$3$D input file concept: Modify CubePers.java $($page $146$ of the textbook$),$ so that it reads in a data file $$cube$.$dat$($instead of hardcoding in the program$)$ and displays the cube in perspective as output. You may run the program by typing the following: java CubePers cube.dat $```$

$//$ CubePers.java: A cube in perspective.

$//$ Uses: Point$2$D $($Section $1\mathrm{.}4),$ Point$3$D $($Section $3\mathrm{.}9).$

import java.awt.$*$;

import java.awt.event.$*$;

public class CubePers extends Frame $\{$

public static void main$($String$[]$ args$)\{$new CubePers$()$;$\}$

CubePers$()\{$

super$("$A cube in perspective"$)$;

addwindowListener$($new WindowAdapter$()\{$

public voidwindowClosing$($WindowEvent e$)\{$System$.$exit$(0)$;$\}$

$))$;

$``````$

setLayout $($new BorderLayout$())$ ;

add $("$Center$",$ new CvCubePers$())$;

Dimension dim $=$ getToolkit$().$getScreenSize$()$;

setSize$($dim$.$width $/2,$ dim.height $/2)$;

setLocation$($dim$.$width $/4,$ dim.height $/4)$;

setVisible$($true$)$;

$\}$

$\}$

class CvCubePers extends Canvas $($

int centerX, centerY;

Obj obj $=$ new Obj $(\}$ ;

int iX$($float x$)\{$

return Math.round$($centerX $+$ x$)$;

$\}$

int iY$($float y$)\{$

return Math.round$($centerY $-$ y$)$;

$\}$

void line$($Graphics g$,$ int i$,$ int j$)\{$

Point$2$D p $=$ obj.vScr$[$i$],$ q $=$ obj.vScr$[$j$]$;

g$.$drawLine$($iX$($p$.$x$),$ iY$($p$.$y$),$ iX$($q$.$x$),$ iY$($q$.$y$))$;

$\}$

public void paint$($Graphics g$)\{$

Dimension dim $=$ getSize$()$;

int maxX $=$ dim.width $=1,$ maxY $=$ dim.height $-1,$

minMaxXY $=$ Math.min$($maxX$,$ maxY$)$;

centerX $=$ maxX $/2$; centerY $=$ maxY $/2$;

obj.d $=$ obj.rho $*$ minMaxXY $/$ obj.objSize;

obj.eyeAndScreen $\{)$;

$//$ Horizontal edges at the bottom:

line$($g$,0,1)$; line$($g$,1,2)$; line$($g$,2,3)$; line$($g$,3,0)$;

$//$ Horizontal edges at the top:

line$($g$,4,5)$; line$($g$,5,6)$; line$($g$,6,7)$; line$($g$,7,4)$;

$//$ Vertical edges:

line$($g$,0,4)$; line$($g$,1,5)$; line$($g$,2,6)$; line$($g$,3,7)$;

$)$

$\}$

$``````$

class Obj $(//$ Contains $3$D object data

float rho, theta $=0\mathrm{.}3$F$,$ phi $=1\mathrm{.}3$F$,$ d$,$ objSize,

v$11,$ v$12,$ v$13,$ v$21,$ v$22,$ v$23,$ v$32,$ v$33,$ v$43$;

$//$ Elements of viewing matrix V

Point$3$D$[]$ w; $//$ World coordinates

Point$2$D$[$l vScr; $//$ Screen coordinates

Obj$()\{$

w $=$ new Point$3$D$[8]$;

vScr $=$ new Point$2$D$[8]$;

$//$ Bottom surface:

w$[0]=$ new Point$3$D$(1,-1,-1)$;

w$[1]=$ new Point$3$D$(1,1,-1)$;

w$[2]=$ new Point$3$D$(-1,1,-1)$;

w$[3]=$ new Point$3$D$(-1,-1,-1)$;

$//$ Top surface:

w$[4]=$ new Point$3$D$(1,-1,1)$;

w$[5]=$ new Point$3$D$(1,1,1)$;

w$[6]=$ new Point$3$D$(-1,1,1)$;

w$[7]=$ new Point$3$D$(-1,-1,1)$;

objSize $=($float$)$ Math.sqrt$(12$F$)$;

$//=$ sqrt$(2*2+2*2+2*2)$

$//=$ distance between two opposite vertices.

rho $=5*$ objSize; $//$ For reasonable perspective effect

$\}$

void initPersp$()\{$

float costh $=($float$)$ Math.cos$($theta$),$

sinth $=($float$)$ Math.sin$($theta$),$

cosph $=($float$)$ Math.cos$($phi$),$

sinph $=($float$)$ Math.sin$($phi$)$;

v$11=-$sinth; v$12=-$cosph $*$ costh; v$13=$ sinph $*$ costh;

v$21=$ costh; v$22=-$cosph $*$ sinth; v$23=$ sinph $*$ sinth;

v$32=$ sinph; v$33=$ cosph;

v$43=-$rho;

$)$

void eyeAndScreen$()\{$

initPersp$()$;

for $($int i $=0$; i $<mtext></mtext><mn>8</mn>$; i$++)\{$

Point$3$D p $=$ w$[$i$]$;

float x $=$ v$11*$ p$.$x $+$ v$21*$ p$.$y$,$

y $=$ v$12*$ p$.$x $+$ v$22*$ p$.$y $+$ v$32*$ p$.$z$,$

z $=$ v$13*$ p$.$x $+$ v$23*$ p$.$y $+$ v$33*$ p$.$z $+$ v$43$;

$``````$

vScr$[$i$]=$ new Point$2$D$(-$d $*$ x $/$ z$,-$d $*$ y $/$ z$)$;

$\}$

$\}$

$\}$

$```$