Abstract
Local coordinates based on the Dirichlet tessellation (Voronoi diagram) provide a means to express a point as a linear combination of certain fixed points by using ratios of areas (or volumes) of certain regions. We add insight into the structure of the local coordinates by proving some of their basic properties by deriving formulas for their gradients from some simple geometry and proving the properties of smoothness and linear precision.
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References
Farin, G.: Surfaces over Dirichlet tessellations. Computer Aided Geometric Design 7 (1–4), 281–292 (1990).
Sibson, R.: A vector identity for the Dirichlet tessellations. Math. Proc. Cambridge Philos. Soc. 87, 151–155 (1980).
Sibson, R.: A brief description of the natural neighbour interpolant. In: Barnett, D. V. (ed.) Interpolation Multivariate Data. New York: Wiley 1981.
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© 1993 Springer-Verlag
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Piper, B. (1993). Properties of Local Coordinates Based on Dirichlet Tessellations. In: Farin, G., Noltemeier, H., Hagen, H., Knödel, W. (eds) Geometric Modelling. Computing Supplementum, vol 8. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6916-2_15
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DOI: https://doi.org/10.1007/978-3-7091-6916-2_15
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82399-6
Online ISBN: 978-3-7091-6916-2
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