Transform matrix: What properties does my matrix need to ensure that the vectors it transforms always remain in the range [0-1]?

This one is a bit tricky. You're trying to constrain your color vectors to the positive octant of a cube, centered on the origin. Here's a sketch of the problem in 2-D: A simple rotation matrix would quickly swing the (1,1) color vector out of the allowed "blue" zone.

Not to mention that it could also push vectors out of the positive quadrant all together. So one idea would be transforming your cube-shaped space to a spherical one, doing the transformation there, and then back-transforming. This transformation is (obviously!) nonlinear.

Some ideas on how to do this can be found here: blog post. Once you're constraining to a sphere instead, things get a little simpler. Compute the eigenvalues of your transform matrix.

Any values greater than one mean that the color vector can grow arbitrary large, so those matrices are out. All of them equal to one means that the vector magnitude will stay the same, regardless of how many times you compose the matrix.(Limited by numerical precision on your computer). All less than one means that your color vector will eventually collapse to (0,0).

Now you still need to prevent any vector component from going negative. I think you can enforce this by having all eigenvalues be non-negative.So in summary, a positive definite matrix with an induced matrix norm of I suggest posting a new question looking for the best technique, rather than trying to hack your given technique in to working.Still... this was a fun thought exercise.

This is a great answer, thanks! I also just thought about using the sphere inside the positive octant, scaling/translating until it is a unit sphere, performing a transformation which is guaranteed to remain within the unit sphere (much easier than for the positive octant), and translate/scale back. It would cut out all of the corners (so all white and all black would be out, as well as the primaries and secondary mixes), but that is not so bad possibly.

– kaleidomedallion Sep 22 at 8:16.

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.