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Approximating minimum bending energy path in a simple corridor.
- Source :
-
Computational Geometry . Apr2014, Vol. 47 Issue 3, p349-366. 18p. - Publication Year :
- 2014
-
Abstract
- Abstract: In this paper, we consider the problem of computing a minimum bending energy path (or MinBEP) in a simple corridor. Given a simple 2D corridor C bounded by straight line segments and arcs of radius 2r, the MinBEP problem is to compute a path P inside C and crossing two pre-specified points s and t located at each end of C so that the bending energy of P is minimized. For this problem, we first show how to lower bound the bending energy of an optimal curve with bounded curvature, and then use this lower bound to design a -approximation algorithm for this restricted version of the MinBEP problem. Our algorithm is based on a number of interesting geometric observations and approximation techniques on smooth curves, and can be easily implemented for practical purpose. It is the first algorithm with a guaranteed performance ratio for the MinBEP problem. [Copyright &y& Elsevier]
- Subjects :
- *APPROXIMATION theory
*ALGORITHMS
*CURVES
*GEOMETRY
*MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 09257721
- Volume :
- 47
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Computational Geometry
- Publication Type :
- Academic Journal
- Accession number :
- 92513306
- Full Text :
- https://doi.org/10.1016/j.comgeo.2013.09.001