# Fit points to spiral

Fits a set of points in the plane to a logarithmic or Archimedes spiral. Useful for characterizing e.g. mollusc shells, teeth, claws and horns. Requires two columns of coordinates (x and y). The points must be given in sequence, either inwards or outwards. Left-handed and right-handed spirals are both acceptable.

The fitted logarithmic spiral in polar coordinates is given by r=ae^{bθ}. The scale a and the exponent b are given, together with the estimated center point, marked with a red cross. The whorl expansion rate W (factor increase in radius per whorl) is calculated from b as W=e^{2πb}. The center position is estimated by nonlinear optimization and the spiral itself by linearization and regression.

Published Aug. 31, 2020 8:40 PM
- Last modified Aug. 31, 2020 8:41 PM