PDA

View Full Version : Transformation Matrix

praveent
03-26-2001, 10:04 PM
hi,
Can anyone help me out abt how to find present location of origin after a no. of transformations ??
Even specific components in 4x4 transformation matrix
Praveen

john
03-27-2001, 04:06 AM
Hello,

i'm sure this has been discuessed before. the simple answer is: check out the fourth column for the position transform. the other transforms (scale and rotation) aren't as easy to rip out.

think about how to work out the position from a transform matrix. You have some matrix which relocates the origin to another point in space. So, where is this new point? well... you can just track the origin vector by M*0 (where M is the transform matrix and 0 is [0 0 0 1]' origin vector). if you do the maths by hand, you'll see that you're nullifying every element in M *except the last row*. ergo, the last row has the translation stuff.

to find out the new orientation, you just need to transform the basis of the origin space. ie. you have a set of vectors [1 0 0 1]', [0 1 0 1] ' and [0 0 1 1]' (a basis of the original coordinate space) and transform each by M like above. this will give you your new basis.

hope this helps,
John