An irregular connectivity mesh representative of a surface having an arbitrary topology is processed using a non-uniform relaxation procedure. The non-uniform relaxation procedure minimizes differences between vectors normal to faces of pairs of triangles having a common edge and located within a designated neighborhood of a given vertex. The relaxation procedure may be used to construct subdivision and pyramid algorithms for performing processing operations such as upsampling, downsampling and filtering on irregular connectivity meshes. The signal processing algorithms may be utilized in applications such as smoothing, enhancement, editing, texture mapping and compression.