Computer Graphics Previous Year Question asked in UGC NET 2021

What is the transformation matrix M that transforms a square in the x-y plane defined by (1, 1) (-1, 1), (-1, -1), (1, -1) to a parallelogram whose corresponding vertices are (2, 1) (0,1) (-2, -1) and (0, -1) ? Following are options below. This is not a homework question.

A. 1 1 0
0 1 0
0 0 1

B. 1 0 0
1 1 0
0 0 1

C. 1 1 1
0 1 0
0 0 1

D. 1 1 0
1 1 0
0 0 1

I can easily find transformation matrix in 2X2 but how 3X3 ? I got confused between Option A and C. How third row and column is added ?

Reply 1

nerak99

13

When dealing in just 2D your Z components are all zero and consequently you just need a matrix that keeps them to zero. Does that help?

Reply 2

rajeshlearns

OP

2

Original post by nerak99

When dealing in just 2D your Z components are all zero and consequently you just need a matrix that keeps them to zero. Does that help?

I did as you said in this solution but got stuck Please see this solution image shared on drive. I could not write matrices here.

https://drive.google.com/file/d/1yk3DitpxrftGl4m2kn3y09RMGijT6Xgg/view?usp=drive_link

Reply 3

nerak99

13

Well, this is probably not the official way of doing this but I used a bit of strategic multiplying with various components and very quickly found a=b, g=h, a=b=1, g=h=0, d=0 and e=1. I can't see why i can't be 0 or indeed anything you like side it only ever multiplies zero in the transformation.
In you answer you have done uM=v. This is wrong, you need to do Mu=v where u and v are the object and image vectors (or matrices if you do all four vectors at once).
So A will work, but the bottom RH element does not need to be one (in my opinion)

Reply 4

rajeshlearns

OP

2

Original post by nerak99

Well, this is probably not the official way of doing this but I used a bit of strategic multiplying with various components and very quickly found a=b, g=h, a=b=1, g=h=0, d=0 and e=1. I can't see why i can't be 0 or indeed anything you like side it only ever multiplies zero in the transformation.
In you answer you have done uM=v. This is wrong, you need to do Mu=v where u and v are the object and image vectors (or matrices if you do all four vectors at once).
So A will work, but the bottom RH element does not need to be one (in my opinion)

I studied about Homogeneous Coordinates and then it was easy to understand and solve this. Thanks for getting involved in the discussion.

Computer Graphics Previous Year Question asked in UGC NET 2021

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you