Discrete surfaces with spherical faces are interesting from a simplified manufacturing viewpoint when compared to other double curved face shapes. Furthermore, by the nature of their definition they are also appealing from the theoretical side leading to a Möbius invariant discrete surface theory.

Straight flat strips of inextensible material can be bent into curved strips

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.

Architectural design and urban planning are complex design tasks. Predicting the thermal impact of design choices at interactive rates enhances the ability of designers to improve energy efficiency and avoid problematic heat islands while maintaining design quality.

Design decisions in urban planning have to be made with particular carefulness as the resulting constraints are binding for the whole architectural design that follows.

We introduce the new concept of C-mesh to capture kinetic structures that can be deployed from a collapsed state.

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.