Encoding Meshes in Differential Coordinates

Representing surfaces in local, rather than global, coordinate systems proves to be useful for various geometry processing applications. In particular, we have been investigating surface representations based on differential coordinates, constructed using the Laplacian operator and discrete forms. Unlike global Cartesian coordinates, that only represent the spatial locations of points on the surface, differential coordinates capture the local surface details which greatly affect the shading of the surface and thus its visual appearance. On polygonal meshes, differential coordinates and the discrete mesh Laplacian operator provide an efficient linear surface reconstruction framework suitable for various mesh processing tasks. In this paper we discuss the important properties of differential coordinates and show their applications for surface reconstruction. In particular, we discuss quantization of the differential coordinates, Least-squares meshes and mesh editing. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations