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Constrained Interpolation using Rational Cubic Spline with Three Parameters

Samsul Ariffin Abdul Karim, Mohammad Khatim Hasan, Ishak Hashim
<span title="2019-03-31">2019</span> <i title="Penerbit Universiti Kebangsaan Malaysia (UKM Press)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/j7jthqydjvevzjnbcyft3nmu7m" style="color: black;">Sains Malaysiana</a> </i> &nbsp;
The C 1 rational cubic spline function (cubic/quadratic) with three parameters is used to construct a constrained interpolating curve that lies below or above an arbitrary straight line or between two  ...  The data dependent sufficient conditions for the rational cubic interpolant bounded by two straight lines are derived on one parameter, while the other two are free parameters that will be useful for shape  ...  ACKNOWLEDGEMENTS This research was fully supported by Universiti Teknologi PETRONAS (UTP) through a research grant YUTP: 0153AA-H24 (Spline Triangulation for Spatial Interpolation of Geophysical Data).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.17576/jsm-2019-4803-23">doi:10.17576/jsm-2019-4803-23</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/chbet7t5efaxdgl5shkatt77xe">fatcat:chbet7t5efaxdgl5shkatt77xe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201211152603/http://www.ukm.my/jsm/pdf_files/SM-PDF-48-3-2019/23%20Samsul%20Ariffin%20Abdul%20Karim.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/54/a2/54a2cd8ba3eaefbe27df60ad7b442306ab6ee54f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.17576/jsm-2019-4803-23"> <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>

C2 Rational Cubic Ball Spline Functions

Wan Nurhadani Wan Jaafar, Muhammad Abbas, Abd Rahni Mt Piah
<span title="2016-05-10">2016</span> <i title="Indian Society for Education and Environment"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wffwpj3q45g5zfjzfeyagk5uea" style="color: black;">Indian Journal of Science and Technology</a> </i> &nbsp;
The alternative curve interpolations are developed using a piecewise C 2 rational cubic Ball spline function with three shape parameters in each subinterval.  ...  This study deals with the problems of shape preserving curves through positive curves through positive, constrained and convex data.  ...  Constrained-Preserving C 2 Rational Cubic Ball Interpolation In this section, we discuss the problem of shape preserving curve through constrained data using C 2 rational cubic Ball spline with three shape  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.17485/ijst/2015/v8i32/92137">doi:10.17485/ijst/2015/v8i32/92137</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lafwzsgldzchvciad7uqpc3fk4">fatcat:lafwzsgldzchvciad7uqpc3fk4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180720122712/http://www.indjst.org/index.php/indjst/article/download/92137/69221" 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 noreferrer" href="https://doi.org/10.17485/ijst/2015/v8i32/92137"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Shape Preserving Interpolation using Rational Cubic Spline

Samsul Ariffin Abdul Karim, Kong Voon Pang
<span title="2014-07-10">2014</span> <i title="Maxwell Scientific Publication Corp."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/itifugluyrhulokjxf64yqrfey" style="color: black;">Research Journal of Applied Sciences Engineering and Technology</a> </i> &nbsp;
This study proposes new C 1 rational cubic spline interpolant of the form cubic/quadratic with three shape parameters to preserves the geometric properties of the given data sets.  ...  The sufficient conditions ensure the existence of positive and constrained rational interpolant.  ...  MATERIALS AND METHODS Rational cubic spline interpolant: This section will introduce a new rational cubic spline interpolant with three parameters.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.19026/rjaset.8.956">doi:10.19026/rjaset.8.956</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gcd4ezodqjhbnnqm4ioba5mjva">fatcat:gcd4ezodqjhbnnqm4ioba5mjva</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200807182507/https://www.maxwellsci.com/announce/RJASET/8-167-178.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/63/fe/63fea7526ca3f0be03feb536f051520ec2aab6d0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.19026/rjaset.8.956"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Weighted rational cubic spline interpolation and its application

