ other faces. Confirm that no face is the same as another face. Confirm that each surfaceNormal of opposed Faces $($faces that do not share an edge$)$ is pointing in an opposite direction.

If any of the above is false, set each face in mesh to be an invalid face. $($all fields $0\mathrm{.}000).$

Note: mesh$[0]$ should be instantiated to Face one and so on to mesh$[5]$ being Face six.

public

Cube

none

Construct a newly allocated Cube object and instantiate each Face in the mesh array to be invalid, all values are $0\mathrm{.}000.$

Methods

Method Name

Return Type

Access Modifier

Input Parameters

Description

getMesh

Face$[]$

public

None

Returns the Face array representing the entire surface mesh of the Cube.

toString

String

public

None

Returns the String representation of this Cube.

The output should be in the format of:

$"|$C$"+$ the toString$()$ of each face. $+"|"$