Test uniform redistribution of points

[robz]

Currently, optimization minimizes an error function that is computed by comparing two lists of points--the list from the input path that you draw, and the list that is generated by a trace point on the linkage. In this scheme, points are nonuniformly distributed along the path that was drawn (due to nonuniform mouse movement while drawing the path) or traced (since the linkage's trace point might move faster along a portion of its path and slower along another portion).

This nonuniformity causes the error function to be "weighted" towards clusters of points, which is often unintentional. I think this weighting can be eliminated if each path were regenerated to make the euclidean distance between each point be equal, which can be accomplished through linear interpolation. An added benefit to this is that the user would only need to provide a few point for the path, and the rest will be generated.

However, simple linear interpolation would also remove the user's ability to describe the speed of the tracepoint, and remove any speed constraints on the output path. Allowing that may require the user to provide a list of speeds or vectors along with the points, generating a series of parameterized quadratic paths, and interpolating based intervals of the parameter, rather than some fixed euclidean distance. But that would be a bit involved.

Anyway, it would be interesting to see if uniform redistribution helps the optimization.