Qi Duan, K. Djidjeli, W.G. Price, E.H. Twizell
<span title="">2000</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;
Math. 6 (1) (1999) 203-215), the authors have discussed constrained interpolation problems by means of rational cubic spline interpolation with linear denominators, but there are still some cases in which  ...  In this paper, the weighted rational cubic spline interpolation has been constructed using the rational cubic spline with linear denominator and the rational cubic spline based on function values.  ...  Some examples of rational cubic spline interpolation with linear denominator are given in Figs. 1-6.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0377-0427(99)00336-2">doi:10.1016/s0377-0427(99)00336-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mm3t27qh4vgxvmidac2nsui5la">fatcat:mm3t27qh4vgxvmidac2nsui5la</a> </span>
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Data Visualization Using Rational Trigonometric Spline

Uzma Bashir, Jamaludin Md. Ali
<span title="">2013</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;
Positive, monotone, and constrained curve interpolating schemes, by using aC1piecewise rational cubic trigonometric spline with four shape parameters, are developed.  ...  Two of these shape parameters are constrained and the other two are set free to preserve the inherited shape features of the data as well as to control the shape of the curve.  ...  [2] visualized scientific data with shape preserving 1 rational cubic interpolation by developing positive, monotone, and constrained data preserving schemes.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2013/531497">doi:10.1155/2013/531497</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kg7rscc5xrg25j46776bundevm">fatcat:kg7rscc5xrg25j46776bundevm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170819110846/http://downloads.hindawi.com/journals/jam/2013/531497.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/ff/dd/ffdd6b11d2cf45b6ae08ead6b8c6cc4d43149c67.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2013/531497"> <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>

Constrained Control of C^2 Rational Interpolant with Multiple Shape Parameter

Mridula Dube, Meenal Priya Singh
<span title="2013-06-26">2013</span> <i title="Foundation of Computer Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b637noqf3vhmhjevdfk3h5pdsu" style="color: black;">International Journal of Computer Applications</a> </i> &nbsp;
A C 2 cubic rational spline with cubic numerator and linear denominator has been constructed .This rational spline belongs to C 2 in the interpolating interval.By selecting the suitable value of shape  ...  parameters,it is easy to find the constrains for the shape of interpolating curve to lie above,below or between the given straight lines.Also the error bound for interpolating function is discussed.  ...  M.Sarfraz [10] has worked on rational cubic spline interpolation with shape control.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/12368-8706">doi:10.5120/12368-8706</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o2px3n4pt5d5difzsds73zvl3q">fatcat:o2px3n4pt5d5difzsds73zvl3q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180603002706/https://research.ijcaonline.org/volume71/number7/pxc3888706.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/f9/24/f924415372555a36ed331d8f13fa495b61bb69b8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/12368-8706"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Construction new rational cubic spline with application in shape preservations

Samsul Ariffin Abdul Karim, Saurabh Pratap
<span title="2018-07-27">2018</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3traqp2nfrhnjbxyafpoa3gk6i" style="color: black;">Cogent Engineering</a> </i> &nbsp;
This study considers the construction a new C 1 rational cubic spline (cubic numerator and quadratic denominator) with three parameters.  ...  In order to use the proposed rational cubic spline for positivity preserving interpolation and constrained data that lie above any arbitrary straight line, the automatic choice of one parameter will be  ...  Citation information Cite this article as: Construction new rational cubic spline with application in shape preservations, Samsul Ariffin Abdul Karim, Cogent Engineering (2018), 5: 1505175.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/23311916.2018.1505175">doi:10.1080/23311916.2018.1505175</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/p5cn6rbkt5axpoa4js5ftvgj2u">fatcat:p5cn6rbkt5axpoa4js5ftvgj2u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200225115631/https://www.cogentoa.com/article/10.1080/23311916.2018.1505175.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 noreferrer" href="https://doi.org/10.1080/23311916.2018.1505175"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> tandfonline.com </button> </a>

