Lecture 5, Sept 1: Data structures for embedded graphs
We move from the representation of lines to the representation of planar subdivisions. Just as graphs are fundamental in computer science, embedded graphs are fundamental in spatial modeling applications.
Eulerís relation; a quick review
Here are some notes inLatex or PS that Iíll convert to html as soon as I find the converters here at UNC.
Edge based structures for connected graphs: winged- and quad-edge
Winged edge data structure of Baumgart, notes by Dr. C.-K. Shene:http://www.csl.mtu.edu/cs390-2/www/NOTES/model/winged-e.html
Leonidas Guibas and Jorge Stolfi. "Primitives for the manipulation of general subdivisions and the computation of voronoi diagrams." ACM Transactions on Graphics, 4(2):74-123, April 1985.
Many implementations. C code athttp://www.dcc.unicamp.br/~stolfi/EXPORT/software/c/libquad/
Dani Lischinski. Graphics Gems, volume IV, chapter Incremental Delaunay Triangulation, pages 47-59. Academic Press, Inc, 1994.
Supposed to be atwww.acm.org/tog/GraphicsGems/
In GIS literature usually refers to the study of embedded graphs as Topology; if you want more vocabulary from a GIS perspective:http://www.gisca.adelaide.edu.au/~bbryan/lectures/conc_vec_gis/
The US Census was one of the biggest pushes for topologically-structured GIS data. See, e.g., theTIGER data format manual (in PDF)