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Interpolatory subdivision schemes with infinite masks originated from splines

Valery A. Zheludev
<span title="">2006</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ld5cu4nusveezeot3mom6y4uku" style="color: black;">Advances in Computational Mathematics</a> </i> &nbsp;
A generic technique for the construction of diversity of interpolatory subdivision schemes on the base of polynomial and discrete splines is presented in the paper.  ...  The devised schemes have rational symbols and infinite masks but they are competitive (regularity, speed of convergence, computational complexity) with the schemes that have finite masks.  ...  A seeming drawback in using interpolatory splines is that it requires a convolution of the data with the infinite mask.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10444-004-4149-6">doi:10.1007/s10444-004-4149-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3bpez2634bh2jlh56xil65baf4">fatcat:3bpez2634bh2jlh56xil65baf4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809142025/http://www.cs.tau.ac.il/~zhel/PS/SubdJ.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/8a/28/8a28b1fa253ce73e0ee1af2dcbdc6bc817974ae4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10444-004-4149-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

TERNARY INTERPOLATORY SUBDIVISION SCHEMES ORIGINATED FROM SPLINES

AMIR Z. AVERBUCH, VALERY A. ZHELUDEV, GARY B. FATAKHOV, EDUARD H. YAKUBOV
<span title="">2011</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nt43ge63cnbllg3y2b3kw6sx4a" style="color: black;">International Journal of Wavelets, Multiresolution and Information Processing</a> </i> &nbsp;
A generic technique for construction of ternary interpolatory subdivision schemes, which is based on polynomial and discrete splines, is presented. These schemes have rational symbols.  ...  The ternary subdivision schemes, whose construction is based on continuous splines, become tools for fast computation of interpolatory splines of arbitrary order at triadic rational points.  ...  From Eq. (3.17), Ternary Interpolatory Subdivision Schemes Originated from Splines 6295.2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0219691311004249">doi:10.1142/s0219691311004249</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qbdh7z4bdzbwpczcgwryloqoja">fatcat:qbdh7z4bdzbwpczcgwryloqoja</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120124190915/http://www.cs.tau.ac.il/~amir1/PS/Ternary.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/a4/bc/a4bcdfc9ac9d3c086067ee7bea57c15a4e0fc736.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0219691311004249"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> worldscientific.com </button> </a>

From approximating to interpolatory non-stationary subdivision schemes with the same generation properties [article]

Costanza Conti, Luca Gemignani, Lucia Romani
<span title="2010-04-19">2010</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we describe a general, computationally feasible strategy to deduce a family of interpolatory non-stationary subdivision schemes from a symmetric non-stationary, non-interpolatory one satisfying  ...  For the so obtained interpolatory schemes we prove that they are capable of reproducing the same exponential polynomial space as the one generated by the original approximating scheme.  ...  Any subdivision scheme is defined by an infinite sequence of coefficients collected in the so called refinement masks {a (k) , k ≥ 0}.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1004.3232v1">arXiv:1004.3232v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yz5tmhat6ngrbhxk2ozjyxsc2u">fatcat:yz5tmhat6ngrbhxk2ozjyxsc2u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171004104943/https://core.ac.uk/download/pdf/2118485.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/80/0b/800bd25bb0c6fb92ecaa165e113693775355e972.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1004.3232v1" 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>

From approximating to interpolatory non-stationary subdivision schemes with the same generation properties

Costanza Conti, Luca Gemignani, Lucia Romani
<span title="2011-07-21">2011</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ld5cu4nusveezeot3mom6y4uku" style="color: black;">Advances in Computational Mathematics</a> </i> &nbsp;
In this paper we describe a general, computationally feasible strategy to deduce a family of interpolatory non-stationary subdivision schemes from a symmetric non-stationary, non-interpolatory one satisfying  ...  For the so obtained interpolatory schemes we prove that they are capable of reproducing the same exponential polynomial space as the one generated by the original approximating scheme.  ...  by the interpolatory scheme is the same function space generated by the approximating scheme it is originated from.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10444-011-9175-6">doi:10.1007/s10444-011-9175-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pdh62mifcnf5xo3iekp574zrui">fatcat:pdh62mifcnf5xo3iekp574zrui</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829232851/https://boa.unimib.it/retrieve/handle/10281/17634/21362/quaderno10-2010.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/f1/0a/f10a7fdf7b263c891ac996d1575cde84af7ba70a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10444-011-9175-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

