death_map_2005_vt

death_map_2005_vt, the Latex files for a presentation "The Poison Pump and the Spitting Fish" which I gave to the student chapter of SIAM at Virginia Tech on 26 April 2005.

A brief abstract of the talk is:

Discrete geometry looks at the relationship of points and space. The simplest tools for this analysis include the convex hull, the Voronoi diagram, and the Delaunay triangulation. These objects can readily organize and explain many facts of everyday life, from cholera outbreaks to the mating behavior of fish. In this talk, we will concentrate on the Voronoi diagram, defining it, explaining how it can be computed by hand or on the computer. We will even show how it can be computed (approximately) using random numbers. We will mention applications including coding theory, approximate quadrature, sampling, and mesh generation.

A longer abstract is available in death_map_2005_vt.txt.

• death_map_2005_vt.tex
• death_map_2005_vt.pdf

Files that were used include:

• cvt_movie_p08_0001.png, frame 1 of an animation of a CVT computation in the "holey pie" region. For the whole movie, refer to CVT_MOVIE3.
• cvt_movie_p08_0100.png, frame 100 of an animation of a CVT computation in the "holey pie" region.
• cvt_movie2_0001.png, frame 1 of an animation of a CVT computation in a unit square. For the whole movie, refer to CVT_MOVIE2.
• cvt_movie2_0100.png, frame 100 of an animation of a CVT computation in a unit square.
• cvt_movie4_0001.png, frame 1 of an animation of a CVT computation in a unit square with a nonuniform density that favors the corners. For the whole movie, refer to CVT_MOVIE4.
• cvt_movie4_0100.png, frame 100 of an animation of a CVT computation in a unit square with a nonuniform density that favors the corners.
• diamond_02_00009_l2.png, a pixel plot of the Delaunay triangulation of the diamond points, generated by VORONOI_PLOT.
• diamond_02_00009_l3.png, a pixel plot of the Delaunay triangulation of the diamond points with the L3 distance, generated by VORONOI_PLOT.
• diamond_02_00009_li.png, a pixel plot of the Delaunay triangulation of the diamond points with the L-infinity distance, generated by VORONOI_PLOT.
• diamond_02_00009_l1.png, a pixel plot of the Delaunay triangulation of the diamond points with the L1 distance, generated by VORONOI_PLOT.
• diamond_02_00009_lhalf.png, a pixel plot of the Delaunay triangulation of the diamond points with the L(1/2) distance, generated by VORONOI_PLOT.
• diamond_delaunay.png, the Delaunay triangulation of the diamond points.
• diamond_delaunay_voronoi.png, the Delaunay triangulation and Voronoi diagram of the diamond points.
• diamond_mountains.png, a "mountain" plot of the diamond points shows the generators as peaks, and the diagram lines as straight valleys, generated by VORONOI_MOUNTAINS.
• diamond_points.png, a set of 9 points, whose Voronoi diagram includes a "diamond", generated using MATLAB.
• diamond_voronoi.png, the Voronoi diagram of the diamond points, generated using MATLAB.
• diamond_voronoi_matlab_1.png, MATLAB's default plot of the Voronoi diagram.
• diamond_voronoi_matlab_2.png, MATLAB's improved plot of the Voronoi diagram (using an unreleased version of the voronoi command).
• double_star.png, an image of a star in a star, with nodes and edges, generated by PLOT_TO_PS.
• fsu_logo.pdf, a logo.
• golden_square.png, a map of the Golden Square area, where a highly localized outbreak of cholera occurred in 1854, from the John Snow archive and research companion site at http://www.epi.msu.edu/johnsnow/index.html.
• golden_square_detail.png, a detail of the Golden Square map, showing the suspected pump, and a dotted line around its "neighborhood", from the John Snow archive and research companion site at http://www.epi.msu.edu/johnsnow/index.html.
• hundred_points.png, a hundred points chosen randomly in the unit square, generated using MATLAB.
• hundred_voronoi.png, a plot of the Voronoi diagram of the hundred points, generated using MATLAB.
• p05_nodes.png, a set of points to triangulate.
• p05_triangulation.png, the triangulated points.
• p14_boundary.png, the boundary of a lake, with an island.
• p14_dist.png, the distance-to-the-boundary calculation over the lake.
• p14_mesh.png, a uniform mesh over the lake, using Persson and Strang's DISTMESH program.
• p14_pred.png, the predator density in a time-dependent predator prey calculation, from work by Marcus Garvie.
• random_mountains.png, a "mountain" plot of a set of random points, tilted a bit, and with a banded color map to emphasize contours, generated by VORONOI_MOUNTAINS.
• square.png, an image of a square, with nodes and edges, generated by PLOT_TO_PS.
• stripack.png, plot of a Voronoi diagram on the surface of a sphere, generated by STRIPACK.
• tilapia.png, a photograph of tilapia nests in a sandy bottom, from the paper by Barlow.
• uniform_02_00100_km5.png, 100 random points clustered by K-Means into 5 groups.