Associated Curves

Let B be a base point on the closed curve to be traced. Assume that the holonomy H has no fixed points on [Graphics:PrytzDemgr549.gif]. Then there is a unique vector v such that if the tracing starting at B' = B + v, going to B, going around the curve, then back to B', the resulting holonomy is purely rotational. If this is done for every B on the curve, an associated curve is formed, comprised of the points B'. These curves take several minutes to compute.

Graphs of Norm[v] as a function of L.

Ellipse

Polygons