Mathematics of Surfaces

Mesh parameterization is a key problem in digital geometry processing. By cutting a surface along a set of edges (a seam), one can map an arbitrary topology surface mesh to a single chart. Unfortunately, high distortion occurs when protrusions of the surface (such as fingers of a hand and horses’ legs) are flattened into a plane. This paper presents a novel skeleton-based algorithm for computing a seam on a triangulated surface. The seam produced is a full component Steiner tree in a graph constructed from the original mesh. By generating the seam so that all extremal vertices are leaves of the seam, we can obtain good parametrization with low distortion.