A complex view of barycentric mappings

O. Weber, M. Ben-Chen, C. Gotsman, K. Hormann

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

Barycentric coordinates are very popular for interpolating data values on polyhedral domains. It has been recently shown that expressing them as complex functions has various advantages when interpolating two-dimensional data in the plane, and in particular for holomorphic maps. We extend and generalize these results by investigating the complex representation of real-valued barycentric coordinates, when applied to planar domains. We show how the construction for generating real-valued barycentric coordinates from a given weight function can be applied to generating complex-valued coordinates, thus deriving complex expressions for the classical barycentric coordinates: Wachspress, mean value, and discrete harmonic. Furthermore, we show that a complex barycentric map admits the intuitive interpretation as a complex-weighted combination of edge-to-edge similarity transformations, allowing the design of "home-made" barycentric maps with desirable properties. Thus, using the tools of complex analysis, we provide a methodology for analyzing existing barycentric mappings, as well as designing new ones.

Original languageEnglish (US)
Pages (from-to)1533-1542
Number of pages10
JournalComputer Graphics Forum
Volume30
Issue number5
DOIs
StatePublished - 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design

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