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		<citationkey>MartínezMoreraCarvVelh:2007:ToMoTr</citationkey>
		<author>Martínez Morera, Dimas,</author>
		<author>Carvalho, Paulo Cezar,</author>
		<author>Velho, Luiz,</author>
		<affiliation>IMPA</affiliation>
		<affiliation>IMPA</affiliation>
		<affiliation>IMPA</affiliation>
		<title>Geodesic Bézier Curves: a Tool for Modeling on triangulations</title>
		<conferencename>Brazilian Symposium on Computer Graphics and Image Processing, 20 (SIBGRAPI)</conferencename>
		<year>2007</year>
		<editor>Falcăo, Alexandre Xavier,</editor>
		<editor>Lopes, Hélio Côrtes Vieira,</editor>
		<booktitle>Proceedings</booktitle>
		<date>Oct. 7-10, 2007</date>
		<publisheraddress>Los Alamitos</publisheraddress>
		<publisher>IEEE Computer Society</publisher>
		<conferencelocation>Belo Horizonte</conferencelocation>
		<keywords>geodesic Bézier curve, discrete geodesic, de Casteljau algorithm, spline curves, free-form gesign.</keywords>
		<abstract>We define a new class of curves, called geodesic Bézier curves, that are suitable for modeling on manifold triangulations. As a natural generalization of Bézier curves, the new curves are as smooth as possible. We discuss the construction of C0 and C1 piecewise Bézier splines. We also describe how to perform editing operations, such as trimming, using these curves. Special care is taken to achieve interactive rates for modeling tasks.</abstract>
		<language>en</language>
		<tertiarytype>Full Paper</tertiarytype>
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