Alexander Schiftner

Freeform surfaces from single curved panels

Motivated by applications in architecture and manufacturing, we discuss the problem of covering a freeform surface by single curved panels. This leads to the new concept of semi-discrete surface representation, which constitutes a link between smooth and discrete surfaces. The basic entity we are working with is the developable strip model. It is the semi-discrete equivalent of a quad mesh with planar faces, or a conjugate parametrization of a smooth surface. We present a B-spline based optimization framework for efficient computing with D-strip models. In particular we study conical and circular models, which semi-discretize the network of principal curvature lines, and which enjoy elegant geometric properties. Together with geodesic models and cylindrical models they offer a rich source of solutions for surface panelization problems.

Paneling architectural freeform surfaces

The emergence of large-scale freeform shapes in architecture poses big challenges to the fabrication of such structures. A key problem is the approximation of the design surface by a union of patches, so-called panels, that can be manufactured with a selected technology at reasonable cost, while meeting the design intent and achieving the desired aesthetic quality of panel layout and surface smoothness. The production of curved panels is mostly based on molds. Since the cost of mold fabrication often dominates the panel cost, there is strong incentive to use the same mold for multiple panels. We cast the major practical requirements for architectural surface paneling, including mold reuse, into a global optimization framework that interleaves discrete and continuous optimization steps to minimize production cost while meeting user-specified quality constraints. The search space for optimization is mainly generated through controlled deviation from the design surface and tolerances on positional and normal continuity between neighboring panels. A novel 6-dimensional metric space allows us to quickly compute approximate inter-panel distances, which dramatically improves the performance of the optimization and enables the handling of complex arrangements with thousands of panels. The practical relevance of our system is demonstrated by paneling solutions for real, cutting-edge architectural freeform design projects.

Designing Quad-dominant Meshes with Planar Faces

We study the combined problem of approximating a surface by a quad mesh (or quad‐dominant mesh) which on the one hand has planar faces, and which on the other hand is aesthetically pleasing and has evenly spaced vertices. This work is motivated by applications in freeform architecture and leads to a discussion of fields of conjugate directions in surfaces, their singularities and indices, their optimization and their interactive modeling. The actual meshing is performed by means of a level set method which is capable of handling combinatorial singularities, and which can deal with planarity, smoothness, and spacing issues.

Geodesic patterns

Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend sideways. Likewise a geodesic is the favored shape of timber support elements in freeform architecture, for reasons of manufacturing and statics. Both problem areas are fundamental in freeform architecture, but so far only experimental solutions have been available. This paper provides a systematic treatment and shows how to design geodesic patterns in different ways: The evolution of geodesic curves is good for local studies and simple patterns; the level set formulation can deal with the global layout of multiple patterns of geodesics; finally geodesic vector fields allow us to interactively model geodesic patterns and perform surface segmentation into panelizable parts.

Case Studies in Cost-Optimized Paneling of Architectural Freeform Surfaces

Paneling an architectural freeform surface refers to an approximation of the design surface by a set of panels that can be manufactured using a selected technology at a reasonable cost, while respecting the design intent and achieving the desired aesthetic quality of panel layout and surface smoothness. Eigensatz and co-workers [Eigensatz et al. 2010] have recently introduced a computational solution to the paneling problem that allows handling large-scale freeform surfaces involving complex arrangements of thousands of panels. We extend this paneling algorithm to facilitate effective design exploration, in particular for local control of tolerance margins and the handling of sharp crease lines. We focus on the practical aspects relevant for the realization of large-scale freeform designs and evaluate the performance of the paneling algorithm with a number of case studies.

New Strategies and Developments in Transparent Free-Form Design: From Facetted to Nearly Smooth Envelopes

Free-form geometries in architecture pose new challenges to designers and engineers. Form, structure and fabrication processes are closely linked, which makes the realization of complex architectural free-form structures even harder. Free-form transparent design today is mainly based on triangularly facetted forms or quadrilateral meshes supported by a structure composed of rectilinear bars, with strong shape restrictions. After a brief review of the history, we report on some very recent progress in this area. Beginning with a presentation of improved methods for triangle mesh design, we also discuss experiences in coupling triangular glass panels with continuous curved structures, seeking an optimised structural behaviour and simplified connections. Furthermore, we present how the results of research on planar quadrilateral (PQ) meshes lead the way to optimized beam layouts and the breakdown of free-form shapes using planar quadrilateral panels. PQ meshes are rooted in discrete differential geometry, an active area of mathematical research. Using recent projects as examples, we discuss how transparent free-form envelopes with a smooth visual appearance are achievable if the structure is designed to adhere to the limits of current glazing technology and the surfaces are reasonably simple (e.g. rotational, overall developable, or of a small scale). In section 6 we show how the latter restriction can be relaxed: the theoretical and computational methodology for PQ meshes can easily be extended to create nearly smooth approximations of free-form surfaces by single-curved panels. This has a strong impact on glass panelling design, since it avoids expensive double-curvature glass and exploits cold-bending technology. We elaborate on how this discretisation technique goes hand in hand with the technology for construction of the structure, glazing system and structural joints. Our approach has been tested in three case studies, each one validating a particular aspect of the design process.

Architectural Geometry from Research to Practice: The Eiffel Tower Pavilions

In this paper we analyze, discuss, and propose how recent research findings in architectural geometry enable construction aware design, an integrated approach that takes into account construction and manufacturing already during the earliest stages of design without limiting the designer’s expressiveness.

Tiling Freeform Shapes With Straight Panels: Algorithmic Methods.

This paper shows design studies with bent panels which are originally rectangular or at least approximately rectangular. Based on recent results obtained in the geometry processing community, we algorithmically approach the questions of an exact rectangular shape of panels; of watertightness of the resulting paneling; and of the panel shapes being achievable by pure bending. We conclude the paper with an analysis of stress and strain in bent and twisted panels.