Constrained variational refinement. (English) Zbl 1162.41001
From the introduction: We consider a non-uniform, variational method for refining curves subject to convex set constraints that is a generalization of the uniform, interpolatory refinement scheme in [L. Kobbelt, Comput. Aided Geom. Des. 13, No. 8, 743–761 (1996; Zbl 0875.68878)]. We derive optimality conditions, including conditions for optimal free knots, and we use these and simpler methods of parametrization (such as centripetal parametrizations) to develop computational algorithms [see E. T. Y. Lee, Comput.-Aided Des. 21, No. 6, 363–370 (1989; Zbl 0675.65002)]. We generalize “uniform interpolation” to “non-uniform near-interpolation”. In particular, we assume that the near-interpolatory constraints are convex. The algorithm given here is easy to program, and good for computing approximate solutions.
Reviewer: Boris I. Golubov (Dolgoprudny)
MSC:
| 41A05 | Interpolation in approximation theory |
| 41A15 | Spline approximation |
| 41A29 | Approximation with constraints |
References:
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