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By Jean-Claude, And Pierre Vogel; Hausmann

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Extra resources for Geometry on Poincaré Spaces (Mathematical Notes 41)

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In this paper we discuss the paneling solution recently introduced in [Eigensatz et al. 2010], henceforth referred to as the paneling algorithm, and focus on the practical aspects relevant for the realization of large-scale freeform designs. We enhance the algorithm to handle spatially adaptive quality thresholds and propose an extension that allows incorporating sharp feature lines. With these new functionalities, the algorithm offers improved control for the architect to adapt the paneling according to the design specifications.

3 Paneling Architectural Freeform Surfaces We review both the specification of the paneling problem and the optimization approach presented by Eigensatz and coworkers. For a more detailed description, in particular with respect to mathematical and algorithmic aspects, we refer the reader to [Eigensatz et al. 2010]. 1 Problem Specification Let F be a given input freeform surface, called reference surface, describing the shape of the design. The goal is to find a collection of panels, such that their union approximates the reference surface.

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