Maps, images, spatial displays - Always look at the data
responses, "Y" explanatories, "X"
Saskatchewan, Canada
responses,"Y" explanatories,"X"polygon(), text(), library(maps), ...
Y + X
Examples from the news
Costa Concordia - Giglio
Hetch Hetchy water route - pipelines and tunnels
SF Chronicle centerfold
NY Times 01/27/09
Coal used for electricity circles(), polygon()
Spatial process data.
(s,t): geographic coordinates,
e.g. (latitude, longitude), (x-coord,y-coord)
y(s,t): real-valued
e.g. available for s=0,...,S-1; t=0,...,T-1
(s,t) in A
Height of 500mb surface S=64, T=32
1200 GMT January 1, 1986
data based on many observations, interpolated to grid
display by contours over a world map
overall mean subtracted
map(), lines(), 2
map(), image(...,add=T, col=)
Starkey Reserve, Oregon - persp(), points()
red: eastward blue: westward
http://www.oscar.noaa.gov/
map(), arrows()
Ocean currents
Stacking.
Galton - photos of faces
electron micrographs
crystal, purple membrane
symmetries
160 "units"
j=1160 yj(s,t)/160
stacking via FFT fft(), lines()
micrographs
not stacked and stacked
J=1 J=160
Data may be aggregate, e.g. over polygons
coordinates of vertices
choropleth plot: a thematic map in which areas are shaded
map(), polygon()
computational geometry,
point in polygon library(splancs)
Saskatchewan births, counts, rates
polygon(,density=)
perspective plot persp()
hidden lines
Contouring.
Contour line, , (a function of two variables), is a curve connecting points where the function has the same value.
Smooth function f: R2 R
c: value
f-1 (c) = x,y
There may be more than one component
One method.
Suppose f(s,t) available for a regular grid
Suupose wish f-1(c)
Pick an edge, AB, of a pixel
I. It will be intercepted if min{f(A),f(B)}cmax{f(A),f(B)}
using this can learn all edges intercepted
II. If one edge of a cell is intercepted, so is another one
search in order E-S-W-N
III. Get intersection coordinates by interpolation
connect by line
IV. Move to pertinent adjacent cell and continue
Line process - set of lines {l1 , l2 , ls ,...}
Point process {(p(l1),(l1)),(p(l2),(l2)),...}
p: distance : angle
Tesselation
#{cells completely in set A}
polygon()