An Obstacle-avoiding Minimum Variation B-spline Problem (2003)
| Venue: | in Proceedings of International Conference on Geometric Modeling and Graphics |
| Citations: | 7 - 0 self |
BibTeX
@INPROCEEDINGS{Berglund03anobstacle-avoiding,
author = {Tomas Berglund and Inge Söderkvist},
title = {An Obstacle-avoiding Minimum Variation B-spline Problem},
booktitle = {in Proceedings of International Conference on Geometric Modeling and Graphics},
year = {2003},
pages = {156--161}
}
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Abstract
We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the Minimum Variation B-spline problem which is a linearly constrained optimization problem over curves defined by Bspline functions only. An empirical investigation indicates that this problem has one unique solution among all uniform quartic B-spline functions. Furthermore, we prove that, for any B-spline function, the convexity properties of the problem are preserved subject to a scaling and translation of the knot sequence defining the B-spline. 1
