6533b7d4fe1ef96bd1263233

RESEARCH PRODUCT

PDE triangular Bézier surfaces: Harmonic, biharmonic and isotropic surfaces

A. LluchA. LluchJuan MonterdeJuan MonterdeAna ArnalAna Arnal

subject

Bézier surfaceSurface (mathematics)Bézier surfacePartial differential equationLaplacian operatorPDE surfaceApplied MathematicsMathematical analysisHarmonic (mathematics)Bi-Laplacian operatorBiharmonic Bézier surfaceIsotropyComputational MathematicsPDE surfaceBiharmonic equationLaplace operatorMathematics

description

We approach surface design by solving second-order and fourth-order Partial Differential Equations (PDEs). We present many methods for designing triangular Bézier PDE surfaces given different sets of prescribed control points and including the special cases of harmonic and biharmonic surfaces. Moreover, we introduce and study a second-order and a fourth-order symmetric operator to overcome the anisotropy drawback of the harmonic and biharmonic operators over triangular Bézier surfaces. © 2010 Elsevier B.V. All rights reserved.

yearjournalcountryeditionlanguage
2011-01-01
10.1016/j.cam.2010.07.020