Article Free Access Share on Voronoi-based interpolation with higher continuity Authors: Hisamoto Hiyoshi Department of Mathematical Engineering and Information Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan Department of Mathematical Engineering and Information Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, JapanView Profile , Kokichi Sugihara Department of Mathematical Engineering and Information Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan Department of Mathematical Engineering and Information Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, JapanView Profile Authors Info & Claims SCG '00: Proceedings of the sixteenth annual symposium on Computational geometryMay 2000 Pages 242–250https://doi.org/10.1145/336154.336210Published:01 May 2000Publication History 25citation935DownloadsMetricsTotal Citations25Total Downloads935Last 12 Months50Last 6 weeks9 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

This paper presents a general framework for constructing a variety of multi-dimensional interpolants based on Voronoi diagrams. This framework includes previously known methods such as Sibson's interpolant and Laplace's interpolant; moreover it contains infinitely many new interpolants. Computational experiments suggest that the smoothness can be improved by the proposed generalization. In addition, this framework also includes the piecewise linear interpolant over the Delaunay triangulation, which is a finite-element interpolant. This fact suggests that already established techniques in the finite element method might be brought into the research of the Voronoi-based approach. Hence this framework gives a new and promising direction of research on interpolation based on Voronoi diagrams.

Recently the authors found a local coordinate property based on the planar Voronoi diagram that is simpler than the famous Sibson's local coordinates (R. Sibson, 1980; 1981), and proposed an interpolant using this property. The paper generalizes this property to general dimensions. The proof given in the paper enables us to use more general Voronoi diagrams, e.g., Laguerre Voronoi diagrams and numerically distributed Voronoi diagrams obtained by topology oriented algorithms. The paper also generalizes the author's interpolant to continuously distributed data sites.