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if I do positionVector*worldMatrix the position is transformed into world space. But what happens if I do it the other way around (worldMatrix*positionVector) in terms of 3d space?
I noticed the result is different to the first one. I already googled about matrix, math they explain a lot but not this one, at least I couldn’t find it.
As others have indicated – swapping the order of the multiplication is equivalent to multiplying by the transpose. As it happens, rotation matrices are a special type of matrices known as orthogonal matrices this gets you a number of neat properties.
The most interesting is probably that the transpose of the matrix is its inverse. For your world transform multiplying by the inverse is equivalent to taking a position in world space and pulling it into the local coordinates of the object that transform is associated with.
As an example, consider a box oriented arbitrarily in the world – multiplying by the inverse world transform could (entirely application dependant of course :)) put you in a space where it is axis aligned, and if you were interested in looking for collisions with other objects doing the calculations in the box’s local space would make this easier.