Perfect Laplacians for Polygon Meshes

Philipp Herholz Jan Eric Kyprianidis Marc Alexa

Technische Universität Berlin

Abstract A discrete Laplace-Beltrami operator is called perfect if it possesses all the important properties of its smooth counterpart. It is known which triangle meshes admit perfect Laplace operators and how to fix any other mesh by changing the combinatorics. We extend the characterization of meshes that admit perfect Laplacians to general polygon meshes. More importantly, we provide an algorithm that computes a perfect Laplace operator for any polygon mesh without changing the combinatorics, although, possibly changing the embedding. We evaluate this algorithm and demonstrate it at applications.






(12.7MB, Examples are not animated)

Results Animations of several 2d and 3d examples can be found here .

@Article{Herholz:2015:PLP, journal = {Computer Graphics Forum (Proc. of SGP)}, title = {{Perfect Laplacians for Polygon Meshes}}, author = {Philipp Herholz and Jan Eric Kyprianidis and Marc Alexa}, pages = {}, volume= {}, number= {}, year = {2015}, DOI = {}, }