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Shape Designing of Engineering Images Using Rational Spline Interpolation

Muhammad Sarfraz, Munaza Ishaq, Malik Zawwar Hussain
<span title="">2015</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nazmmg5rvjamleddfnihvz3cai" style="color: black;">Advances in Materials Science and Engineering</a> </i> &nbsp;
The method provides effective results together with the effects of derivatives and shape parameters on the shape of the curves in a local and global manner.  ...  In modern days, engineers encounter a remarkable range of different engineering problems like study of structure, structure properties, and designing of different engineering images, for example, automotive  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2015/260587">doi:10.1155/2015/260587</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vznrng4alrexjn62ho4tvhsdki">fatcat:vznrng4alrexjn62ho4tvhsdki</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190303234715/http://pdfs.semanticscholar.org/b4d5/1bd77df8d9258e47dd438be2f4aa77c17dd6.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/b4/d5/b4d51bd77df8d9258e47dd438be2f4aa77c17dd6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2015/260587"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> hindawi.com </button> </a>

Geometric construction of quintic parametric B-splines

Isabella Cravero, Carla Manni, M. Lucia Sampoli
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/av75skmu6neednu63f27tpk7qu" style="color: black;">Journal of Computational and Applied Mathematics</a> </i> &nbsp;
The aim of this paper is to present a new class of B-spline-like functions with tension properties.  ...  The construction is based on a geometric approach which uses parametric curves with piecewise quintic components.  ...  We have described the construction and salient properties of C 3 and C 4 B-spline-like functions with shape parameters.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cam.2007.10.047">doi:10.1016/j.cam.2007.10.047</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/w5hkbnp6szcm5le6hv34de2jpm">fatcat:w5hkbnp6szcm5le6hv34de2jpm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190330082707/https://core.ac.uk/download/pdf/82629108.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/59/8c591951bd4174ce6edd1dfe36e22cd8685214a3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cam.2007.10.047"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

A Rational Quadratic Trigonometric Spline (RQTS) as a Superior Surrogate to Rational Cubic Spline (RCS) with the Purpose of Designing

Shamaila Samreen, Muhammad Sarfraz, Nabila Jabeen, Saad Althobaiti, Abdullah Mohamed
<span title="2022-04-14">2022</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/smrngspzhzce7dy6ofycrfxbim" style="color: black;">Applied Sciences</a> </i> &nbsp;
The established method yields a curve with the best geometric properties, such as convex hull, partition of unity, affine invariance, and diminishing variation.  ...  The parameters in the suggested method's construction are helpful for several critical shape features such as local, global, and biased tension qualities, which give good control over the curve and allow  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/app12083992">doi:10.3390/app12083992</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d4q625ibpnfdfcbgmte3tkyhw4">fatcat:d4q625ibpnfdfcbgmte3tkyhw4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220423022623/https://mdpi-res.com/d_attachment/applsci/applsci-12-03992/article_deploy/applsci-12-03992-v2.pdf?version=1650013878" 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/de/ca/decadfcfefefb5ba3b3d0c4b26d84352444f4db6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/app12083992"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> mdpi.com </button> </a>

A sinusoidal polynomial spline and its Bezier blended interpolant

K.F. Loe
<span title="">1996</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/av75skmu6neednu63f27tpk7qu" style="color: black;">Journal of Computational and Applied Mathematics</a> </i> &nbsp;
The blending factor has the effect similar to the "tension" control of tension splines.  ...  Functional polynomials composed of sinusoidal functions are introduced as basis functions to construct an interpolatory spline.  ...  Goto for his hospitality when I was on leave in the RIKEN Goto Laboratory where part of the work was done. I also wish to thank C.L. Tai for comments and beneficial discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0377-0427(95)00241-3">doi:10.1016/0377-0427(95)00241-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/muuzxj3vnbbcxgoc6xlvsytvhy">fatcat:muuzxj3vnbbcxgoc6xlvsytvhy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190225122535/https://core.ac.uk/download/pdf/82819513.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/17/8b/178b378f0a84f2ff647e620d54fef05e1d2fcce7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0377-0427(95)00241-3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

