You can do rotations and translations "via linear algebra" without homogeneous coordinates (the 4-element tuple representing a 3d point or vector), since adding two vectors is linear algebra.
What this lets you do is composing multiple transforms into one matrix multiplication instead of a sequence of multiplications and additions; that's what dramatically increases performance, on modern computing devices but most especially on ancient ones, where we were fighting for every MUL.
What this lets you do is composing multiple transforms into one matrix multiplication instead of a sequence of multiplications and additions; that's what dramatically increases performance, on modern computing devices but most especially on ancient ones, where we were fighting for every MUL.
More details: https://gabrielgambetta.com/computer-graphics-from-scratch/1...