Differential Representations for Mesh Processing

Abstract

Surface representation and processing is one of the key topics in computer graphics and geometric modeling, since it greatly affects the range of possible applications. In this paper we will present recent advances in geometry processing that are related to the Laplacian processing framework and differential representations. This framework is based on linear operators defined on polygonal meshes, and furnishes a variety of processing applications, such as shape approximation and compact representation, mesh editing, watermarking and morphing. The core of the framework is the definition of differential coordinates and new bases for efficient mesh geometry representation, based on the mesh Laplacian operator.