Marc Alexa, Hang Si, Boris Springborn
01.01.2019 – 31.12.2021
Delaunay triangulations are fundamental for processing geometry, yet they are too rigid to conform to given shapes. We introduce conforming regular triangulations, offering new ways to generate shapes spaces and discrete Laplace-Beltrami operators. The project investigates their computational and mathematical properties.
Regular (or weighted Delaunay) triangulations are useful structures for computations (such as FE bases, or shape analysis) because they admit orthogonal dual tessellations – similar to (unweighted) Delaunay triangulations. Yet, they cover a richer combinatorial space compared to Delaunay triangulations and may conform to a variety of boundary configurations without the need for additional (so-called Steiner) vertices.
Research focuses on the necessary mathematical foundation of regular triangulations of point sets as well as developing efficient algorithms for all aspects of computing conforming weighted Delaunay triangulations.
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