caa a22 4500 467939187 CHVBK 20180406153007.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10444-004-7611-6 doi (NATIONALLICENCE)springer-10.1007/s10444-004-7611-6 A general construction of barycentric coordinates over convex polygons [Elektronische Daten] [Michael Floater, Kai Hormann, Géza Kós] Barycentric coordinates are unique for triangles, but there are many possible generalizations to convex polygons. In this paper we derive sharp upper and lower bounds on all barycentric coordinates over convex polygons and use them to show that all such coordinates have the same continuous extension to the boundary. We then present a general approach for constructing such coordinates and use it to show that the Wachspress, mean value, and discrete harmonic coordinates all belong to a unifying one-parameter family of smooth three-point coordinates. We show that the only members of this family that are positive, and therefore barycentric, are the Wachspress and mean value ones. However, our general approach allows us to construct several sets of smooth five-point coordinates, which are positive and therefore barycentric. Springer, 2006 barycentric coordinates nationallicence convex polygons nationallicence rational polynomials nationallicence Floater Michael Computer Science Department, University of Oslo, Blindern, P.O. Box 1053, 0316, Oslo, Norway aut Hormann Kai Institute of Information Science and Technologies, Italian National Research Council, Via G. Moruzzi 1, 56124, Pisa, Italy aut Kós Géza Computer and Automation Research Institute, Kenda u.13-17, Budapest, Hungary aut Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 311-331 1019-7168 24:1-4<311 2006 24 10444 https://doi.org/10.1007/s10444-004-7611-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7611-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Floater Michael Computer Science Department, University of Oslo, Blindern, P.O. Box 1053, 0316, Oslo, Norway aut NATIONALLICENCE 700 1- Hormann Kai Institute of Information Science and Technologies, Italian National Research Council, Via G. Moruzzi 1, 56124, Pisa, Italy aut NATIONALLICENCE 700 1- Kós Géza Computer and Automation Research Institute, Kenda u.13-17, Budapest, Hungary aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 311-331 1019-7168 24:1-4<311 2006 24 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer