Author Topic: Matrices for Tech Artists  (Read 2388 times)

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Matrices for Tech Artists
« on: December 09, 2019, 01:53:13 PM »
Matrices used to be black magic to me. This year, I started working through every page and every problem in Introduction to Linear Algbera by Strang. A book which I highly recommend. It made me see the bigger picture of matrices and Linear Algebra. Having learned alot, now I am convinced that Morpheus was right. “Nobody can be told what the matrix is, you have to see it for yourself.” No wonder I had such a hard time following matrices before, there are way more to matrices than their multiplication rules.

Having learned so much, I am also convinced that, specially for tech art, you can use matrices with a sense of direction, without needing to spend hundard of hours mastering linear Algebra (although I strongly recommend that). There is something there between the two extremes of being lost every time you see MVP in vertex shader, and manipulating n dimensional spaces like a god. In graphics, we mostly transform three dimensional vectors using 3x3 matrices (let’s ignore homogeneous coordinates for now). We can intuitively think about 3 dimensional spaces and which properties they have, because it matches the world we live in. Hence we can view matrices with regards to the space spanned by its columns (more on that below). This is not that easy to do, if you are dealing with a 100 in 100 matrix, which is not that uncommon in other fields. Another advantage of graphics is, we mostly deal with square matrices with linearly Independent columns, that makes it easy again to view them just in terms of their column space and not worry about the other subspaces of the matrix such as its left null space.