From symmetric subdivision masks of Hurwitz type to interpolatory subdivision masks

Costanza Conti, Luca Gemignani, Lucia Romani
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wsx3rzhpingfvewcn5nwhfkq3e" style="color: black;">Linear Algebra and its Applications</a> </i> &nbsp;
This brings back to a polynomial equation involving the symbol of the non-interpolatory scheme we start with.  ...  In this paper we present a general strategy to deduce a family of interpolatory masks from a symmetric Hurwitz non-interpolatory one.  ...  This brings back to a polynomial equation involving the symbol of the non-interpolatory subdivision scheme we start with.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.laa.2009.06.037">doi:10.1016/j.laa.2009.06.037</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x62czhprxjegtkp63ma2bjtxp4">fatcat:x62czhprxjegtkp63ma2bjtxp4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190413070720/https://core.ac.uk/download/pdf/82816473.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/a5/39/a539daca9350f690b764438c6affd177a17d82ec.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.laa.2009.06.037"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Exponential pseudo-splines: Looking beyond exponential B-splines

C. Conti, L. Gemignani, L. Romani
<span title="">2016</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7a65khxirfbfljbnqng5zzeslu" style="color: black;">Journal of Mathematical Analysis and Applications</a> </i> &nbsp;
This extends the analogous property of primal pseudo-spline stationary subdivision schemes.  ...  schemes.  ...  4-point scheme with k-level mask . . .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jmaa.2016.02.019">doi:10.1016/j.jmaa.2016.02.019</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q7opswcvjrfzzjzw5lqe46x4eu">fatcat:q7opswcvjrfzzjzw5lqe46x4eu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922011305/https://arpi.unipi.it/retrieve/handle/11568/774984/74776/CGR_3dic15.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/90/85/90853627452fc341b2c71022e9f161cde7af9ec9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jmaa.2016.02.019"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Subdivision surfaces for CAD—an overview

Weiyin Ma
<span title="">2005</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;
This paper provides an overview of subdivision surfaces with a particular emphasis on schemes generalizing splines. Some common issues on subdivision surface modelling are addressed.  ...  Subdivision surfaces refer to a class of modelling schemes that define an object through recursive subdivision starting from an initial control mesh.  ...  Wu for the implementation of several subdivision schemes at CityU.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cad.2004.08.008">doi:10.1016/j.cad.2004.08.008</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bb7q74g5xjab5i2qsbc2cmnu4q">fatcat:bb7q74g5xjab5i2qsbc2cmnu4q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170705074635/http://kowon.dongseo.ac.kr/~lbg/web_lecture/grapprog/20122/WeiyinMa.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/cb/8f/cb8f6003d3b704b91e343ae77a31a1ab7ea0d9e4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cad.2004.08.008"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

WAVELET TRANSFORMS GENERATED BY SPLINES

AMIR Z. AVERBUCH, VALERY A. ZHELUDEV
<span title="">2007</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nt43ge63cnbllg3y2b3kw6sx4a" style="color: black;">International Journal of Wavelets, Multiresolution and Information Processing</a> </i> &nbsp;
The wavelet transforms are constructed from various types of interpolatory and quasi-interpolatory splines.  ...  The transforms use finite and infinite impulse response filters and are implemented in a fast lifting mode. We analyze properties of the generated wavelets.  ...  We consider a subdivision scheme S a with symbol a(z) = 1 + z −1 U 2r i (z 2 ) derived from an interpolatory spline of degree 2r.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0219691307001756">doi:10.1142/s0219691307001756</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ks2bgqohlvbc7mhdxq7dhs6bvu">fatcat:ks2bgqohlvbc7mhdxq7dhs6bvu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20060603162204/http://www.cs.tau.ac.il:80/~zhel/PS/splitr3AA.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/8c/4d/8c4d549365c52874928205b677936c683f47dda2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0219691307001756"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> worldscientific.com </button> </a>

Multivariate refinable Hermite interpolant

Bin Han, Thomas P.-Y. Yu, Bruce Piper
<span title="2003-12-22">2003</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5bz4zmidbngqxk6yv4msbkm54u" style="color: black;">Mathematics of Computation</a> </i> &nbsp;
Some of the Hermite interpolants constructed here are related to well-known spline interpolation schemes developed in the computer-aided geometric design community (e.g., the Powell-Sabin scheme).  ...  The bivariate symmetric refinable Hermite interpolants constructed in this article, along with algorithmic developments elsewhere, give an application of vector refinability to subdivision surfaces.  ...  Armed with our construction recipe, the number of new schemes one can create is, of course, infinite.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0025-5718-03-01623-5">doi:10.1090/s0025-5718-03-01623-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/t5lj3gv3ivbknmksrjgwhjz6e4">fatcat:t5lj3gv3ivbknmksrjgwhjz6e4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170827200136/http://www.ams.org/journals/mcom/2004-73-248/S0025-5718-03-01623-5/S0025-5718-03-01623-5.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/d9/a8d91b8ba5ecf60a88d9cd0e468d7d3116a560d7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0025-5718-03-01623-5"> <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>

Manifold-valued subdivision schemes based on geodesic inductive averaging [article]

Nira Dyn, Nir Sharon
<span title="2016-03-01">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Subdivision schemes have become an important tool for approximation of manifold-valued functions.  ...  In this paper, we describe a construction of manifold-valued subdivision schemes for geodesically complete manifolds.  ...  Many families of subdivision schemes, e.g. [4] , consist of subdivision schemes with symmetric masks, namely with mask coefficients satisfying a i = a −i , i ∈ Z.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1407.8361v2">arXiv:1407.8361v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tsefchui5jcbvhnbl2kav7fime">fatcat:tsefchui5jcbvhnbl2kav7fime</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200901140759/https://arxiv.org/pdf/1407.8361v2.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/af/17/af170ec188244cbb3e6861f10641c2dd3482f006.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1407.8361v2" 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>

Exponential Splines and Pseudo-Splines: Generation versus reproduction of exponential polynomials [article]

Costanza Conti, Luca Gemignani, Lucia Romani
<span title="2014-11-13">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The members of this family are known in the literature with the name of pseudo-splines.  ...  One important property of subdivision schemes is their capability of exactly reproducing in the limit specific types of functions from which the data is sampled.  ...  2 z 2 − 9 4v (k) z + 3+16(v (k) ) 2 4(v (k) ) 2 − 9 4v (k) z −1 + 3 8(v (k) ) 2 z −2 and thus the resulting exponential pseudo spline is an interpolatory 6-point scheme with k-level mask (7.9) 3 256(v  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1404.6624v2">arXiv:1404.6624v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nevjxpga45ga5lztajw6b57t5e">fatcat:nevjxpga45ga5lztajw6b57t5e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191025102538/https://arxiv.org/pdf/1404.6624v2.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/27/ef/27ef4e38f0971f8a80dfabb59f883ada787d296a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1404.6624v2" 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 New Method for the Analysis of Univariate Nonuniform Subdivision Schemes

