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I'm interested in the subdivision of planar quadrilateral meshes (PQ-Meshes). Meshes consisting only of planar quadrilaterals, like discrete Voss surfaces and alike. I've been searching the web for any existing research/papers on the topic, but haven't been able to come up with anything?

If someone can provide some resources on this matter I would be more than happy. What approaches have been taken to subdivide PQ-Meshes while retaining planarity?

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up vote 1 down vote accepted

Here is one recent reference, which cites others that you can follow (or use Google Scholar on its title):

Tim Hoffmann, "On local deformations of planar quad meshes," In K. Fukuda, J. V. D. Hoeven, M. Joswig, & N. Takayama (Eds.), Mathematical Software–ICMS 2010 (Vol. 6327, pp. 167-169). Springer Berlin Heidelberg. Springer link here.

But this gives me the opportunity to mention this (literally!) beautiful book, which includes substantive coverage of PQ meshes (with citations, of course):

H. Pottmann, A. Asperl, M. Hofer and A. Kilian: Architectural Geometry. Bentley Institute Press (2007), 724 pages, 2200 figures in color, ISBN 978-1-934493-04-5. Book link here.


           AG

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I know the first one, and it's references therein, though they are sadly not very concerned with subdivision. I've seen the second one mentioned before but had not had a chance to get my hands on it. Thanks! –  angerman Feb 9 '11 at 13:49
    
Note: "2200 figures" is not a typo! –  Joseph O'Rourke Feb 9 '11 at 13:52
    
Ok, I guess no one else wants to chime in. Thank you Joseph! –  angerman Feb 10 '11 at 8:52
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