.png){kind=icon}
Return
Weighted Triangulations for Geometry Processing
.png){kind=icon}
OA
AI
DOI：10.1145/2602143.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
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.
Keywords:
Theory
Algorithms
Discrete differential geometry
discrete metric
weighted triangulations
orthogonal dual diagram
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
9.5
Papers:
4.8K
Citations:
3.6W
Organization
Cited Papers
ShareSaveShareSave
An algorithm for the construction of intrinsic delaunay triangulations with applications to digital geometry processing.png)
COMPUTING
COMPUTINGIF2.8
PREAI
ShareSaveShareSave
View more