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Epi-convergence of minimum curvature variation B-splinesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2003 (English)Report (Other academic)
##### Abstract [en]

##### 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
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt737",{id:"formSmash:j_idt737",widgetVar:"widget_formSmash_j_idt737",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt754",{id:"formSmash:j_idt754",widgetVar:"widget_formSmash_j_idt754",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt774",{id:"formSmash:j_idt774",widgetVar:"widget_formSmash_j_idt774",multiple:true});
##### Note

Godkänd; 2003; 20080527 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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.

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CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1905",{id:"formSmash:lower:j_idt1905",widgetVar:"widget_formSmash_lower_j_idt1905",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1906_j_idt1908",{id:"formSmash:lower:j_idt1906:j_idt1908",widgetVar:"widget_formSmash_lower_j_idt1906_j_idt1908",target:"formSmash:lower:j_idt1906:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});