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Open Access Highly Accessed Research

Geometric computing for freeform architecture

Johannes Wallner12* and Helmut Pottmann23

Author Affiliations

1 TU Graz, Kopernikusgasse 24, 8010, Graz, Austria

2 TU Wien, Wiedner Hauptstr. 8-10, 1040, Wien, Austria

3 King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

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Journal of Mathematics in Industry 2011, 1:4  doi:10.1186/2190-5983-1-4

Published: 3 June 2011

Abstract

Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area, dealing with meshes with planar faces and meshes which allow multilayer constructions (which is related to discrete surfaces and their curvatures), triangles meshes with circle-packing properties (which is related to conformal uniformization), and with the paneling problem. We emphasize the combination of numerical optimization and geometric knowledge.