Scribbles: The Ensmoothening, Part II

One thing I noticed in that last series of charts is that more than one degree of discontinuity doesn’t help: the best-looking curves are mostly on the diagonal, where only the last nonzero derivative is discontinuous. Here, therefore, are those curves all together.

In column zero, the tangent angle is piecewise constant; in column one, it is a piecewise linear function of path length, resulting in six circular arcs; in column two it is piecewise quadratic, resulting in six clothoid arcs with continuous curvature; and so on.

Of course the arcs are approximated by cubics; to improve the match, I put a knot wherever any derivative crosses zero, as well as at the discontinuities. (See the knots.)

This entry was posted in curve-fitting. Bookmark the permalink.

2 Responses to Scribbles: The Ensmoothening, Part II

  1. Maybe you should try using Metapost to produce smooth curves.

  2. Anton says:

    What can Metapost do for me that SVG cannot?

Leave a Reply

Your email address will not be published. Required fields are marked *