surface analysis

CS 128/ES 228 - Lecture 13a 1

Surface Analysis


Network Analysis Given a network

What is the shortest path from s to t? What is the cheapest route from s to

t? How much “flow” can we get through

the network? What is the shortest route visiting all

points?

Image from: http://www.eli.sdsu.edu/courses/fall96/cs660/notes/NetworkFlow/NetworkFlow.html#RTFToC2


Network complexitiesShortest path EasyCheapest path EasyNetwork flow MediumTraveling salesperson

Exact solution is IMPOSSIBLY HARD but can be approximated

All answers learned in CS 232!


When is an Elevation NOT an Elevation? When it is rainfall, income, or any

other scalar measurement

Bottom Line: It’s one more dimension (any dimension!) on top of the geographic data


How do we display a map with “elevation”?

Choropleth map

Contour map

Surface map


Choropleth maps Show areas of equal “elevation” in a

uniform manner

Are usually “exact” approximations (through aggregation)

Subject to classification issues

Often intimately connected to queries


Simple uses of choroplethsOrdinal

Population

Per capita income

Crop yield

Categorical

Soil type

Political party control

Primary industry


Display issues for choropleths Classification

Type

Number of intervals

Colors


How do we select choropleth regions?

Based on existing polygons

Based on dissolved polygons

Based on nearest points


A Choropleth you built


More complex queries using choropleths Time series data

Population change % of land in agricultural use

Computation driven Total spending power = Average income x population Average wheat yield = Total yield / Acreage of farms


Basic model for “computed choropleths” Create new attribute data (usually

within attribute table; sometimes with selection layer)

Set the display to key off that new data

Choose remaining display options


A riddle (sans funny punch line) What is the difference between a

choropleth map and a 2-D query such as “how many points are in this polygon”?

A fine (boundary) line

In truth, it is a matter of style of output.


Review of surface approximation “dimensions” Local vs. Gradual

Exact vs. Approximate

Gradual vs. Abrupt

Deterministic vs. Stochastic


Thiessen polygons Local

Exact

Abrupt

Deterministic


More sophisticated surface generation (trend surface)

Use a “least squares”-

like technique

to fit a surface to the data


Trend Surfaces

Global Approximate (in most cases) Gradual Deterministic

Better quality obtained by using higher order surface, but takes longer


Inverse distance interpolation

Value of a point is related to the sum of the values of all other points divided by their distance from the given point


Inverse distance

Global (but effectively local)

Approximate (but close to exact)

Gradual Deterministic

Can use different functions, e.g. inverse distance squared


Spatial moving average

Global (but heavily local)

Approximate (but close to exact)

Gradual

Deterministic


“Realistic” surface modeling Requires approximating

“Show the impression, not the data”

Often involves slope and aspect

Commonly used for shading maps


Building “shade” Shaded maps intrinsically include a

“camera” and a “direction”

For “perspective”, color is determined using the dot product (trigonometry alert) of the value of the normal (aspect) and the camera vector (line of sight)


Some shaded surfaces

Image from: Burrough & McDonnell, Principles of Geographic Information Systems, p. 192


Where has all the rainfall gone?

Image from: Burrough & McDonnell, Principles of Geographic Information Systems, p. 194


It’s not calculus Much analysis is done through “cellular”

computation

Conway’s game of Life is an example

http://www.bitstorm.org/gameoflife/

Use the gradient to move “cells” of water to show flow and/or flooding

http://www.bitstorm.org/gameoflife/


More complex models To compute the irradiance, I, use the

following formula

I = [cos0cos + sin0sincos(0-A)]S0

x exp(-T0/ cos0)

where S0 is the exatmospheric solar flux, 0 is the solar zenith angle, etc.


Thoughts on surface analysis Surface analysis is handy, but

requires Moderately complex database queries,

or Moderately complex mathematics

Fortunately, much of this is “built-in” through wizards (e.g. buffer wizard)


Some thoughts on surface generation “There are three kinds of lies: lies, damned lies

and statistics” Benjamin Disraeli, popularized by Mark Twain

“Anyone can lie with statistics” Anonymous

“A picture can lie more effectively than words” Anonymous

surface analysis

Documents

lecture 13a7simple

lecture 13a1414cs

lecture 13a9how

lecture 13a4when

lecture 13a16

lecture 13a5how

lecture 13a18value

lecture 13a10a choropleth