<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>6909</id>
    <completedYear/>
    <publishedYear>2013</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>722</pageFirst>
    <pageLast>732</pageLast>
    <pageNumber/>
    <edition/>
    <issue>7</issue>
    <volume>30</volume>
    <type>article</type>
    <publisherName>CAGD</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2013-10-01</completedDate>
    <publishedDate>2013-10-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">De Casteljau's Algotithm on Manifolds</title>
    <abstract language="eng">This paper proposes a generalization of the ordinary de Casteljau algorithm to manifold-valued data including an important special case which uses the exponential map of a symmetric space or Riemannian manifold. We investigate some basic properties of the corresponding Bézier curves and present applications to curve design on polyhedra and implicit surfaces as well as motion of rigid body and positive definite matrices. Moreover, we apply our approach to construct canal and developable surfaces.</abstract>
    <parentTitle language="eng">Computer Aided Geometric Design</parentTitle>
    <identifier type="doi">10.1016/j.cagd.2013.06.002</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-69096</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SourceTitle">Computer Aided Geometric Design</enrichment>
    <enrichment key="AcceptedDate">2013-10-01</enrichment>
    <submitter>Esfandiar Nava-Yazdani</submitter>
    <author>Esfandiar Nava-Yazdani</author>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="navayazdani">Navayazdani, Esfandiar</collection>
    <collection role="projects" number="ECMath-CH15">ECMath-CH15</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6909/1-s2.0-S0167839613000551-main.pdf</file>
  </doc>
</export-example>
