Computational design of weingarten surfaces

In this paper we study Weingarten surfaces and explore their potential for fabrication-aware design in freeform architecture. are characterized by a functional relation between 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 find is close given input design. Leveraging insights from differential geometry, our method aligns curvature isolines order contract diagram 2D region into 1D curve. The unknown then emerges as result optimization. show how robust efficient numerical shape approximation implemented using guided projection high-order B-spline representation. This algorithm applied several studies illustrate define versatile space exploration Our provides first practical tool compute general with arbitrary relation, thus enabling new investigations rich, but yet largely unexplored class surfaces.