@INPROCEEDINGS{ClRuTe04b, author = {Clarenz, U. and Rumpf, M. and Telea, A.}, title = {Finite Elements on Point Based Surfaces}, booktitle = {Eurographics Symposium of Point Based Graphics}, year = {2004}, abstract = {We present a framework for processing point-based surfaces via partial differential equations (PDEs). Our framework ef ciently and effectively brings well-known PDE-based processing techniques to the eld of point-based surfaces. Our method is based on the construction of local tangent planes and a local Delaunay triangulation of adjacent points projected onto this plane. The de nition of tangent spaces relies on moment-based computation with proven scaling and stability properties. Once local couplings are obtained, we are able to easily assemble PDE-specific mass and stiffness matrices and solve corresponding linear systems by standard iterative solvers. We demonstrate our framework by different classes of PDE-based surface processing applications, such as texture synthesis and processing, geometric fairing, and segmentation.}, journal = {Computers \& Graphics} }