Weighted Triangulations for Geometry Processing
Abstract
In this article we investigate the use of weighted triangulations as discrete, augmented approximations of surfaces for digital geometry processing. By incorporating a scalar weight per mesh vertex, we introduce a new notion of discrete metric that defines an orthogonal dual structure for arbitrary triangle meshes and thus extends weighted Delaunay triangulations to surface meshes. We also present alternative characterizations of this primal-dual structure (through combinations of angles, areas, and lengths) and, in the process, uncover closed-form expressions of mesh energies that were previously known in implicit form only. Finally, we demonstrate how weighted triangulations provide a faster and more robust approach to a series of geometry processing applications, including the generation of well-centered meshes, self-supporting surfaces, and sphere packing.
Additional Information
© 2014 ACM, Inc. Received August 2013; accepted January 2014. Pensatore model (Figure 1), hand model (Figure 5), squirrel model (Figure 6) are courtesy of Aim@Shape; Lilium tower (Figure 6) is courtesy of Evolute GmbH; and twisted torus (Figure 6) is courtesy of Keenan Crane. The authors wish to acknowledge support through a Ph.D. Google Fellowship and a grant (CCF-1011944) from the National Science Foundation.Attached Files
Accepted Version - dGMMD14.pdf
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Additional details
- Eprint ID
- 46870
- DOI
- 10.1145/2602143
- Resolver ID
- CaltechAUTHORS:20140707-093812947
- Google Fellowship
- CCF-1011944
- NSF
- Created
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2014-07-07Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field