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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>
The B-spline-like basis shares many characterizing properties with classical univariate B-splines and may easily be incorporated in existing spline codes.  ...  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.  ...  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>

Computation of multi-degree B-splines [article]

Hendrik Speleers
<span title="2019-03-26">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This enables the use of existing efficient algorithms for B-spline evaluations and refinements in the context of multi-degree splines.  ...  We describe a simple algorithmic construction of a set of basis functions for the space of multi-degree splines, with similar properties to standard B-splines.  ...  ACKNOWLEDGMENTS This work was partially supported by the Mission Sustainability Programme of the University of Rome Tor Vergata through the project IDEAS (CUP E81I18000060005) and by the MIUR Excellence  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1809.01598v2">arXiv:1809.01598v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s5rplv34k5eezc637hmq5cpnoi">fatcat:s5rplv34k5eezc637hmq5cpnoi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191015000018/https://arxiv.org/pdf/1809.01598v2.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] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0e/6e/0e6e91e264696ff3a3d802eb59957583c7c00a70.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1809.01598v2" 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>

Computation of multi-degree Tchebycheffian B-splines [article]

Hendrik Speleers
<span title="2021-01-31">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Under quite mild assumptions, they can be represented in terms of a so-called MDTB-spline basis; such basis possesses all the characterizing properties of the classical polynomial B-spline basis.  ...  These are a natural extension of multi-degree polynomial splines.  ...  ACKNOWLEDGMENTS This work was partially supported by the Beyond Borders Programme of the University of Rome Tor Vergata through the project ASTRID (CUP E84I19002250005) and by the MIUR Excellence Department  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2102.00418v1">arXiv:2102.00418v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d5dur6vqjfhapjvcv457uosewa">fatcat:d5dur6vqjfhapjvcv457uosewa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210203195832/https://arxiv.org/pdf/2102.00418v1.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] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3a/bc/3abc320521a7e07386be2dd2ff769d1ded0fee72.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2102.00418v1" 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>

On multi-degree splines [article]

Carolina Vittoria Beccari, Giulio Casciola, Serena Morigi
<span title="2017-09-14">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree splines that can be derived by existing approaches.  ...  We then propose a new alternative method for constructing and evaluating the B-spline basis, based on the use of so-called transition functions.  ...  Transition functions for multi-degree splines In this section we introduce the transition functions as a tool for the computation of the B-spline basis.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1709.04998v1">arXiv:1709.04998v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6klfpbpsvvcbnaln23slgu6en4">fatcat:6klfpbpsvvcbnaln23slgu6en4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200906182222/https://arxiv.org/pdf/1709.04998v1.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] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5e/bd/5ebd62db4af6246ec331112f2b0f98429d9958bc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1709.04998v1" 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>

Knot intervals and multi-degree splines

Thomas W. Sederberg, Jianmin Zheng, Xiaowen Song
<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/d7m3pqsgunbsrmcxdnyqqx2uxm" style="color: black;">Computer Aided Geometric Design</a> </i> &nbsp;
Using knot interval notation, the paper introduces MD-splines, which are B-spline-like curves that are comprised of polynomial segments of various degrees (MD stands for "multi-degree").  ...  MD-splines are a generalization of B-spline curves in that if all curve segments in an MD-spline have the same degree, it reduces to a B-spline curve.  ...  MD-splines maintain many desirable properties of B-spline curves, such as the convex hull and variation diminishing properties.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0167-8396(03)00096-7">doi:10.1016/s0167-8396(03)00096-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/eylxsgqrabhdfabqwbjpq7t7di">fatcat:eylxsgqrabhdfabqwbjpq7t7di</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922003748/http://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2055&amp;context=facpub" 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/cb/27/cb27044fe1f894572fbd3ad4a005144f933ea9b9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0167-8396(03)00096-7"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Weighted quadrature for hierarchical B-splines [article]

Carlotta Giannelli, Tadej Kanduc, Massimiliano Martinelli, Giancarlo Sangalli, Mattia Tani
<span title="2021-09-26">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The proposed algorithm has a computational cost proportional to the number of degrees of freedom and advantageous properties with increasing spline degree.  ...  We present weighted quadrature for hierarchical B-splines to address the fast formation of system matrices arising from adaptive isogeometric Galerkin methods with suitably graded hierarchical meshes.  ...  The proposed algorithm has a computational cost proportional to the number of degrees of freedom and advantageous properties with increasing spline degree.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2109.12632v1">arXiv:2109.12632v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tqtn6xen6vd35inyt3ogbxmx2u">fatcat:tqtn6xen6vd35inyt3ogbxmx2u</a> </span>
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Implicit B-Spline Surface Reconstruction

Mohammad Rouhani, Angel D. Sappa, Edmond Boyer
<span title="">2015</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dhlhr4jqkbcmdbua2ca45o7kru" style="color: black;">IEEE Transactions on Image Processing</a> </i> &nbsp;
This paper presents a fast and flexible curve/surface reconstruction technique based on implicit b-spline. This representation does not require any parameterization and it is locally supported.  ...  The experimental results show the flexibility and accuracy of the proposed algorithm to describe objects with complex topologies.  ...  to construct the B-splines in 1D.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tip.2014.2366374">doi:10.1109/tip.2014.2366374</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/25373084">pmid:25373084</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/as6qtv2p7rdeze225c2h2zreg4">fatcat:as6qtv2p7rdeze225c2h2zreg4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20151101014715/https://hal.inria.fr/hal-01101037/file/TIP_2014_v4_double_column.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] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f6/d0/f6d0ba54b64d959a2402cc04c0848e6a952caee8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tip.2014.2366374"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Multivariate Lévy Adaptive B-Spline Regression [article]

Sewon Park, Jaeyong Lee
<span title="2021-08-31">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
By changing a set of degrees of the tensor product basis function, MLABS can adapt the smoothness of target functions due to the nice properties of B-spline bases.  ...  The B-spline basis can express systematically functions with varying degrees of smoothness.  ...  The B-spline basis has nice properties such as local support and differentiability.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.11863v3">arXiv:2108.11863v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xnuwnfv2ubf7jfbwxvninbcf74">fatcat:xnuwnfv2ubf7jfbwxvninbcf74</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210902112907/https://arxiv.org/pdf/2108.11863v3.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] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/25/42/2542104784b075fe8c885e6a104b57e9d45978c9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.11863v3" 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>

Adaptive resolution of 1D mechanical B-spline

Julien Lenoir, Laurent Grisoni, Christophe Chaillou, Philippe Meseure
<span title="">2005</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lmfbfntycbd2hlv5cs4ryztpce" style="color: black;">Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia - GRAPHITE &#39;05</a> </i> &nbsp;
This article presents an adaptive approach to B-spline curve physical simulation. We combine geometric refinement and coarsening techniques with an appropriate continuous mechanical model.  ...  To achieve real-time local adaptation of spline curves, some criteria and optimizations are shown.  ...  [Eck and Hadenfeld 1995; Tiller 1992] provide general algorithm for B-spline knot removal.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1101389.1101467">doi:10.1145/1101389.1101467</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/graphite/LenoirGCM05.html">dblp:conf/graphite/LenoirGCM05</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hrb4tftnmjbwxmvogitrolm6wa">fatcat:hrb4tftnmjbwxmvogitrolm6wa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170811222717/http://www.cristal.univ-lille.fr/%7Egrisoni/lenoirGraphite05.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] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e6/a2/e6a292f59b5881e05cab88d33bade4890a63a188.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1101389.1101467"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Scale-space derived from B-splines

Yu-Ping Wang, S.L. Lee
<span title="">1998</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3px634ph3vhrtmtuip6xznraqi" style="color: black;">IEEE Transactions on Pattern Analysis and Machine Intelligence</a> </i> &nbsp;
On the other hand, the behavior of edge models, the properties of completeness, causality, and other properties in such a scale-space representation are examined in the framework of B-splines.  ...  In the dyadic case, e cient frame algorithms are derived using B-spline techniques to analyze the geometry of an image.  ...  Discussions on the properties of the B-spline based scale-space We now discuss the advantages and properties of the B-spline based scale-space.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/34.722612">doi:10.1109/34.722612</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/eqet6avljbfujibl7u66wrl2oi">fatcat:eqet6avljbfujibl7u66wrl2oi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190302190512/http://pdfs.semanticscholar.org/a812/005804b007dc24573e3b69031eb365fad87c.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] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a8/12/a812005804b007dc24573e3b69031eb365fad87c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/34.722612"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

An Algorithm for Direct Multiplication of B-Splines

Xianming Chen, R.F. Riesenfeld, E. Cohen
<span title="">2009</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sv6lf6p3jrf4vbz5puthqdqmae" style="color: black;">IEEE Transactions on Automation Science and Engineering</a> </i> &nbsp;
symbolic computation operations on B-splines.  ...  Algorithms for B-spline multiplication standardly use indirect approaches such as nodal interpolation or computing the product of each set of polynomial pieces using various bases.  ...  As the whole process is computationally expensive, Lee developed a scheme to evaluate the coefficients of the product B-spline a group at a time by computing a chain of blossoms.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tase.2009.2021327">doi:10.1109/tase.2009.2021327</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yaouqyisfvb37pgyk3lffv5day">fatcat:yaouqyisfvb37pgyk3lffv5day</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20101225061929/http://www.cs.utah.edu/~xchen/papers/multiply-tase.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] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/14/e4/14e4dc526943a7e031bae1899d8352cb5239bfbb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tase.2009.2021327"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Constrained global optimization of multivariate polynomials using polynomial B-spline form and B-spline consistency prune approach

