# Problem with Translation matrix

Discussion in 'Homework Help' started by zulfi100, Apr 7, 2015.

1. ### zulfi100 Thread Starter Active Member

Jun 7, 2012
386
1
Hi,
I have got a problem related to understanding Translation matrix in the context of 3d Rotation about an arbitrary axis. I have got a question from a website:

The first step is the formation of a translation matrix. Following image illustrates the translation process which involves moving P1 to origin

The translation matrix given in the book is:

However in the solution, they have written translation matrix in the different form and they are also multiplying it by a matrix of P1 and P2. I cant understand this.

Can somebody please guide me?

Zulfi.

2. ### panic mode Senior Member

Oct 10, 2011
1,420
347
you may want to try some youtube videos...

3. ### zulfi100 Thread Starter Active Member

Jun 7, 2012
386
1
Hi,
Thanks for your response. I dont want to try youtube. They are also not accessible from here. I would then use what's given in the book.

Zulfi.

4. ### MrChips Moderator

Oct 2, 2009
14,505
4,271
Here is the translation matrix operation:

What is it that you do not understand?

5. ### zulfi100 Thread Starter Active Member

Jun 7, 2012
386
1
Hi,
In the 4th figure (Post# 1), they have written the Translation matrix as:
1 0 0 0
0 1 0 0
0 0 1 0
-Tx -Ty -Tz 1

instead of the standard form which you have written. I cant understand why we have -Tx -Ty -Tz at the last row (in that figure) instead of being at the last column as you have written.

Kindly guide me.

Zulfi.

6. ### MrChips Moderator

Oct 2, 2009
14,505
4,271
They have interchanged the rows and columns.
Data points are written a (x y z 1). Hence they have transposed the two matrices.

7. ### zulfi100 Thread Starter Active Member

Jun 7, 2012
386
1
Hi,
My friend I cant understand the reason behind the transpose. Kindly tell me the reason for the transpose.

Zuli.

8. ### MrChips Moderator

Oct 2, 2009
14,505
4,271
It depends on how you want to define your object matrix.
The object is defined by a structure of points, lines and planes. Each point has three values (x, y, z) that defines its location in 3-D space.
So you have n values of (x, y, z).
You can define this as n rows of 3 columns or 3 rows of n columns. One is the transpose of the other.