PHYSICS BASED GEOMETRIC DESIGN

HONG QIN
<span title="">1996</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wkp6ef7uxzdjvbwvq2oe42h5xe" style="color: black;">International journal of shape modeling</a> </i> &nbsp;
We demonstrate that, among various geometric representations, NURBS have become an industrial standard primarily because of their many superior properties.  ...  D-NURBS can unify the features of the industry-standard NURBS geometry with the many demonstrated conveniences of interaction within the new physics-based design framework.  ...  Geometric and Variational Splines The main task in CAGD is to smoothly construct complex shapes with a parsimonious number of curve spans or surface patches.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0218654396000099">doi:10.1142/s0218654396000099</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ctnoubb7vvaubpbxuiev5dpmpe">fatcat:ctnoubb7vvaubpbxuiev5dpmpe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110401172833/http://www.cs.sunysb.edu/~vislab/papers/ijsm1996-modeling-survey.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/88/32/8832262492a91fceac897856f3586a997bddf56c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0218654396000099"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> worldscientific.com </button> </a>

v-quaternion splines for the smooth interpolation of orientations

G.M. Nielson
<span title="">2004</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hjrujdrg7zaghbdsp5pdzq7cmm" style="color: black;">IEEE Transactions on Visualization and Computer Graphics</a> </i> &nbsp;
It is based upon quaternions and a particular construction of -spline curves.  ...  The new method has tension parameters and variable knot (time) spacing which both prove to be effective in designing and controlling key frame animations.  ...  ACKNOWLEDGMENTS The author wishes to acknowledge the support of the US Office of Naval Research (N00014-97-1-0243 and N00014-00-1-0281), the US National Science Foundation (NSF IIS-9980166 and ACI-0083609  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tvcg.2004.1260774">doi:10.1109/tvcg.2004.1260774</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/15384647">pmid:15384647</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7235vuat4fgpxemi3ysyiduff4">fatcat:7235vuat4fgpxemi3ysyiduff4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20090115234442/http://www.ann.jussieu.fr/~frey/papers/scivi/Nielson%20G.M.,%20nu%20Quaternion%20splines%20for%20the%20smooth%20interpolation%20of%20orientations.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/78/fb/78fbd5cb184135e357110cc36ec1480b7cbb45cc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tvcg.2004.1260774"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application

Yuanpeng Zhu, Xuli Han, Shengjun Liu
<span title="">2014</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xdzjuti5nzejrghubfpezefpqi" style="color: black;">Journal of Applied Mathematics</a> </i> &nbsp;
The new basis is applied to generate a class ofC1continuous quartic rational Hermite interpolation splines with local tension shape parameters.  ...  The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing aC1positivity- or monotonicity- preserving interpolation spline.  ...  By using the new basis, a class of 1 continuous quartic rational Hermite interpolation spline with local tension shape parameters is also constructed.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2014/857840">doi:10.1155/2014/857840</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4i635b46n5bmbkuuwzdy5gtiae">fatcat:4i635b46n5bmbkuuwzdy5gtiae</a> </span>
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Page 505 of Mathematical Reviews Vol. , Issue 90A [page]

<span title="">1990</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
v-splines with the same shape control param- eters of the network curves.  ...  These results extend recent work on beta-splines and nu-splines, which are used as design tools in computer-aided geometric design of free form curves and surfaces.  ... 
<span class="external-identifiers"> </span>
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Uniform hyperbolic polynomial B-spline curves

Yonggang Lü, Guozhao Wang, Xunnian Yang
<span title="">2002</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;
Hyperbolic polynomial B-splines share most of the properties as those of the B-splines in the polynomial space.  ...  Hyperbolic polynomial B-splines can take care of freeform curves as well as some remarkable curves such as the hyperbola and the catenary.  ...  This work was partial supported by the National Natural Science Foundation of China (Grant No. 19971079) and Foundation of State Key Basic Research 973 Development Programming Item of China (No.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0167-8396(02)00092-4">doi:10.1016/s0167-8396(02)00092-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wznm75m6j5bvfg6665bs5gp2iq">fatcat:wznm75m6j5bvfg6665bs5gp2iq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170811071031/http://www.math.zju.edu.cn/yxn/papers/hB-spline.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/5b/97/5b972b4aeb33c501c034964ceca40c1c7d025c5b.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(02)00092-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Modeling of Objects Using Conic Splines