Deepak Devidasrao Gawali, Bhagyesh V. Patil, Ahmed Zidna, P. S. V. Nataraj
<span title="2021-12-02">2021</span> <i title="EDP Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/inei2pvlvnaw7lwfzvf7meb67e" style="color: black;">Reserche operationelle</a> </i> &nbsp;
In improved algorithm we introduce several new ingredients, such as B-spline box consistency and B-spline hull consistency algorithm to prune the search regions and make the search more efficient.  ...  In this paper, we propose basic and improved algorithms based on polynomial B-spline form for constrained global optimization of multivariate polynomial functions.  ...  In improved algorithm during each iteration B-spline coefficients are computed after domain pruning by the B-spline box and B-spline hull consistency.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1051/ro/2021179">doi:10.1051/ro/2021179</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cmst3q62pjcsvoj3hrgrvf237e">fatcat:cmst3q62pjcsvoj3hrgrvf237e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220206080838/https://www.rairo-ro.org/articles/ro/pdf/2021/07/ro210272.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] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e4/51/e451da9955280066a39f88eaed48b8e412eee12e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1051/ro/2021179"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Sliding windows algorithm for B-spline multiplication

Xianming Chen, Richard F. Riesenfeld, Elaine Cohen
<span title="">2007</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sl7g43a53farbgnszuvagjd5jm" style="color: black;">Proceedings of the 2007 ACM symposium on Solid and physical modeling - SPM &#39;07</a> </i> &nbsp;
symbolic computation operations on B-splines.  ...  Algorithms for B-spline multiplication standardly use indirect approaches such as nodal interpolation or computing the product of each set of polynomial pieces using various bases.  ...  The algorithm is motivated by the efficiency issue of NURBS symbolic computation involving B-splines of high degrees and especially high dimensions, which we believe is a current trend in the CAD community  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1236246.1236283">doi:10.1145/1236246.1236283</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/sma/ChenRC07.html">dblp:conf/sma/ChenRC07</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xjobizvo6vhkhpys5r4wjy7m64">fatcat:xjobizvo6vhkhpys5r4wjy7m64</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20100610194409/http://www.cs.utah.edu/gdc/publications/papers/chen-multiply-spm07-final-new.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] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cd/51/cd513bbe4d2a8d479c5e70f389cffe9f4b57cc08.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1236246.1236283"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Dynamic manipulation of triangular B-splines

Hong Qin, Demetri Terzopoulos
<span title="">1995</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sl7g43a53farbgnszuvagjd5jm" style="color: black;">Proceedings of the third ACM symposium on Solid modeling and applications - SMA &#39;95</a> </i> &nbsp;
Triangular B-splines provide a unified representation scheme for all piecewise polynomials.  ...  Dynamic triangular B-splines provide a systematic and unified approach for a variety of solid modeling problems including shape blending, constraint-based design, and parametric design.  ...  Acknowledgments We are grateful to Professor Hans-Peter Seidel for kindly making available the software for triangular B-spline surfaces that he developed with Philip Fong.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/218013.218084">doi:10.1145/218013.218084</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/sma/QinT95.html">dblp:conf/sma/QinT95</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/aadkvyhr7rf2zhnzruekddjqny">fatcat:aadkvyhr7rf2zhnzruekddjqny</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20131002061637/http://alum.cs.sunysb.edu/~qin/research/qin-sm1995-camera-ready.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] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0f/d5/0fd5cd404e0e84ecc4bf42ed3c05d210d568dcc0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/218013.218084"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Generalized B-spline surfaces of arbitrary topology

Charles Loop, T. D. DeRose
<span title="1990-09-01">1990</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cyadgb7oezb4fbrq3h6xqzp4xi" style="color: black;">Computer graphics</a> </i> &nbsp;
In this paper, we present generalizations of biquadratic and bicubic B-spline surfaces that are capable of capturing surfaces of arbitrary topology (although restrictions are placed on the connectivity  ...  These results are obtained by relaxing the sufficient but not necessary smoothness constraints imposed by B-splines and through the use of an n-sided generalization of B6zier surfaces called Spatches.  ...  One of the methods is a generalization of biquadratic B-splines, the other a generalization of bicubic B-splines.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/97880.97917">doi:10.1145/97880.97917</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2lawxbwjabevhhzrkwnf5vxjr4">fatcat:2lawxbwjabevhhzrkwnf5vxjr4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170811203736/http://graphics.pixar.com/people/derose/publications/GeneralizedBSplines/paper.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] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9f/39/9f3997f1559b365710b6ec2312f553115154b80b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/97880.97917"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>
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