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dc.contributor.authorMonterde, J.*
dc.contributor.authorUgail, Hassan*
dc.date.accessioned2009-07-14T09:10:33Z
dc.date.available2009-07-14T09:10:33Z
dc.date.issued2006
dc.identifier.citationMonterde, J. and Ugail, H. (2006). A General 4th-Order PDE Method to Generate Bézier Surfaces from the Boundary. Computer Aided Geometric Design. Vol. 23, No. 2, pp. 208-225.en
dc.identifier.urihttp://hdl.handle.net/10454/3002
dc.descriptionNoen
dc.description.abstractIn this paper we present a method for generating Bézier surfaces from the boundary information based on a general 4th-order PDE. This is a generalisation of our previous work on harmonic and biharmonic Bézier surfaces whereby we studied the Bézier solutions for Laplace and the standard biharmonic equation, respectively. Here we study the Bézier solutions of the Euler¿Lagrange equation associated with the most general quadratic functional. We show that there is a large class of fourth-order operators for which Bézier solutions exist and hence we show that such operators can be utilised to generate Bézier surfaces from the boundary information. As part of this work we present a general method for generating these Bézier surfaces. Furthermore, we show that some of the existing techniques for boundary based surface design, such as Coons patches and Bloor¿Wilson PDE method, are indeed particular cases of the generalised framework we present here.en
dc.language.isoenen
dc.subjectGeneral biharmonic operatoren
dc.subject; PDE freeform surfacesen
dc.subject; Quadratic functionalsen
dc.subject; Permanence principleen
dc.subject; Coons patchesen
dc.titleA General 4th-Order PDE Method to Generate Bézier Surfaces from the Boundaryen
dc.status.refereedYesen
dc.typeArticleen
dc.type.versionNo full-text available in the repositoryen
dc.identifier.doihttps://doi.org/10.1016/j.cagd.2005.09.001


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