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.

 

you may want to try some youtube videos...

 

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.

 

Here is the translation matrix operation:

What is it that you do not understand?

 

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.

 

They have interchanged the rows and columns.
Data points are written a (x y z 1). Hence they have transposed the two matrices.

 

Hi,

Data points are written a (x y z 1). Hence they have transposed the two matrices.

My friend I cant understand the reason behind the transpose. Kindly tell me the reason for the transpose.

Zuli.

 

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.