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IASS-SLTE Symposium 2014: Shells, Membranes and Spatial Structures: Footprints


IASS Symposium 2014

SESSION: General 9: Computational Tools, Shape Finding and Optimization

Planarization of quad meshes using dynamic relaxation principles

< Table of Contents for General 9: Computational Tools, Shape Finding and Optimization
  • Proceedings Name: IASS-SLTE Symposium 2014: Shells, Membranes and Spatial Structures: Footprints
  • ISSN: (Electronic Version) 2518-6582
  • Session: General 9: Computational Tools, Shape Finding and Optimization
  • Title: Planarization of quad meshes using dynamic relaxation principles
  • Author(s): Florian GAUSS
  • Keywords: planar quad mesh, dynamic relaxation, optimization, lines of principle curvature
Abstract
Free form architecture building envelopes need to be broken down into elements that not only size-wise but also with respect to their geometrical description can be manufactured and assembled. This process always requires the faceting of surfaces. Triangulation of a surface is a well-documented process however from an architectural and economical point of view the planar quadrilateral (PQ) faceting of a surface offers several advantages. So far the accurate generation of PQ facets is only possible for certain sub-classes of surfaces which in themselves feature simple generating methods thus restricting the design freedom. To address this problem an approximation network is generated which has to follow certain rules: the topology of the network is determined by the properties of the surface which shall be approximated. This means the faces are positioned in such a way so their edges will always follow the principal curvature lines of the surface. Usually the singular points of a PQ mesh surface are characterised by the number of 4 edges per joint. By considering the position/ location of those singular points whose number of members differ from the usual 4 edges in a typical joint of a PQ to be continued. Depending on the complexity of the input surface the generated quads are planar or nearly planar within a tolerance that can be determined by the user before generating the approximation network. Obviously the acceptable tolerance is linked directly to the material the quads shall be manufactured of. The final step of the process is to optimise the approximation network by using dynamic relaxation principles.

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