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.
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.
Last revised on 01 February 2024.