1) Uniform scaling with a factor of 2 in XY plane.

2) Non uniform scaling with a factor of 2 and 1.5 in X and Y directions, while anchoring point (1,1)

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

Marks : 8M

Difficulty : Easy

i. Uniform Scaling with a factor of 2 in xy plane and anchoring point (1, 1)

Step 1: Transformation of Point A (1, 1) to origin O (0, 0).

Translation Matrix is given as:

Step 2: Uniform Scaling with a factor of 2 in xy plane

Step 3: Inverse translation of Point P from origin to its original position.

Translation Matrix is:

Now, combined Transformation matrix is

Now, new resultant coordinates of square are: [X'] = [X] [T]

Hence,

A' = (1,1)

B' = (3, 1)

C' = (3, 2)

D' = (1, 3)

ii. Non uniform scaling with a factor of 2 and 1.5 in x and y directions, while anchoring Point (1,1)

Step 1: Translation of Point P(1,1) to origin O(0,0)

Translation Matrix is given as:

Step 2: Non-Uniform Scaling

Step 3: Inverse translation of Point P from origin to its original position.

Translation Matrix is:

Now, combine Transformation Matrix is

Now, new resultant coordinates of square are: [X'] = [X] [T]

Hence,

A' = (1, 1)

B' = (3, 1)

C' = (3, 2.5)

D' = (1,2.5)