Computational geometry: an introduction
Computational geometry: an introduction
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Surfaces over Dirichlet Tessellations
Computer Aided Geometric Design
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Improving continuity of Voronoi-based interpolation over Delaunay spheres
Computational Geometry: Theory and Applications
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The natural neighbour interpolation is a potential interpolationmethod for multidimensional data. However, only globallyC1 interpolants have been known so far. In this paper wepropose a globally C2 interpolant, and write it in anexplicit form. When the data are supplied to the interpolant from athird-degree polynomial, the interpolant can reproduce thatpolynomial exactly. The idea used to derive the interpolant isapplicable to obtain a globally Cq interpolant for anarbitrary non-negative integer q. Hence, this paper gets rid of thecontinuity limitation of the natural neighbour interpolation, andthus leads it to a new research stage.