Muhammad Sarfraz, Malik Z. Hussain, Munazah Ishaq
<span title="">2013</span> <i title="Scientific Research Publishing, Inc,"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/siea63ugazhotdhlrexmuoemia" style="color: black;">Journal of Software Engineering and Applications</a> </i> &nbsp;
JSEA 68 , (c) Rational quadratic spline for 3  i γ , (d) Rational quadratic spline, with global shape control, for 5,10, 50  i γ and , (e) Rational quadratic spline, with local shape control, for 1,  ...  The 2D curve model has then been extended for the designing of 3D objects to produce fancy objects.  ...  It is in continuation of the spline introduced in [27] . Spline curves and surfaces play significant role in the construction and re-construction of objects.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4236/jsea.2013.63b015">doi:10.4236/jsea.2013.63b015</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/l4pmi3g3qbesdhemsicqzjdul4">fatcat:l4pmi3g3qbesdhemsicqzjdul4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170923114607/http://file.scirp.org/pdf/JSEA_2013041109544571.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/db/a6/dba6fa719ff5518d54adb33567d15f74b1e35445.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4236/jsea.2013.63b015"> <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>

Page 2691 of Mathematical Reviews Vol. , Issue 99d [page]

<span title="">1991</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The algebraic splines, or A-splines, consid- ered here consist of convex arcs of cubic algebraic curves, joined with G?-continuity.  ...  Summary: “Using piecewise affine transformations, a C' parame- ter spline curve can be produced from an arbitrary C' curve, each segment has the same geometric properties under affine transfor- mation.  ... 
<span class="external-identifiers"> </span>
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Page 2192 of Mathematical Reviews Vol. , Issue 91D [page]

<span title="">1991</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Some important properties of Bézier curves and B-splines, such as the convexity and variation-diminishing properties, the approximation properties and the envelopes of Bézier curves, are discussed.  ...  The methods of the classification of cubic curves can be used not only to analyse the curves but also to control the curves when they are constructed.  ... 
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A rational cubic spline with tension

John A. Gregory, Muhammad Sarfraz
<span title="">1990</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;
A rational cubic spline curve is described which has tension control parameters for manipulating the shape of the curve.  ...  The spline is presented in both interpolatory and rational B-spline forms, and the behaviour of the resulting representations is analysed with respect to variation of the control parameters.  ...  Acknowledgements The authors are pleased to acknowledge helpful discussions with N. Dyn and D. Levin in the development of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0167-8396(90)90017-l">doi:10.1016/0167-8396(90)90017-l</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yuczu7ir6bawtcirotx7cvfswq">fatcat:yuczu7ir6bawtcirotx7cvfswq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808193415/http://dspace.brunel.ac.uk/bitstream/2438/2340/1/TR_03_89.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/f2/fb/f2fba841de5f47edda448926f2d98ef36c69470f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0167-8396(90)90017-l"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Page 6523 of Mathematical Reviews Vol. , Issue 87k [page]

<span title="">1987</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
This fact is illustrated in the paper: The first three chapters contain a treatment of basic properties, and these properties are sufficient to address geometric concepts in order to formulate algorithms  ...  Summary: “An extension of Overhauser’s parabolic blending in- terpolation is given by introducing a tension-like behaviour to the interpolation curves.  ... 
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The singular cases for γ-spline interpolation

G. Farin, D. Hansford, A. Worsey
<span title="">1990</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;
Comparisons are made to the behavior of the interpolating v-spline.  ...  We derive a natural extension of Boehm's free-form y-spline, the G* interpolating y-spline. Primarily, the conditions under which singularities in the spline formulation occur are investigated.  ...  Geometric analysis of the singularities From (1) and (2) the construction of the free-form curve involved divisions which may result in singularities.  ... 
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