6533b851fe1ef96bd12aa04b

RESEARCH PRODUCT

On harmonic and biharmonic Bézier surfaces

Hassan UgailJuan Monterde

subject

Surface (mathematics)DiscretizationMathematical analysisAerospace EngineeringBoundary (topology)Harmonic (mathematics)Bézier curveBiharmonic Bézier surfaceTopologyComputer Graphics and Computer-Aided DesignPDE surfaceModeling and SimulationAutomotive EngineeringBiharmonic equationMathematics

description

We present a new method of surface generation from prescribed boundaries based on the elliptic partial differential operators. In particular, we focus on the study of the so-called harmonic and biharmonic Bezier surfaces. The main result we report here is that any biharmonic Bezier surface is fully determined by the boundary control points. We compare the new method, by way of practical examples, with some related methods such as surfaces generation using discretisation masks and functional minimisations.

yearjournalcountryeditionlanguage
2004-09-01Computer Aided Geometric Design
https://doi.org/10.1016/j.cagd.2004.07.003