Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Epi-convergence of minimum curvature variation B-splines
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
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.
2003 (English)Report (Other academic)
Abstract [en]

We study the curvature variation functional, i.e., the integral over the square of arc-length derivative of curvature, along a planar curve. With no other constraints than prescribed position, slope angle, and curvature at the endpoints of the curve, the minimizer of this functional is known as a cubic spiral. It remains a challenge to effectively compute minimizers or approximations to minimizers of this functional subject to additional constraints such as, for example, for the curve to avoid obstacles such as other curves. In this paper, we consider the set of smooth curves that can be written as graphs of three times continuously differentiable functions on an interval, and, in particular, we consider approximations using quartic uniform B- spline functions. We show that if quartic uniform B-spline minimizers of the curvature variation functional converge to a curve, as the number of B-spline basis functions tends to infinity, then this curve is in fact a minimizer of the curvature variation functional. In order to illustrate this result, we present an example of sequences of B-spline minimizers that converge to a cubic spiral.

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2003. , 12 p.
Series
Technical report / Luleå University of Technology, ISSN 1402-1536 ; 2003:14
National Category
Mathematical Analysis Computer Sciences Computational Mathematics
Research subject
Mathematics; Dependable Communication and Computation Systems; Scientific Computing
Identifiers
URN: urn:nbn:se:ltu:diva-23274Local ID: 65571df0-2bc6-11dd-8657-000ea68e967bOAI: oai:DiVA.org:ltu-23274DiVA: diva2:996323
Note
Godkänd; 2003; 20080527 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

Open Access in DiVA

fulltext(223 kB)109 downloads
File information
File name FULLTEXT01.pdfFile size 223 kBChecksum SHA-512
ff4bb531d9c70d5014752e1d34ef1b614695eea8dbca0b802d968387c9579e5b95e1c859dd8bbb22752dd3e86c2dc5a76ea9b15513833a0b7e5867b92695de81
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Berglund, TomasStrömberg, ThomasJonsson, HåkanSöderkvist, Inge
By organisation
Department of Computer Science, Electrical and Space EngineeringMathematical ScienceComputer Science
Mathematical AnalysisComputer SciencesComputational Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 109 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 195 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf