Finite Elements on Point Based Surfaces

Clarenz, U.; Rumpf, M.; Telea, A.

Finite Elements on Point Based Surfaces

Files

201-211.pdf (1.93 MB)

Date

2004

Authors

Clarenz, U.
Rumpf, M.
Telea, A.

Publisher

The Eurographics Association

Abstract

framework efficiently and effectively brings well-known PDE-based processing techniques to the field 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 definition 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.

        @inproceedings{:10.2312/SPBG/SPBG04/201-211
,
booktitle = {SPBG'04 Symposium on Point - Based Graphics 2004
},
editor = {Markus Gross and Hanspeter Pfister and Marc Alexa and Szymon Rusinkiewicz
},
title = {{Finite Elements on Point Based Surfaces
}},
author = {Clarenz, U. and 
Rumpf, M. and 
Telea, A.
},
year = {2004
},
publisher = {The Eurographics Association
},
ISSN = {1811-7813
},
ISBN = {3-905673-09-6
},
DOI = {/10.2312/SPBG/SPBG04/201-211
}
}