Assignment $03-$ Due on$(10)/(14)()/(24),11\mathrm{.}59$pm

Question $1$

Write a java program that achieves the rotation of a unit cube about an arbitrary

fixed point $($page $79-$ first special case of $3$D rotation$).$ Produce only text output for

this program $($similar to Rota$3$DTest demo program shown in class$).$ Output should

display the desired angle of rotation, principle axis of rotation, and the arbitrary

point used for rotating the unit cube. Output should also display the vertices of the

unit cube along with their co$-$ordinate values before and after the $3$D rotation.

The program should take $5$ command$-$line arguments for the three customizable

parameters $-$ arbitrary point A $($a$1,$ a$2,$ a$3),$ desired angle of rotation alpha, and the

principle axis of rotation $($x$\_($a$)$xis$,$ y$\_($a$)$xis$,$ or z$\_($a$)$xis$).$ In other words, after compiling

your program, you may run it by typing the following as an example:

java Rota$3$DCube $22245$ y$\_($a$)$xis

where a$1=2,$a$2=2,$a$3=2,$ alpha $=45$ degrees, and y$\_($a$)\backslash$xi s is the principle axis

of rotation.

Note:

The initial vertices of the cube before rotation should be $-$

$,$

$[0,1,1],[1,1,1],[1,1,0],[0,1,0]$

Name the main java file as Rota$3$DCube.java

SAMPLE OUTPUT FOR QUESTION $1$

a$)$ Rotation of unit cube about arbitrary point $(2,2,2)$ by $45$ degrees, x$\_(-)$axis is the principle axis of

rotation

C:$\backslash$Users$\backslash$pkumar$\backslash$Documents$\backslash$UTD$\backslash$CS$4361\_1\backslash$grjava$3$e$>$java Rota$3$DCube $22245$ x$\_$axis

Rotate unit cube $0\mathrm{.}785398$ radians about x$-$axis at point $(2\mathrm{.}000000,2\mathrm{.}000000,2\mathrm{.}000000)$

Initial Vertices Rotated Vertices

$0$: $0\mathrm{.}0000000\mathrm{.}0000000\mathrm{.}0000000\mathrm{.}0000002\mathrm{.}000000-0\mathrm{.}828427$

$1$: $1\mathrm{.}0000000\mathrm{.}0000000\mathrm{.}0000001\mathrm{.}0000002\mathrm{.}000000-0\mathrm{.}828427$

$2$: $1\mathrm{.}0000000\mathrm{.}0000001\mathrm{.}0000001\mathrm{.}0000001\mathrm{.}292893-0\mathrm{.}121320$

$3$: $0\mathrm{.}0000000\mathrm{.}0000001\mathrm{.}0000000\mathrm{.}0000001\mathrm{.}292893-0\mathrm{.}121320$

$4$: $0\mathrm{.}0000001\mathrm{.}0000001\mathrm{.}0000000\mathrm{.}0000002\mathrm{.}0000000\mathrm{.}585786$

$5$: $1\mathrm{.}0000001\mathrm{.}0000001\mathrm{.}0000001\mathrm{.}0000002\mathrm{.}0000000\mathrm{.}585786$

$6$: $1\mathrm{.}0000001\mathrm{.}0000000\mathrm{.}0000001\mathrm{.}0000002\mathrm{.}707107-0\mathrm{.}121320$

$7$: $0\mathrm{.}0000001\mathrm{.}0000000\mathrm{.}0000000\mathrm{.}0000002\mathrm{.}707107-0\mathrm{.}121320$

b$)$ Rotation of unit cube about arbitrary point $(2,2,2)$ by $45$ degrees, y$\_(-)$axis is the principle axis of

rotation

C:$\backslash$Users$\backslash$pkumar$\backslash$Documents$\backslash$UTD$\backslash$CS$4361\_1\backslash$grjava$3$e$>$java Rota$3$DCube $22245$ y$\_$axis

Rotate unit cube $0\mathrm{.}785398$ radians about y$-$axis at point $(2\mathrm{.}000000,2\mathrm{.}000000,2\mathrm{.}000000)$

Initial Vertices Rotated Vertices

$0$: $0\mathrm{.}0000000\mathrm{.}0000000\mathrm{.}000000-0\mathrm{.}8284270\mathrm{.}0000002\mathrm{.}000000$

$1$: $1\mathrm{.}0000000\mathrm{.}0000000\mathrm{.}000000-0\mathrm{.}1213200\mathrm{.}0000001\mathrm{.}292893$

$2$: $1\mathrm{.}0000000\mathrm{.}0000001\mathrm{.}0000000\mathrm{.}5857860\mathrm{.}0000002\mathrm{.}000000$

$3$: $0\mathrm{.}0000000\mathrm{.}0000001\mathrm{.}000000--0\mathrm{.}1213200\mathrm{.}0000002\mathrm{.}707107$

$4$: $0\mathrm{.}0000001\mathrm{.}0000001\mathrm{.}000000--0\mathrm{.}1213201\mathrm{.}0000002\mathrm{.}707107$

$5$: $1\mathrm{.}0000001\mathrm{.}0000001\mathrm{.}0000000\mathrm{.}5857861\mathrm{.}0000002\mathrm{.}000000$

$6$: $1\mathrm{.}0000001\mathrm{.}0000000\mathrm{.}000000-0\mathrm{.}1213201\mathrm{.}0000001\mathrm{.}292893$

$7$: $0\mathrm{.}0000001\mathrm{.}0000000\mathrm{.}000000--0\mathrm{.}8284271\mathrm{.}0000002\mathrm{.}000000$

c$)$ Rotation of unit cube about arbitrary point $(2,2,2)$ by $45$ degrees, z$\_$axis is the principle axis of

rotation

C:$\backslash$Users$\backslash$pkumar$\backslash$Documents$\backslash$UTD$\backslash$CS$4361\_1\backslash$grjava$3$e$>$java Rota$3$DCube $22245$ z$\_$axis

Rotate unit cube $0\mathrm{.}785398$ radians about z$-$axis at point $(2\mathrm{.}000000,2\mathrm{.}000000,2\mathrm{.}000000)$

Initial Vertices Rotated Vertices

$0$: $0\mathrm{.}0000000\mathrm{.}0000000\mathrm{.}0000002\mathrm{.}000000-0\mathrm{.}8284270\mathrm{.}000000$

$1$: $1\mathrm{.}0000000\mathrm{.}0000000\mathrm{.}0000002\mathrm{.}707107-0\mathrm{.}1213200\mathrm{.}000000$

$2$: $1\mathrm{.}0000000\mathrm{.}0000001\mathrm{.}0000002\mathrm{.}707107-0\mathrm{.}1213201\mathrm{.}000000$

$3$: