期刊
ACM TRANSACTIONS ON GRAPHICS
卷 40, 期 4, 页码 -出版社
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3450626.3459939
关键词
fabrication-aware design; computational differential geometry; geometric optimization; Weingarten surface; architectural geometry; paneling; mold reduction
资金
- Swiss National Science Foundation through NCCR Digital Fabrication [51NF40-141853]
- Austrian Science Fund FWF through SFB Advanced Computational Design [F77]
- Austrian Science Fund (FWF) [F77] Funding Source: Austrian Science Fund (FWF)
This paper studies Weingarten surfaces and their potential in freeform architecture design. By leveraging the symmetries of Weingarten surfaces, surface paneling of double-curved architectural skins can be simplified. An optimization approach is presented to find a Weingarten surface close to a given input design.
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.
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