Logarithmic Spiral - Is Point on Spiral (cartesian coordinates

Question

Lets Say I have a 3d Cartesian grid. Lets also assume that there are one or more log spirals emanating from the origin on the horizontal plane.

If I then have a point in

Answer 1

Not sure this is what you want, but you can reverse the log function (or "any" other for that matter). Say you have ln A = B, to get A from B you do e^B = A.

So you get your point and pass it as B, you'll get A. Then you just need to check if that A (with a certain +- range) is in the values you first passed on to ln to generate the spiral.

I think this might work...