Do rotation, reflection, scaling, and shearing cover all possible 3D linear transformations? In other words, is it the case that every real 3x3 matrix can be decomposed into the product of the 5 transformations?
I see slide 27 on SVD shows that scaling, reflection and rotation are the most irreducible pieces.
bcagan
Obviously the more individual transformations you apply, the more computationally expensive it is going to become. If the transformations are all combined into a single matrix, if some of the transformations were dependent of a variable, I would assume that this would still be more expensive than a single constant transformation matrix right? (For instance, all three of these transformations are dependent on t).
Do rotation, reflection, scaling, and shearing cover all possible 3D linear transformations? In other words, is it the case that every real 3x3 matrix can be decomposed into the product of the 5 transformations?
I see slide 27 on SVD shows that scaling, reflection and rotation are the most irreducible pieces.
Obviously the more individual transformations you apply, the more computationally expensive it is going to become. If the transformations are all combined into a single matrix, if some of the transformations were dependent of a variable, I would assume that this would still be more expensive than a single constant transformation matrix right? (For instance, all three of these transformations are dependent on t).