Computational Design of Weingarten Surfaces

DAVIDE PELLIS, Martin Kilian, Helmut Pottmann, Mark Pauly

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


In this paper we study Weingarten surfaces and explore their potential for fabrication-aware design in freeform architecture. Weingarten surfaces are characterized by a functional relation between their principal curvatures that implicitly defines approximate local congruences on the surface. These symmetries can be exploited to simplify surface paneling of double-curved architectural skins through mold re-use. We present an optimization approach to find a Weingarten surface that is close to a given input design. Leveraging insights from differential geometry, our method aligns curvature isolines of the surface in order to contract the curvature diagram from a 2D region into a 1D curve. The unknown functional curvature relation then emerges as the result of the optimization. We show how a robust and efficient numerical shape approximation method can be implemented using a guided projection approach on a high-order B-spline representation. This algorithm is applied in several design studies to illustrate how Weingarten surfaces define a versatile shape space for fabrication-aware exploration in freeform architecture. Our optimization algorithm provides the first practical tool to compute general Weingarten surfaces with arbitrary curvature relation, thus enabling new investigations into a rich, but as of yet largely unexplored class of surfaces.
Original languageEnglish (US)
JournalAccepted by ACM Transactions on Graphics
StatePublished - 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-05-04
Acknowledgements: This work was supported by the Swiss National Science Foundation through NCCR "Digital Fabrication" (agreement No. 51NF40-141853), and by the Austrian Science Fund FWF through SFB "Advanced Computational Design" (project No. F77).


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