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Nonnegative Interpolation with Clough‐Tocher Splines of Cubic Precision
Author(s) -
Bastian Marion,
Schmidt Jochen W.
Publication year - 2001
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200108115128
Subject(s) - interpolation (computer graphics) , piecewise , mathematics , quadratic equation , constant (computer programming) , parametric statistics , spline interpolation , point (geometry) , mathematical analysis , statistics , computer science , bilinear interpolation , geometry , artificial intelligence , motion (physics) , programming language
In ]4[ the Clough‐Tocher splines of quadratic precision are shown to allow always nonnegative interpolation of scattered data. The aim of the present note is to point out that Clough‐Tocher splines of cubic precision are suitable, too. This result extends to range restricted interpolation if the obstacles are piecewise constant. For piecewise linear and continuous obstacles the Clough‐Tocher splines may fail. However, for this type of restrictions it seems to be possible to derive an always working interpolation algorithm by means of the parametric Clough‐Tocher splines recently introduced in ]1[.