Convexity preserving splines over triangulations |
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Authors: | Larry L Schumaker Hendrik Speleers |
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Affiliation: | a Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States b Department of Computer Science, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium |
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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. |
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Keywords: | Spline interpolation Shape preservation Convex surfaces |
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