View Full Version : hierarchy transformation

05 May 2005, 07:31 PM
hmm could any of you guys please point me to somewhere i could learm how to do hierarchy 2d transformation. i doing some test and i want to being able so that i have a parent layer and a child layer. and i want it to behave like when you parent any object in 3d space. if you rotate the parent the child rotates as well as move. i been looking but all i found in the transformation matrix. i kinda underteand how that works but now how do the calculate the inharited movement

05 May 2005, 10:25 AM
The transformation for the child is the result of the concatenation of the parent's transform matrix and the child's transform matrix.

A good way to lay it out is


Then the transform for Object2 is Transform1 X Transform2

05 May 2005, 08:04 AM
You should look up "scenegraph" in google for that.
As posted above it's quite simple. You can describe every scale, rotation, translation (movement) and shearing as Matrix. In 2D that would be 3x3 Matrixes, in 3D that would be 4x4. You should use homogene (hope that's the same as in german =) coordinates (for 2D that's 2 coordinates + one which's value is always 1) because otherwise translations won't work. Also be aware that matrix-multiplication is not commutative, meaning that M1 * M2 is NOT M2 * M1 and that vec1 * M1 is NOT M1 * vec1 (but Transpose(M1) * vec1 is).
You can look the details up on mathworld ( if you like.

The 2D matrixes are only slightly different from 3D, e.g. Translation:

1 0 0 x
0 1 0 y
0 0 1 z
0 0 0 1

1 0 x
0 1 y
0 0 1

That's for matrix * vector with the vector being one column (a vector is a matrix with one column and 3 rows in that case - again - see mathworld for details).
Ok - now for concatenations.
You can describe ANY movement bei a series of matrix-multiplications - but - as I said - the order is significant. E.g. you are always rotating around the center (0,0) now imagine a square around 0,0, translate that by 10 to the right and now rotate 45 degrees -> your square will be (roughly) 3 to the right and 3 to the top.
BUT - if you rotate first you will have a square, rotated by 45 degress 10 to the right.

So what's helping you there? Quite simple. You can see the matrix-multiplications as a stack, meaning you can put a matrix on top AND remove one from the top. That screams "recursion" =)

So a little example: two platforms, one with an object on top and one without. I put in a world transformation matrix for better understanding. Each matrix here can be a concatenation of different matrixes too, e.g. M_translation * M_rotation = M_pa.
You would put each of that Matrixes on the stack, too.

Platform A Translation:
M_world * M_pa * platformSprite

Object Translation
M_world * M_pa * M_obj * object

Platform B Translation
M_world * M_pb * platformSprite

You can now see that as a tree

+-- M_pa
| +--- platform
| +--- M_obj
| +---- object
+-- M_pb
+--- platform

If you see that as a stack that would be the following operations:

calculate complete Stack and paint platform
calculate complete Stack and paint object
pop() <-- returning to M_pa
pop() <-- returning to M_world
calculate complete Stack and paint platform

See the beauty? =)

For further readings I would suggest searching or the Book "Peter Shirley: Fundamentals of Computer Graphics".

CGTalk Moderation
05 May 2005, 08:05 AM
This thread has been automatically closed as it remained inactive for 12 months. If you wish to continue the discussion, please create a new thread in the appropriate forum.