Transfinite mean value interpolation over polygons. (English) Zbl 1452.65026
Summary: Mean value interpolation is a method for fitting a smooth function to piecewise-linear data prescribed on the boundary of a polygon of arbitrary shape, and has applications in computer graphics and curve and surface modelling. The method generalizes to transfinite interpolation, i.e., to any continuous data on the boundary but a mathematical proof that interpolation always holds has so far been missing. The purpose of this note is to complete this gap in the theory.
MSC:
| 65D05 | Numerical interpolation |
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
| 41A05 | Interpolation in approximation theory |
References:
| [1] | Dyken, C.; Floater, MS, Transfinite mean value interpolation, Comput. Aided Geom. Des., 26, 117-134 (2009) · Zbl 1205.65034 · doi:10.1016/j.cagd.2007.12.003 |
| [2] | Floater, MS, Mean value coordinates, Comput. Aided Geom. Des., 20, 19-27 (2003) · Zbl 1069.65553 · doi:10.1016/S0167-8396(03)00002-5 |
| [3] | Floater, MS, Generalized barycentric coordinates and applications, Acta Numerica, 24, 161-214 (2015) · Zbl 1317.65065 · doi:10.1017/S0962492914000129 |
| [4] | Floater, MS; Hormann, K.; Kós, G., A general construction of barycentric coordinates over convex polygons, Adv. Comput. Math., 24, 311-331 (2006) · Zbl 1095.65016 · doi:10.1007/s10444-004-7611-6 |
| [5] | Floater, MS; Kos, G.; Reimers, M., Mean value coordinates in 3D, Comput. Aided Geom. Des., 22, 623-631 (2005) · Zbl 1080.52010 · doi:10.1016/j.cagd.2005.06.004 |
| [6] | Hormann, K.; Floater, MS, Mean value coordinates for arbitrary planar polygons, ACM Trans. Graph., 25, 1424-1441 (2006) · doi:10.1145/1183287.1183295 |
| [7] | Ju, T.; Schaefer, S.; Warren, J., Mean value coordinates for closed triangular meshes, ACM Trans. Graph., 24, 561-566 (2005) · doi:10.1145/1073204.1073229 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
