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Use matrices instead of rotors for transforms #193

@HactarCE

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@HactarCE

reasons:

  • in general, it's not actually easier to interpolate rotors compared to matrices
  • matrices are better-studied so it's easier to find algorithms
  • matrices scale better in high dimensions (rotors win in 6D and below; matrices win in 7D and above)

distance(A, B) = entrywise dot product

Notes (from things Milo was saying)

entrywise dot product of A and B = trace(A BH)

(BH = conjugate transpose of B)

for unitary matrices, BH = B^-1

trace = sum of diagonal = sum of eigenvalues

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