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On Local Deformations of Planar Quad-Meshes

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 6327)

Abstract

Planar quad-meshes (meshes with planar quadrilateral faces – PQ-meshes for short) are an important class of meshes (see e.g. Bobenko and Suris [2008]). Although they are often desirable in computer graphics – since planar quads can be rendered with out triangulating them – and architectual geometry (see Pottmann et al. [2007]) – because building with planar tiles is more cost effective – modelling freeform surfaces with planar quadrilaterals is problematic (in fact in practical applications one deforms or subdivides PQ-meshes without obeying the planarity constraint and ensures it afterwards in a global optimization step). In this paper we present a method that allows local deformations of PQ-meshes (with square grid combinatorics) that makes it possible to modify a PQ-mesh while keeping all quadrilaterals planar through the whole process (without a minimization step). In principle the method allows for PQ-mesh subdivision as well.

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References

  1. Pottmann, H., Asperl, A., Hofer, M., Kilian, A.: Architectural Geometry. Bentley Institute Press, Exton (2007)

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  2. Bobenko, A.I., Suris, Y.B.: Discrete Differential Geometry: Integrable Structure. Graduate Studies in Mathematics, vol. 98. AMS, Providence (2008)

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© 2010 Springer-Verlag Berlin Heidelberg

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Hoffmann, T. (2010). On Local Deformations of Planar Quad-Meshes. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_31

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  • DOI: https://doi.org/10.1007/978-3-642-15582-6_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15581-9

  • Online ISBN: 978-3-642-15582-6

  • eBook Packages: Computer ScienceComputer Science (R0)