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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Pottmann, H., Asperl, A., Hofer, M., Kilian, A.: Architectural Geometry. Bentley Institute Press, Exton (2007)
Bobenko, A.I., Suris, Y.B.: Discrete Differential Geometry: Integrable Structure. Graduate Studies in Mathematics, vol. 98. AMS, Providence (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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)
