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.

Euler’s relation; a quick review

Here are some notes in Latex or PS that I’ll 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 at http://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 at www.acm.org/tog/GraphicsGems/

Other Links

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., the TIGER data format manual (in PDF)