Investigations of a functional version of a blending surface scheme for regular data interpolation. (English) Zbl 1542.65022
Summary: This paper describes an implementation and tests of a blending scheme for regularly sampled data interpolation, and in particular studies the order of approximation for the method. This particular implementation is a special case of an earlier scheme by Fang for fitting a parametric surface to interpolate the vertices of a closed polyhedron with \(n\)-sided faces, where a surface patch is constructed for each face of the polyhedron, and neighbouring faces can meet with a user specified order of continuity. The specialization described in this paper considers functions of the form \(z = f(x, y)\) with the patches meeting with \(C^2\) continuity. This restriction allows for investigation of order of approximation, and it is shown that the functional version of Fang’s scheme has polynomial precision.
MSC:
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
| 41A05 | Interpolation in approximation theory |
Keywords:
data interpolation; \(n\)-sided patches; continuity; order of approximation; blending schemeReferences:
| [1] | de Boor, C.; Ron, A., Computational aspects of polynomial interpolation in several variables, Math. Comput., 58, 705-727, 1992 · Zbl 0767.41003 |
| [2] | Fang, X., A Generalized Blending Scheme for Arbitrary Order of Continuity, 2023, University of Waterloo, Ph.D. thesis |
| [3] | Franke, R., A Critical Comparison of Some Methods for Interpolation of Scattered Data, 1979, Navel Postgraduate School: Navel Postgraduate School Monterey, California, Technical Report NPS-53-79-003 |
| [4] | Kashyap, P., Improving Clough-Tocher interpolants, Comput. Aided Geom. Des., 13, 629-651, 1996 · Zbl 0900.68409 |
| [5] | Mann, S., Cubic precision Clough-Tocher interpolation, Comput. Aided Geom. Des., 16, 85-88, 1999 · Zbl 0909.68184 |
| [6] | Mann, S., Order of Approximation and Some Tests of a Functional Variation of a Blending Surface Scheme for Scattered Data Interpolation, 2023, Computer Science, University of Waterloo, Technical Report CS-2023-02 |
| [7] | Mann, S.; Lounsbery, M.; Loop, C.; Meyers, D.; Painter, J.; DeRose, T.; Sloan, K., A survey of triangular scattered data fitting, (Hagen, H., Curve and Surface Design, 1992, SIAM), 145-172 · Zbl 0823.41020 |
| [8] | Peters, J., Joining smooth patches around a vertex to form a \(C^k\) surface, Comput. Aided Geom. Des., 9, 387-411, 1992 · Zbl 0760.65015 |
| [9] | Tosun, E.; Zorin, D., Manifold-based surfaces with boundaries, Comput. Aided Geom. Des., 28, 1-22, 2011 · Zbl 1209.65023 |
| [10] | Várady, T.; Rockwood, A.; Salvi, P., Transfinite surface interpolation over irregular n-sided domains, Comput. Aided Des., 43, 1330-1340, 2011 |
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