POSITIVITY PRESERVING INTERPOLATION BY USING RATIONAL CUBIC BALL SPLINE

Samsul Ariffin Abdul Karim
<span title="2016-10-31">2016</span> <i title="Penerbit UTM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xgym76lve5dw7bbeqkndyfil2u" style="color: black;">Jurnal Teknologi</a> </i> &nbsp;
This paper discusses the positivity preserving by using rational cubic Ball interpolant of the form cubic/quadratic with two parameters.  ...  From numerical results, the rational cubic Ball spline with two parameters gives smooth interpolating positive curves as well as visually pleasing for computer graphics visualization.  ...  For instance Karim [14] proposed rational cubic Ball interpolant with two parameters.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.11113/jt.v78.8107">doi:10.11113/jt.v78.8107</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5qmqe2i32jge7ggjnul4k5s6kq">fatcat:5qmqe2i32jge7ggjnul4k5s6kq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180720162056/https://jurnalteknologi.utm.my/index.php/jurnalteknologi/article/download/8107/5931" 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/79/04/7904e5996190e63b89295c80c6be5f91209ae0b3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.11113/jt.v78.8107"> <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>

Rational Trigonometric Interpolation and Constrained Control of the Interpolant Curves

S SRana, Mridula Dube, Preeti Tiwari
<span title="2013-04-18">2013</span> <i title="Foundation of Computer Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b637noqf3vhmhjevdfk3h5pdsu" style="color: black;">International Journal of Computer Applications</a> </i> &nbsp;
This rational cubic trigonometric spline is used to constrain the shape of the interpolant such as to force it to be in the given region by selecting suitable parameters.  ...  In the present paper a new method is developed for smooth rational cubic trigonometric interpolation based on values of function which is being interpolated.  ...  A 1 C RATIONAL CUBIC TRIGONOMETRIC SPLINE INTERPOLATION i i i i i i i p t f U Vf                     (2) 1} , 0,1,..., = : ) , {(  n n i f t i i with ) ( ) ( ) ( i i t g t  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/11387-6671">doi:10.5120/11387-6671</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/khmhbmrl2bcp3eqqwev5bwpcuq">fatcat:khmhbmrl2bcp3eqqwev5bwpcuq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180722145242/https://research.ijcaonline.org/volume67/number4/pxc3886671.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/1d/ea/1dea7e989f27f1e22bece300de7578c1faf8346f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/11387-6671"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

TOWARDS A MORE GENERAL TYPE OF UNIVARIATE CONSTRAINED INTERPOLATION WITH FRACTAL SPLINES

A. K. B. CHAND, P. VISWANATHAN, K. M. REDDY
<span title="">2015</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wun4xe4i4vdylmx62cwxbptp5e" style="color: black;">Fractals</a> </i> &nbsp;
Recently, in [Electronic Transaction on Numerical Analysis, 41 (2014), pp. 420-442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal  ...  The main goal of the current article is to embark on univariate constrained fractal interpolation that is more general than what was considered so far.  ...  Constrained Interpolation with Rational Cubic Spline FIF This section features a systematic discussion of selection of parameters involved in the rational cubic spline FIF, focusing on its applicability  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0218348x15500401">doi:10.1142/s0218348x15500401</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sjj2cwsktbephf75undflhpobu">fatcat:sjj2cwsktbephf75undflhpobu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200930200903/https://arxiv.org/pdf/1503.08116v1.pdf" title="fulltext PDF download [not primary version]" 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] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a3/97/a397c33b0f5680e53a027c50f13c0afd69bd305a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0218348x15500401"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> worldscientific.com </button> </a>

Shape Preserving Data Interpolation Using Rational Cubic Ball Functions

Ayser Nasir Hassan Tahat, Abd Rahni Mt Piah, Zainor Ridzuan Yahya
<span title="">2015</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;
A smooth curve interpolation scheme for positive, monotone, and convex data is developed. This scheme uses rational cubic Ball representation with four shape parameters in its description.  ...  [5] constructed a 1 rational cubic Ball interpolant with four shape parameters to preserve the shape of positive and constrained data.  ...  (b) Monotonicity preserving interpolation curve with = 0.05, = 0.5. (c) Monotone curve using rational cubic spline Figure 3 : 3 (a) Rational cubic Ball curve.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2015/908924">doi:10.1155/2015/908924</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/f5qsetedynekldcyjszk7buzlm">fatcat:f5qsetedynekldcyjszk7buzlm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200215084245/http://downloads.hindawi.com/journals/jam/2015/908924.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/d2/17d22f6cdff97fcd201d75ce7c37374a26541041.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2015/908924"> <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>

