×

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.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bloor, M.I.G.; Wilson, M.J., Using partial differential equations to generate freeform surfaces, Comput. aided design, 22, 202-212, (1990) · Zbl 0754.65016
[2] Farin, G.; Hansford, D., Discrete coons patches, Comput. aided geom. design, 16, 7, 691-700, (1999) · Zbl 0997.65033
[3] Kim, B., Rossignac, J., 2004. Localized bi-Laplacian solver on a triangle mesh and its applications, Georgia Institute of Technology, GVU Technical Report Number: GIT-GVU-04-12
[4] Monterde, J., Bézier surfaces of minimal area: the Dirichlet approach, Comput. aided geom. design, 21, 117-136, (2004) · Zbl 1069.65559
[5] Monterde, J., The plateau-Bézier problem, (), 262-273 · Zbl 1274.65047
[6] Schneider, R.; Kobbelt, L., Geometric fairing of irregular meshes for free-form surface design, Comput. aided geom. design, 18, 4, 359-379, (2001) · Zbl 0969.68154
[7] Schneider, R.; Kobbelt, L.; Seidel, H.-P., Improved bi-Laplacian mesh fairing, (), 445-454 · Zbl 1002.65027
[8] Ugail, H.; Bloor, M.I.G.; Wilson, M.J., Techniques for interactive design using the PDE method, ACM trans. graphics, 18, 2, 195-212, (1999)
[9] Ugail, H., On the spine of a PDE surface, (), 366-376 · Zbl 1274.65052
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.