On the 19th September 2014 Thilo Rörig, Stefan Sechelmann, Agata Kycia and Moritz Fleischmann presented a  paper “Surface panelization using periodic conformal maps” at the ADVANCES IN ARCHITECURAL GEOMETRY 2014 conference in London and received “Best paper award” of the year. AAG 2014 Announcement can be found here.

Conference: ADVANCES IN ARCHITECURAL GEOMETRY 2014

Location: London

Dates: 18-21.09.14

Paper: Surface panelization using periodic conformal maps

Authors: T. Rörig, S. Sechelmann (TU Berlin), A. Kycia, M. Fleischmann (HENN)

Fig.1: Quantized periodic hexagonal panelizations. [T. Rörig, S. Sechelmann, A. Kycia, M. Fleischmann]

ABSTRACT

We present a new method to obtain periodic conformal parameterizations of surfaces with cylinder topology and describe applications to architectural design and rationalization of surfaces. The method is based on discrete conformal maps from the surface mesh to a cylinder or cone of revolution. It accounts for a number of degrees of freedom on the boundary that can be used to obtain a variety of alternative panelizations. We illustrate different choices of parameters for NURBS surface designs. Further, we describe how our parameterization can be used to get a periodic boundary aligned hex-mesh on a doubly-curved surface and show the potential on an architectural facade case study. Here we optimize an initial mesh in various ways to consist of a limited number of planar regular hexagons that panel a given surface.

Fig.2: State of the art unroll methods can crete patterns on a closed surface. The ApplyCrv command of Rhinoceros produces boundary aligned periodic patterns but introduces unacceptable non-isotropic stretch (left). The SquishBack method creates sufficiently regular elements but does nor respect the periodicity of the surface (middle). Non-periodic conformal maps align with the boundary of a cut surface. Along the cut the map is not continous (right).

Fig.3: Conformal mapping (method preserving the angles)

Fig. 4: Panelization case study/Data for the component-like construction of each panel was derived from the mesh

Fig.5: Panelization of a double-curved design alternative of the case study. Unquantized panelization (left). Quantization to 3 panel sizes with the edge varying from 1,5 to 2m

The full paper can be found in the AAG 2014 Proceedings publication or here.