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Are Transform3D's commutative?
(self.godot)
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this post was submitted on 12 Jul 2023
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I likewise don't really use Godot, but for graphics in general, the 4th coordinate is important, even if it is "usually" 1. It's most obvious to correctly interpolate near the poles of a sphere with a single rectangular texture, but think for a minute what "near" means.
Back to the main point though: the important things we normally rely on for matrix math are associativity (particularly, for exponentiation!) and anticommutativity (beware definitions that are sloppy about "inverse").
Who said it isn't? Transformation matrices acting on R^3^ are 4x4 (since transformation matrices acting on R^n^ are of dimension n+1 in general), whether they're full rank or not.