6533b821fe1ef96bd127c0f9

RESEARCH PRODUCT

A general 4th-order PDE method to generate Bézier surfaces from the boundary

Hassan UgailJuan Monterde

subject

Surface (mathematics)Partial differential equationAerospace EngineeringBoundary (topology)Harmonic (mathematics)Bézier curveTopologyComputer Graphics and Computer-Aided DesignEuler–Lagrange equationPDE surfaceComputer Science::GraphicsModeling and SimulationAutomotive EngineeringBiharmonic equationApplied mathematicsMathematics

description

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.

yearjournalcountryeditionlanguage
2006-02-01Computer Aided Geometric Design
https://doi.org/10.1016/j.cagd.2005.09.001