In second assignment you have derived Homogeneous Transformations for the Table and Triangle problems. Now plot the homogeneous transformations and verify for the Question $2,$ triangle problem in MATLAB. Reference code:

$|$H$4$x$4$ Transforms

clear all;

close all;

win $=[\{$:$[-2,1,-1,3,-1,4]$:$\}]$;$\%\%$ Plotiing WIndow

$\%$ Global Refrence Frame F$0$

H$0=$ eye$(4)$;

trplot$($H$0,$ 'color', $\text{'}$k$\text{'},$ 'length', $1,$ 'arrow', 'frame', $\text{'}0\text{'},$ 'axis', win$)$

view$(100,30),$ hold on

$\%$ Second frame F$1$

H$01=$ H$0*$ transl$(0,1,1)$;

trplot$($H$01,$ 'color', $\text{'}$b$\text{'},$ 'length', $1,$ 'arrow', 'frame', $\text{'}1\text{'})$

$\%$ Thrid frame F$2$

H$02=$ H$01*$ transl$(-0\mathrm{.}5,0\mathrm{.}5,0)$;

trplot$($H$02,$ 'color', $\text{'}$m$\text{'},$ 'length', $1,$ 'arrow', 'frame', $\text{'}2\text{'})$

$\%$ Camera frame F$3$

H$23=$ transl$(0,0,2)*$ troty$($pi$)*$ trotz$($pi$/2)$;

H$03=$ H$02*$ H$23$

trplot$($H$03,$ 'color', $\text{'}$c$\text{'},$ 'length', $1,$ 'arrow', 'frame', $\text{'}3\text{'})$

hold off;

Consider the diagram, Find the homogeneous transformations

Consider the diagram, Find the homogeneous transformations H$01,$H$02,$H$12$ representing

the transformations among the three frames shown. Show that H$02=$ H$01*$ H$12.(10$ Points$)$

Extra Credit $(5$ Points$)$

Try to develop a homogeneous transform H$\_(2)^(1)$ from frame $1$ to frame $2,$ by translating along

the hypotenuse of the right triangle shown in the figure.

Hint: Step I$-$Align an axis of your choice such that it is collinear with the hypotenuse

Step $2-$ Translate along the hypotenuse

Step $3-$ Undo Step $1($advisable but not necessary$)$

Step $4-$ Align frames $1$ and $2.$