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C1 Hermite interpolation using MPH quartic

Gwang-Il Kim, Min-Ho Ahn
<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;
In this paper, we study the C 1 Hermite interpolation problem using Minkowski Pythagorean Hodograph (MPH) quartics in R 2,1 .  ...  We present two schemes for this interpolation problem: one is a subdivision scheme using direct C 1 interpolation and the other is a two step scheme using a new concept, C 1/2 interpolation.  ...  Two step C 1 interpolation using MPH quartic As we know, one step C 1 Hermite interpolation using MPH quartic is not possible in general.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cagd.2003.06.001">doi:10.1016/j.cagd.2003.06.001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dbnwvvdwszf35fzmu6fdail4l4">fatcat:dbnwvvdwszf35fzmu6fdail4l4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809124638/http://fractal.dam.fmph.uniba.sk/~chalmo/GM/cagd5-110304.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/7c/24/7c247e90cafdab6efeead5a563c52524db87c287.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cagd.2003.06.001"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Geometry of root-related parameters of PH curves

Min-Ho Ahn, Gwang-Il Kim, Chung-Nim Lee
<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/deqidnohqjdu7gsln5vdm6obre" style="color: black;">Applied Mathematics Letters</a> </i> &nbsp;
The loci of root-related parameters of PH curves show us very interesting geometric properties. They include regular 2n + 1-gon and isosceles triangles with the ratio of sides n : 1 : n. (~)  ...  Thus, we are seeking a regular PH quintic curve (~(t) such that a(O) =0, ~'(0) =vo, Hermite Interpolation with Higher Degree Curves We can solve the C 1 Hermite interpolation problem using PH curves  ...  We also solved C 1 Hermite interpolation in our scheme and get four interpolants. .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0893-9659(02)00143-x">doi:10.1016/s0893-9659(02)00143-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/l57a2ks62naevat65dar43az5u">fatcat:l57a2ks62naevat65dar43az5u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190416220021/https://core.ac.uk/download/pdf/82489473.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/d6/2d/d62defb5cf4a91e4959a8fdb94efbbd5a4e2ec18.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0893-9659(02)00143-x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

C 1 Hermite interpolation by Pythagorean hodograph quintics in Minkowski space

Jiří Kosinka, Bert Jüttler
<span title="2007-11-09">2007</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;
We construct MPH quintics which interpolate two points with associated first derivative vectors and analyze the properties of the system of solutions, including the approximation order of the 'best' interpolant  ...  Among them, Minkowski Pythagorean hodograph (MPH) curves correspond to domains where both the boundaries and their offsets admit rational parameterizations [4, 13] .  ...  A C 1/2 interpolation scheme using MPH quartics has been discussed in [12] . C 2 Hermite interpolation using PH curves of degree 9 in R 3 gives a fourparameter family of interpolants [17] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10444-007-9059-y">doi:10.1007/s10444-007-9059-y</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nvpn45jdxfhwfc7rk6u2xqrf6u">fatcat:nvpn45jdxfhwfc7rk6u2xqrf6u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150429194551/https://www.cl.cam.ac.uk/~jk520/papers/09KoJu.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/f6/64/f6646b083500f992211311b84eac5bb9b390df7a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10444-007-9059-y"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>