3 ms·

This called "affine transformation" in linear algebra language. (Linear algebra is stretches and rotations. Affine (affinity?) adds translations) https://peopl

by lupire 3y ago

This called "affine transformation" in linear algebra language. (Linear algebra is stretches and rotations. Affine (affinity?) adds translations) https://people.computing.clemson.edu/~dhouse/courses/401/notes/affines-matrices.pdf https://people.computing.clemson.edu/~dhouse/courses/401/not... In 2 dimensions: Rotation = multiplying by an imaginary unit. Stretches = multiplying by a real number Translation = adding a complex number. In higher dimensions, the analogy to complex numbers breaks down.

xeonmc 3y ago
It is not affine transforms per se but rather the expansion into homogeneous coordinates that enables translation by treating it as if it's a shear that leaves the reciprocal dimension untouched. > Rotation = multiplying by an imaginary unit. This is also not quite right. Rotation is multiplying by a complex number with a magnitude of 1 (or perhaps you meant to say "raising a number to the power of i"?)
- lupire 3y ago
  Sorry I meant "complex unit". "complex number with a magnitude of 1" is the definition of a "complex unit".
  - xeonmc 3y ago
    I like "roots of unity" (not necessarily rational) or "unit phasor" or "non-integer powers of -1"