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Oh yeah, stuff like that is very common in graphics! I remember a college exercise where I had to prove this by calculating the resulting transformation matrix
by crote 4y ago
Oh yeah, stuff like that is very common in graphics!
I remember a college exercise where I had to prove this by calculating the resulting transformation matrix which would apply these three shears in order and comparing it to the rotation matrix as provided.
Similarly, translation in 2D is the same as shearing in 3D - and translating in 3D is the same as shearing in 4D. That's why a lot of game engines use a 4D matrix for, well, everything: it's a very convenient way to scale, orient, and position an object.
Takes a while to get used to - especially if you have never used matrices before - but they are actually really easy in practice.
- contravariant 4y agoOf course the most important trick matrices have is that you can't just do all of those transformations with them. The matrix product is associative, and the matrix product is the composition of the linear maps, so you can do all those transformations at the same time, or multiple times, in any order.