BPM: Blended Piecewise Moebius Maps

We propose a novel Moebius interpolator that takes as an input a discrete map between the vertices of two planar triangle meshes, and outputs a smooth map on the input domain. The output map interpolates the discrete map, is continuous between triangles, and has low quasi-conformal distortion when the input map is discrete conformal. Our map leads to considerably smoother texture transfer compared to the alternatives, even on very coarse triangulations. Furthermore, our approach has a closed-form expression, is local, applicable to any discrete map, and leads to smooth results even for extreme deformations. Finally, by working with local intrinsic coordinates, our approach is easily generalizable to discrete maps between a surface triangle mesh and a planar mesh, i.e., a planar parameterization. We compare our method with existing approaches, and demonstrate better texture transfer results, and lower quasi-conformal errors

Visualizing shape transformation between chimpanzee and human braincases

The quantitative comparison of the form of the braincase is a central issue in paleoanthropology (i.e., the study of human evolution based on fossil evidence). The major difficulty is that there are only few locations defining biological correspondence between individual braincases. In this paper, we use mesh parameterization techniques to tackle this problem. We propose a method to conformally parameterize the genus-0 surface of the braincase on the sphere and to calibrate the parameterization to match biological constraints. The resulting consistent parameterization gives detailed information about shape differences between the braincase of human and chimp. This opens up new perspectives for the quantitative comparison of "featureless” biological structure