Convex Surface Interpolation
This work is a contribution towards the graphical display of 3D data over a regular grid when it is convex. A piecewise rational bi-cubic function  has been utilized for this objective. Simple sufficient data dependent conditions are derived on free parameters in the description of rational bi-cubic function to preserve the shape of data. The presented method applies equally well to data or data with derivatives. The developed scheme is not only local and computationally economical but also visually pleasing.
KeywordsSurface interpolation Convexity Rational bi-cubic function Shape parameters Free parameters
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- 1.Asaturyan, S.: Shape Preserving Surface Interpolation, Ph.D. Thesis, Department of Mathematics and Computer Science, University of Dundee, Scotland, UK (1990)Google Scholar
- 7.Goodman, T.N.T.: Refinable Spline Functions and Hermite Interpolation. In: Lyche, T., Schumaker, L. (eds.) Mathematical Methods for Curves and Surfaces, Oslo, pp. 147–161. Vanderbilt University Press, Nashville (2001)Google Scholar