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A Tchebycheffian extension of multi-degree B-splines: Algorithmic computation and properties [article]

Rene R. Hiemstra, Thomas J. R. Hughes, Carla Manni, Hendrik Speleers, Deepesh Toshniwal
<span title="2020-01-22">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we present an efficient and robust approach to compute a normalized B-spline-like basis for spline spaces with pieces drawn from extended Tchebycheff spaces.  ...  The B-spline-like basis shares many characterizing properties with classical univariate B-splines and may easily be incorporated in existing spline codes.  ...  For polynomial B-splines of non-uniform degree, so-called multidegree B-splines, Bézier extraction has been analyzed and successfully applied in [41, 42] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2001.07967v1">arXiv:2001.07967v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nieodsm5qjadho7bb66gycmqby">fatcat:nieodsm5qjadho7bb66gycmqby</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200321103333/https://arxiv.org/pdf/2001.07967v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2001.07967v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A General Class of C1 Smooth Rational Splines: Application to Construction of Exact Ellipses and Ellipsoids

Hendrik Speleers, Deepesh Toshniwal
<span title="">2020</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wquzxyrherhzfhmbojag5cxcra" style="color: black;">Computer-Aided Design</a> </i> &nbsp;
In this paper, we describe a general class of C 1 smooth rational splines that enables, in particular, exact descriptions of ellipses and ellipsoids -some of the most important primitives for CAD and CAE  ...  Finally, all C 1 spline constructions yield spline basis functions that are locally supported and form a convex partition of unity.  ...  He is a member of Gruppo Nazionale per il Calcolo Scientifico, Istituto Nazionale di Alta Matematica.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cad.2020.102982">doi:10.1016/j.cad.2020.102982</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jeptshga6bgqnd4robn4n7rmfq">fatcat:jeptshga6bgqnd4robn4n7rmfq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210428041605/https://repository.tudelft.nl/islandora/object/uuid%3A92180757-f15e-4709-b129-88abe71798b1/datastream/OBJ/download" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6f/6c/6f6ccde8613b1207fd9d3fa9c23417d0b7ff9b79.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cad.2020.102982"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a>