Transformation Matrix

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


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,