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Fuda_2024_CAGD
Journal article

A new stable method to compute mean value coordinates

  • Fuda, Chiara Facoltà di scienze informatiche, Università della Svizzera italiana, Svizzera
  • Hormann, Kai ORCID Facoltà di scienze informatiche, Università della Svizzera italiana, Svizzera
  • 2024
Published in:
  • Computer aided geometric design. - 2024, vol. 111
Mean value coordinates
Numerical stability
Rounding errors
English The generalization of barycentric coordinates to arbitrary simple polygons with more than three vertices has been a subject of study for a long time. Among the different constructions proposed, mean value coordinates have emerged as a popular choice, particularly due to their suitability for the non-convex setting. Since their introduction, they have found applications in numerous fields, and several equivalent formulas for their evaluation have been presented in the literature. However, so far, there has been no study regarding their numerical stability. In this paper, we aim to investigate the numerical stability of the algorithms that compute mean value coordinates. We show that all the known methods exhibit instability in some regions of the domain. To address this problem, we introduce a new formula for computing mean value coordinates, explain how to implement it, and formally prove that our new algorithm provides a stable evaluation of mean value coordinates. We validate our results through numerical experiments.
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Language
  • English
Classification
Computer science and technology
License
CC BY-NC-ND
Open access status
hybrid
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Persistent URL
https://n2t.net/ark:/12658/srd1329025
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