Maps, images, spatial displays - Always look at the data

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()