I learned today that the CCCG 2005 proceedings are online, thanks to a pointer from Suresh. Suresh already pointed to two papers of recreational math interest, on cross-stitch needlepoint and drumming rhythms and musical scales. Here are two others I found entertaining:

  • Morphing Polyhedra Preserving Face Normals: A Counterexample, by Biedl, Lubiw, and Spriggs. Constructs two polyhedra, with axis-aligned faces, that have the topology of the sphere and where the boundary features correspond in connectivity and orientation, but that can't be morphed one into each other without tilting some faces off-axis or changing the connectivity. The construction involves building a "glove" portion of the polyhedron that fits around the rest of the polyhedron in one of the two copies, and hangs loose from it in the other. Somehow it reminds me of the rope and puzzle tricks in Winning Ways.
  • Minimizing the Total Absolute Gaussian Curvature in a Terrain is Hard, by Buchin and Giesen. Shows that it's difficult to turn point elevation data into a 3d surface, if the quality criterion is to minimize the sum of the amounts by which the sums of angles at each vertex differ from 360 degrees. The technique involves transforming a two-dimensional line segment arrangement into a three-dimensional point set that's flat except for spikes above the endpoints of the line segments, in such a way that the only valid triangulations are formed by hanging curtains between pairs of spikes; the optimal triangulation is the one that maximizes the number of curtains that can be hung simultaneously.

I was a little curious to see three papers citing my old work with Jeff Erickson on finding close sets of k points in a larger point set (DCG 1994); historically that paper's had more of a slow and steady cite rate, but for some reason the subject seems to be more popular this year. The citations gave me a good excuse for reloading Fano, which I hadn't done for months; Fano's new CCCG'05 entry is here.