PDE triangular Bézier surfaces: Harmonic, biharmonic and isotropic surfaces
PDE surfaces result as a solution of partial differential equations (PDEs). In this article, two general PDEs with constant coefficients of second-order and fourth-order are investigated to create harmonic and biharmonic triangular Bézier surfaces with prescribed set of control points. It is shown that two lines of control points must be given for a harmonic triangular Bézier surface and four lines of control points must be given for biharmonic triangular Bézier surface. Moreover, a second-order and a fourth-order isotropic operator is studied and introduced to overcome the non-isotropy of the harmonic and the biharmonic equations over triangular Bézier surfaces. The method of modelling PDE triangular Bézier surfaces suggested in this article is useful in geometric modelling and computer graphics for creating smooth surfaces by prescribed a set of control points. The results can be used in various physical application areas, too.
scientific article; zbMATH DE number 5821385