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The problem of computing an obstacle-avoiding minimum variation B-spline
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0003-3811-062X
2003 (English)Report (Other academic)
Abstract [en]

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 B-spline 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.

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2003.
Series
Technical report / Luleå University of Technology, ISSN 1402-1536 ; 2003:06
National Category
Computational Mathematics Computer Sciences
Research subject
Scientific Computing; Dependable Communication and Computation Systems
Identifiers
URN: urn:nbn:se:ltu:diva-23772Local ID: 859d9350-2b44-11dd-8657-000ea68e967bOAI: oai:DiVA.org:ltu-23772DiVA, id: diva2:996822
Note
Godkänd; 2003; 20080526 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-08Bibliographically approved

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Berglund, TomasJonsson, HåkanSöderkvist, Inge

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  • apa
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Language
  • de-DE
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  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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  • asciidoc
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