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Convexity preserving splines over triangulations
Authors:Larry L Schumaker  Hendrik Speleers
Affiliation:a Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States
b Department of Computer Science, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium
Abstract:A general method is given for constructing sets of sufficient linear conditions that ensure convexity of a polynomial in Bernstein-Bézier form on a triangle. Using the linear conditions, computational methods based on macro-element spline spaces are developed to construct convexity preserving splines over triangulations that interpolate or approximate given scattered data.
Keywords:Spline interpolation  Shape preservation  Convex surfaces
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