Piecewise regular meshes: construction and compression

We present an algorithm which splits a 3D surface into reliefs, relatively fiat regions that have smooth boundaries. The surface is then resampled in a regular manner within each of the reliefs. As a result, we obtain a piecewise regular mesh (PRM) having a regular structure on large regions. Experimental results show that we are able to approximate the input surface with the mean square error of about 0.01- 0.02% of the diameter of the bounding box without increasing the number of vertices. We introduce a compression scheme tailored to work with our remeshed models and show that it is able to compress them losslessly (after quantizing the vertex locations) without significantly increasing the approximation error using about 4 bits per vertex of the resampled model.