Nira Dyn, David Levin, Jungho Yoon
<span title="2014-07-08">2014</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/vmvnzyf55regxlw74fpri5p4qe" style="color: black;">Constructive approximation</a> </i> &nbsp;
The analysis involves ideas from the theory of asymptotically equivalent subdivision schemes and non-uniform Laurent polynomial representation together with a new perturbation result.  ...  Application of the new method is presented for the analysis of interpolatory subdivision schemes based upon extended Chebyshev systems and for a class of smoothly varying schemes.  ...  An important class of schemes with Property B are smoothly varying perturbations of spline subdivision schemes.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00365-014-9247-1">doi:10.1007/s00365-014-9247-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fqm3dtvybjaqhmr24dr6ws3bou">fatcat:fqm3dtvybjaqhmr24dr6ws3bou</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809114721/http://math.ewha.ac.kr/~yoon/approx/DLY-CA.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/41/5c/415c235936ce9b96b233695dcb7f89fcf46626a9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00365-014-9247-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Surface Design using Locally Interpolating Subdivision Schemes

Adi Levin
<span title="">2000</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ajfp2t4ucrcbxh6e6fdg6pwf74" style="color: black;">Journal of Approximation Theory</a> </i> &nbsp;
Our schemes differ from the known interpolatory subdivision schemes, in that only some of the original control points are interpolated, and not the control points in every level.  ...  These new schemes are combinations of a non-interpolatory schemes with different local schemes near some of the original control points.  ...  We will answer this questions in the restricted case where the uniform scheme away from the origin, S, has positive stencil coefficients (which is the case for B-spline and box spline subdivision schemes  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/jath.1999.3444">doi:10.1006/jath.1999.3444</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x44ytzfk65et5drnrohfsprh3u">fatcat:x44ytzfk65et5drnrohfsprh3u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171001125729/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/a3a/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDAyMTkwNDU5OTkzNDQ0NQ%3D%3D.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/97/f7/97f7362eeaaad1a60fecee08378ddb0562642a9a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/jath.1999.3444"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Non-uniform interpolatory curve subdivision with edge parameters built upon compactly supported fundamental splines

Carolina Vittoria Beccari, Giulio Casciola, Lucia Romani
<span title="2011-03-30">2011</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zhnaqo2cv5epniuk4xnpmuqb74" style="color: black;">BIT Numerical Mathematics</a> </i> &nbsp;
In this paper we present a family of Non-Uniform Local Interpolatory (NULI) subdivision schemes, derived from compactly supported interpolatory fundamental splines with non-uniform knots (NULIFS).  ...  This subdivision scheme has all the fundamental features of the quadratic fundamental spline basis it is originated from, namely compact support, C 1 smoothness, second order polynomials reproduction and  ...  Conclusions and future work We have presented a family of non-uniform interpolating subdivision schemes originated from order-n locally supported fundamental splines with arbitrary knots.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10543-011-0328-2">doi:10.1007/s10543-011-0328-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3wace5thdfgrlkbm5aj2dnqodi">fatcat:3wace5thdfgrlkbm5aj2dnqodi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808144901/http://amsacta.unibo.it/2947/1/BCR_BIT.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/2e/84/2e8409792badfd25e8726b4b22861896956f3794.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10543-011-0328-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A multiresolution framework for variational subdivision

Leif Kobbelt, Peter Schröder
<span title="1998-10-01">1998</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cqrugwalkvcezgalqorn4fwnuu" style="color: black;">ACM Transactions on Graphics</a> </i> &nbsp;
a subdivision scheme.  ...  We present several examples of such schemes including one that reproduces non-uniform interpolating cubic splines.  ...  This research was supported in part through grants from the Intel Corporation, the Charles Lee Powell Foundation, the Sloan Foundation, and an NSF CAREER award (ASC-9624957) to the second author.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/293145.293146">doi:10.1145/293145.293146</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c5x4vcjevjcoriuxxe57u6iote">fatcat:c5x4vcjevjcoriuxxe57u6iote</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20100611211630/http://www.multires.caltech.edu/pubs/variation.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/a9/84/a98418090fe319d481072fbc5aacf4142ae42449.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/293145.293146"> <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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