Problem with Translation matrix

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

  1. zulfi100

    Thread Starter Member

    Jun 7, 2012
    320
    0
    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:
    example 3d rotation about an arbitrary axis.png
    The first step is the formation of a translation matrix. Following image illustrates the translation process which involves moving P1 to origin
    Translation Image_Arbitrary Axis.png
    The translation matrix given in the book is:
    3d translation matrix.png
    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.
    sol of example AA_translation.png
    Can somebody please guide me?

    Zulfi.
     
  2. panic mode

    Senior Member

    Oct 10, 2011
    1,320
    304
    you may want to try some youtube videos...
     
  3. zulfi100

    Thread Starter Member

    Jun 7, 2012
    320
    0
    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
    12,440
    3,361
    Here is the translation matrix operation:

    [​IMG]

    What is it that you do not understand?
     
  5. zulfi100

    Thread Starter Member

    Jun 7, 2012
    320
    0
    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
    12,440
    3,361
    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 Member

    Jun 7, 2012
    320
    0
    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
    12,440
    3,361
    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.
     
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