CS 128/ES Lecture 13a1 Surface Analysis

CS 128/ES Lecture 13a2 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:

CS 128/ES Lecture 13a3 Network complexities Shortest pathEasy Cheapest pathEasy Network flowMedium Traveling salesperson Exact solution is IMPOSSIBLY HARD but can be approximated All answers learned in CS 232!

CS 128/ES Lecture 13a4 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

CS 128/ES Lecture 13a5 How do we display a map with “elevation”? Choropleth map Contour map Surface map

CS 128/ES Lecture 13a6 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

CS 128/ES Lecture 13a7 Simple uses of choropleths Ordinal Population Per capita income Crop yield Categorical Soil type Political party control Primary industry

CS 128/ES Lecture 13a8 Display issues for choropleths Classification Type Number of intervals Colors

CS 128/ES Lecture 13a9 How do we select choropleth regions? Based on existing polygons Based on dissolved polygons Based on nearest points

CS 128/ES Lecture 13a10 A Choropleth you built

CS 128/ES Lecture 13a11 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

CS 128/ES Lecture 13a12 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

CS 128/ES Lecture 13a13 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 CS 128/ES Lecture 13a14

CS 128/ES Lecture 13a15 Thiessen polygons Local Exact Abrupt Deterministic

More sophisticated surface generation (trend surface) CS 128/ES Lecture 13a16 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 CS 128/ES Lecture 13a17

Inverse distance interpolation CS 128/ES Lecture 13a18 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 CS 128/ES Lecture 13a19

Spatial moving average CS 128/ES Lecture 13a20 Global (but heavily local) Approximate (but close to exact) Gradual Deterministic

CS 128/ES Lecture 13a21 “Realistic” surface modeling Requires approximating “Show the impression, not the data” Often involves slope and aspect Commonly used for shading maps

CS 128/ES Lecture 13a22 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)

CS 128/ES Lecture 13a23 Some shaded surfaces Image from: Burrough & McDonnell, Principles of Geographic Information Systems, p. 192

CS 128/ES Lecture 13a24 Where has all the rainfall gone? Image from: Burrough & McDonnell, Principles of Geographic Information Systems, p. 194

CS 128/ES Lecture 13a25 It’s not calculus Much analysis is done through “cellular” computation Conway’s game of Life is an example Use the gradient to move “cells” of water to show flow and/or flooding

CS 128/ES Lecture 13a26 More complex models To compute the irradiance, I, use the following formula I = [cos 0 cos + sin 0 sincos( 0 -A)]S 0 x exp(-T 0 / cos 0 ) where S 0 is the exatmospheric solar flux,  0 is the solar zenith angle, etc.

CS 128/ES Lecture 13a27 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)

CS 128/ES Lecture 13a28 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