Comparing two different approaches to shape transformation:
The top is the interpolation technique in this demo: add points until both shapes have an equal number and then pick the optimal winding order by the sum of squared distances.
The bottom is inspired by Procrustes superimposition, which decomposes the transform necessary to align two shapes into scale, translation, and rotation components. By interpolating those three components separately, it can produce nicer transitions in certain cases (e.g. in the extreme case, a shape turning into a rotated version of itself). But since it’s meant for aligning similar shapes with meaningful point-to-point correspondences, it seems to do more harm than good in most cases with two unrelated shapes, though evenly spacing the points around each ring helps.
See also: Smoother polygon transitions, Triangle morphing #2