A new stable method to compute mean value coordinates
Informazioni aggiuntive
Autori
Fuda C.,
Hormann K.
Tipo
Articolo pubblicato in rivista scientifica
Anno
2024
Lingua
Inglese
Sommario
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.
Parole chiave
Mean value coordinates, Numerical stability, Rounding errors
Periodico
Computer aided geometric design
Volume
111
Diffusione
Licenza
CC BY-NC-ND
Visibilità
Pubblico
Status open access
Hybrid
