Polygon Laplacian Made Simple

Bunge A, Herholz P, Kazhdan M, Botsch MU (2020)
Computer Graphics Forum 39(2): 303-313.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Bunge, AstridUniBi; Herholz, Philipp; Kazhdan, Misha; Botsch, Mario UlrichUniBi
Abstract / Bemerkung
The discrete Laplace-Beltrami operator for surface meshes is a fundamental building block for many (if not most) geometry processing algorithms. While Laplacians on triangle meshes have been researched intensively, yielding the cotangent discretization as the de-facto standard, the case of general polygon meshes has received much less attention. We present a discretization of the Laplace operator which is consistent with its expression as the composition of divergence and gradient operators, and is applicable to general polygon meshes, including meshes with non-convex, and even non-planar, faces. By virtually inserting a carefully placed point we implicitly refine each polygon into a triangle fan, but then hide the refinement within the matrix assembly. The resulting operator generalizes the cotangent Laplacian, inherits its advantages, and is empirically shown to be on par or even better than the recent polygon Laplacian of Alexa and Wardetzky [AW11] - while being simpler to compute.
Erscheinungsjahr
2020
Zeitschriftentitel
Computer Graphics Forum
Band
39
Ausgabe
2
Seite(n)
303-313
Konferenz
Eurographics 2020
Konferenzort
Norrköping, Sweden
Konferenzdatum
2020-05-25 – 2020-05-29
ISSN
0167-7055
Page URI
https://pub.uni-bielefeld.de/record/2940801

Zitieren

Bunge A, Herholz P, Kazhdan M, Botsch MU. Polygon Laplacian Made Simple. Computer Graphics Forum. 2020;39(2):303-313.
Bunge, A., Herholz, P., Kazhdan, M., & Botsch, M. U. (2020). Polygon Laplacian Made Simple. Computer Graphics Forum, 39(2), 303-313.
Bunge, A., Herholz, P., Kazhdan, M., and Botsch, M. U. (2020). Polygon Laplacian Made Simple. Computer Graphics Forum 39, 303-313.
Bunge, A., et al., 2020. Polygon Laplacian Made Simple. Computer Graphics Forum, 39(2), p 303-313.
A. Bunge, et al., “Polygon Laplacian Made Simple”, Computer Graphics Forum, vol. 39, 2020, pp. 303-313.
Bunge, A., Herholz, P., Kazhdan, M., Botsch, M.U.: Polygon Laplacian Made Simple. Computer Graphics Forum. 39, 303-313 (2020).
Bunge, Astrid, Herholz, Philipp, Kazhdan, Misha, and Botsch, Mario Ulrich. “Polygon Laplacian Made Simple”. Computer Graphics Forum 39.2 (2020): 303-313.

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