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Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
A recursive relation for the determinant of a pentadiagonal matrix
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Computer Aided Geometric Design
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On harmonic and biharmonic Bézier surfaces
Computer Aided Geometric Design
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Computer Aided Geometric Design
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GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
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Computer Aided Geometric Design
An elementary algorithm for computing the determinant of pentadiagonal Toeplitz matrices
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In this paper we present a method for generating Bezier surfaces from the boundary information based on a general 4th-order PDE. This is a generalisation of our previous work on harmonic and biharmonic Bezier surfaces whereby we studied the Bezier solutions for Laplace and the standard biharmonic equation, respectively. Here we study the Bezier 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 Bezier solutions exist and hence we show that such operators can be utilised to generate Bezier surfaces from the boundary information. As part of this work we present a general method for generating these Bezier 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.