Shape Preserving Interpolation UsingC2Rational Cubic Spline

Samsul Ariffin Abdul Karim, Kong Voon Pang
<span title="">2016</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;
This paper discusses the construction of newC2rational cubic spline interpolant with cubic numerator and quadratic denominator.  ...  The idea has been extended to shape preserving interpolation for positive data using the constructed rational cubic spline interpolation. The rational cubic spline has three parametersαi,βi, andγi.  ...  Figure 1 : 1 Interpolating curve for data inTable 1. (a) Default 1 cubic spline with = = 1 and = 0. (b) 1 rational cubic spline with = = 1 and = 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2016/4875358">doi:10.1155/2016/4875358</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ijmu4h3anneufigq4oshoci3dm">fatcat:ijmu4h3anneufigq4oshoci3dm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190222122120/http://pdfs.semanticscholar.org/3864/ea77fb86aeaaeb5f3e35626690dde50a7190.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/38/64/3864ea77fb86aeaaeb5f3e35626690dde50a7190.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2016/4875358"> <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>

A Rational Spline for Preserving the Shape of Positive Data

Muhammad Abbas, Ahmad Abd. Majid, Jamaludin Md. Ali
<span title="">2013</span> <i title="IACSIT Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7wdo44rafbg5rfskrbd6snu7yy" style="color: black;">International Journal of Computer and Electrical Engineering</a> </i> &nbsp;
A rational cubic spline function with three shape parameters has been developed.  ...  It was extended to bi-cubic partially blended rational function with eight shape parameters in [4] to preserve the positivity of positive 3D data and a surface constrained by a plane through constrained  ...  Positivity-preserving curve using rational cubic spline Interpolation with 0.5 and 0.5 ii uv  (b) when 0.1 and 0.1 ii uv     Fig . 3 (a) Cubic Hermite Spline curve (b) Positive rational cubic spline  ... 
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Shape-preserving curve interpolation

Muhammad Sarfraz, Malik Zawwar Hussain, Maria Hussain
<span title="">2012</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/y4k3i2fvabgarkvywismzvy23a" style="color: black;">International Journal of Computer Mathematics</a> </i> &nbsp;
Figure 8 . 8 The rational cubic function with α i = δ i = 0.05 and r i = s i = 0.1. Figure 10 . 10 The rational cubic function with α i = δ i = 2 and n i = o i = 1.9.  ...  Figure 1 . 1 The rational cubic function(3)with α i = 1, β i = 2, γ i = 100 and δ i = 1. Figure 2 . 2 The rational cubic function(3)with α i = 1, β i = 100, γ i = 2 and δ i = 1.  ...  rational cubic function has been developed to preserve the shape of positive, monotone and convex data.  ... 
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Data Visualization using Spline Functions

Maria Hussain, Malik Zawwar Hussain, Muhammad Sarfraz
<span title="2013-10-21">2013</span> <i title="Pakistan Journal of Statistics and Operation Research"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xoyy36qwhrh3vexanflvx76xia" style="color: black;">Pakistan Journal of Statistics and Operation Research</a> </i> &nbsp;
A two parameter family of 1 C rational cubic spline functions is presented for the graphical representation of shape preserving curve interpolation for shaped data.  ...  The approximation order of the proposed rational cubic function is also investigated and is found to be   3 i O h .  ...  Figure 12 . 12 Constrained rational cubic spline. . 2 . 2 Consider another positive data set of Figure 13 . 13 Cubic Hermite spline. Figure 14 . 14 Constrained rational cubic spline.  ... 
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