On harmonic and biharmonic Bézier surfaces. (English) Zbl 1069.65526

Summary: 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 Bézier surfaces. The main result we report here is that any biharmonic Bézier 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.


65D17 Computer-aided design (modeling of curves and surfaces)
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