Abstract
This paper concerns two fundamental interpolants to convex bivariate scattered data. The first,u, is the supremum over all convex Lagrange interpolants and is piecewise linear on a triangulation. The other,l, is the infimum over all convex Hermite interpolants and is piecewise linear on a tessellation. We discuss the existence, uniqueness, and numerical computation ofu andl and the associated triangulation and tessellation. We also describe how to generate convex Hermite data from convex Lagrange data.
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Communicated by M. Gasca
Research partially supported by the EU Project FAIRSHAPE, CHRX-CT94-0522. The first author was also partially supported by DGICYT PB93-0310 Research Grant.
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Carnicer, J.M., Floater, M.S. Piecewise linear interpolants to Lagrange and Hermite convex scattered data. Numer Algor 13, 345–364 (1996). https://doi.org/10.1007/BF02207700
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DOI: https://doi.org/10.1007/BF02207700