Mumbai university > mechanical engineering > sem 7 > cad/cam/cae

Marks: 10 M

Year: May 2014

Difficulty: Medium

Steps:

1. Translate Point P(3,2) to origin O(0,0)
2. Rotate the object by
3. Inverse translation of Point P to its original position P(3,2) from origin O(0,0)

Step 1:

Translation Matrix is given as:

Step 2:

Note: CCw is taken as +ve angle and CW is taken as –ve angle. Rotation Matrix is given as,

Step 3 :

Now,

i. The composite Transformation Matrix / Affine Matrix

ii. The new coordinates of rectangle

[X'] = [X] [T]

A' = A

B' = B

C' = C

D' = D

[T] =

Hence, new coordinates of rectangle are :

A' = (1.77, 0.136)

B' = (2.36, 0.636)

C' = (1.63, 2.368)

D' = (0.77, 1.868)