The property of a surface being developable can be expressed in different equivalent ways, by vanishing Gauss curvature, or by the existence of isometric mappings to planar domains. Computational contributions to this topic range from special parametrizations to discrete-isometric mappings.
In this paper we investigate geometric properties and modeling capabilities of quad meshes with planar faces whose mesh polylines enjoy the additional property of being contained in a single plane.
Small-scale cut and fold patterns imposed on sheet material enable its morphing into threedimensional shapes. This manufacturing paradigm has been receiving much attention in recent years and poses challenges in both fabrication and computation.
CNC machining is the leading subtractive manufacturing technology. Although it is in use since decades, it is far from fully solved and still a rich source for challenging problems in geometric computing.
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.
We solve the task of representing free forms by an arrangement of panels that are manufacturable by precise isometric bending of surfaces made from a small number of molds. In fact we manage to solve the paneling task with surfaces of constant Gaussian curvature alone. This includes the case of developable surfaces which exhibit zero curvature.
Abstract. We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on larger parameter rectangles.
The isolines of principal symmetric surface parametrizations run symmetrically to the principal directions. We describe two discrete versions of these special nets/quad meshes which are dual to each other and show their usefulness for various applications in the context of fabrication and architectural design.
We discretize isometric mappings between surfaces as correspondences
A significant amount of research in Architectural Geometry has dealt with skins and structures which follow a quadrilateral layout with double curvature. In many cases, such quad networks are computationally accessed by quad meshes which obey various constraints.
The realization of architectural freeform skins is a big challenge, in particular if one desires a smooth appearance and uses curved panels. These have to be brought into shape by special manufacturing technologies, most of which require the costly production of molds.
Kirigami, the traditional Japanese art of paper cutting and folding generalizes origami and has initiated new research in material science as well as graphics. In this paper we use its capabilities to perform geometric modeling with corrugated surface representations possessing an isometric unfolding into a planar domain after appropriate cuts are made.
Cold bent glass is a promising and cost-efficient method for realizing doubly curved glass façades. They are produced by attaching planar glass sheets to curved frames and must keep the occurring stress within safe limits.