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Discrete geometric structures for architecture

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Helmut PottmannAuthors Info & Claims

SoCG '10: Proceedings of the twenty-sixth annual symposium on Computational geometry

Page 38

https://doi.org/10.1145/1810959.1810966

Published: 13 June 2010 Publication History

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Abstract

The emergence of freeform structures in contemporary architecture raises numerous challenging research problems, most of which are related to the actual fabrication and are a rich source of research topics in geometry and geometric computing. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization of supporting beams and nodes.

A study of quadrilateral meshes with planar faces reveals beautiful relations to discrete differential geometry. In particular, we discuss meshes which discretize the network of principal curvature lines. Conical meshes are among these meshes; they possess conical offset meshes at a constant face/face distance, which in turn leads to a supporting beam layout with so-called torsion free nodes. This work can be generalized to a variety of multilayer structures and laid the ground for an adapted curvature theory for these meshes. There are also efforts on segmenting surfaces into planar hexagonal panels. Though these are less constrained than planar quadrilateral panels, this problem is still waiting for an elegant solution.

Inspired by freeform designs in architecture which involve circles and spheres, we present a new kind of triangle mesh whose faces' in-circles form a packing, i.e., the in-circles of two triangles with a common edge have the same contact point on that edge. These "circle packing (CP) meshes" exhibit an aesthetic balance of shape and size of their faces. They are closely tied to sphere packings on surfaces and to various remarkable structures and patterns which are of interest in art, architecture, and design. CP meshes constitute a new link between architectural freeform design and computational conformal geometry.

Recently, certain timber structures motivated us to study discrete patterns of geodesics on surfaces. This topic is closely related to the classical geometry of webs. There are numerous open problems in the geometry of webs, in particular when one asks for webs formed by special types of curves, as preferred in applications such as architecture.

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Discrete geometric structures for architecture

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Published In

SoCG '10: Proceedings of the twenty-sixth annual symposium on Computational geometry

June 2010

452 pages

ISBN:9781450300162

DOI:10.1145/1810959

Program Chairs:
David Kirkpatrick
University of British Columbia, Canada
,
Joseph Mitchell
SUNY Stony Brook, USA

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 13 June 2010

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SoCG '10

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SoCG '10: Symposium on Computational Geometry

June 13 - 16, 2010

Utah, Snowbird, USA

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Abstract

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Recommendations

Geometry of multi-layer freeform structures for architecture

Geometry of multi-layer freeform structures for architecture

Geometric modeling with conical meshes and developable surfaces

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