Using partial differential equations to generate free-form surfaces: 91787
Computer-Aided Design
Functional optimization for fair surface design
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
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Transfinite Surface Interpolation
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
An architecture for universal CAD data exchange
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
On harmonic and biharmonic Bézier surfaces
Computer Aided Geometric Design
Spine based shape parameterisation for PDE surfaces
Computing - Geometric modelling dagstuhl 2002
Solutions of differential equations in a Bernstein polynomial basis
Journal of Computational and Applied Mathematics
A general 4th-order PDE method to generate Bézier surfaces from the boundary
Computer Aided Geometric Design
Fourth-order partial differential equations for noise removal
IEEE Transactions on Image Processing
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We present an explicit polynomial solution method for surface generation. In this case the surface in question is characterized by some boundary configuration whereby the resulting surface conforms to a fourth order linear elliptic Partial Differential Equation, the Euler-Lagrange equation of a quadratic functional defined by a norm. In particular, the paper deals with surfaces generated as explicit Bezier polynomial solutions for the chosen Partial Differential Equation. To present the explicit solution methodologies adopted here we divide the Partial Differential Equations into two groups namely the orthogonal and the non-orthogonal cases. In order to demonstrate our methodology we discuss a series of examples which utilize the explicit solutions to generate smooth surfaces that interpolate a given boundary configuration. We compare the speed of our explicit solution scheme with the solution arising from directly solving the associated linear system.