Fast polynomial spline interpolation algorithm with shape-preserving properties
In this article, we address the problem of interpolating data points by regular L sub(1-spline polynomial curves of smoothness C) super(k), k[greater-or-equal, slanted]1, that are invariant under rotation of the data. To obtain a C super(1 cubic interpolating curve, we use a local minimization metho...
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| Published in: | Computer aided geometric design Vol. 28; no. 1; pp. 65 - 74 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
01.01.2011
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| Subjects: | |
| ISSN: | 0167-8396 |
| Online Access: | Get full text |
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| Summary: | In this article, we address the problem of interpolating data points by regular L sub(1-spline polynomial curves of smoothness C) super(k), k[greater-or-equal, slanted]1, that are invariant under rotation of the data. To obtain a C super(1 cubic interpolating curve, we use a local minimization method in parallel on five data points belonging to a sliding window. This procedure is extended to create C) super(k)-continuous L sub(1 splines, k[greater-or-equal, slanted]2, on larger windows. We show that, in the C) super(k)-continuous (k[greater-or-equal, slanted]1) interpolation case, this local minimization method preserves the linear parts of the data well, while a global L sub(1 minimization method does not in general do so. The computational complexity of the procedure is linear in the global number of data points, no matter what the order C) super(k) of smoothness of the curve is. |
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| Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| ISSN: | 0167-8396 |
| DOI: | 10.1016/j.cagd.2010.10.002 |