SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
A recursive relation for the determinant of a pentadiagonal matrix
Communications of the ACM
Bézier surfaces of minimal area: the Dirichlet approach
Computer Aided Geometric Design
T-spline simplification and local refinement
ACM SIGGRAPH 2004 Papers
An intuitive framework for real-time freeform modeling
ACM SIGGRAPH 2004 Papers
On harmonic and biharmonic Bézier surfaces
Computer Aided Geometric Design
An analytic pseudo-spectral method to generate a regular 4-sided PDE surface patch
Computer Aided Geometric Design
Geometric fairing of irregular meshes for free-form surface design
Computer Aided Geometric Design
Construction of blending surfaces by parametric discrete interpolation PDE splines
Mathematics and Computers in Simulation
Two C1-methods to generate Bézier surfaces from the boundary
Computer Aided Geometric Design
Method of surface reconstruction using partial differential equations
ICCOMP'06 Proceedings of the 10th WSEAS international conference on Computers
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In 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.