I've been actually wanting this arbitrary exponent as a way to interpolate between placements.wmayer wrote: ↑Mon Sep 30, 2019 12:22 pmOn Wikipedia you can find some information for square roots of a matrix but it's only well-defined for positive-definite matrices while for arbitrary matrices it causes ambiguities. But what when using 1/3 as exponent instead? Here I couldn't find a valid definition. So, a power function for arbitrary exponents makes probably not much sense (especially not in a CAD program) and it should be limited to integers only as done by the current implementation.This is true for numbers (1/X = X^-1), but there is a rigorous mathematical notion behind it, that allows to define X^-3 or X^(1/2), but for matrices or Placements, what would mean :
You don't have to define, what ^(1/3) means, as 1/3 can't be precisely represented by a float anyway. A fractional part of float is a sum of fractions:
bit1*1/2 + bit2*1/4 + bit3*1/8 +...
Power-of-two fractional powers can be easily calculated by multiplying M^(1/2) by itself.