1. CS 128/ES 228 - Lecture 13a1 Surface Analysis

2. CS 128/ES 228 - 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: http://www.eli.sdsu.edu/courses/fall96/cs660/notes/NetworkFlow/NetworkFlow.html#RTFToC2

3. CS 128/ES 228 - 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!

4. CS 128/ES 228 - 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

5. CS 128/ES 228 - Lecture 13a5 How do we display a map with “elevation”? Chloropleth map Contour map Surface map

6. CS 128/ES 228 - Lecture 13a6 Chloropleth 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

7. CS 128/ES 228 - Lecture 13a7 Simple uses of chloropleths Ordinal Population Per capita income Crop yield Categorical Soil type Political party control Primary industry

8. CS 128/ES 228 - Lecture 13a8 Display issues for chloropleths Classification Type Number of intervals Colors

9. CS 128/ES 228 - Lecture 13a9 How do we select chloropleth regions? Based on existing polygons Based on dissolved polygons Based on nearest points

10. CS 128/ES 228 - Lecture 13a10 A Chloropleth you built

11. CS 128/ES 228 - Lecture 13a11 More complex queries using chloropleths Time series data Population change % of land in agricultural use Computation driven Total spending power = Average income x population Average wheat yield = Total yield / Number of farms

12. CS 128/ES 228 - Lecture 13a12 Basic model for “computed chloropleths” 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

13. CS 128/ES 228 - Lecture 13a13 A riddle (sans funny punch line) What is the difference between a chloropleth 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.

14. CS 128/ES 228 - Lecture 13a14 More sophisticated analysis By testing adjacent regions of the Voronoi diagram, interesting questions can be answered.

15. CS 128/ES 228 - Lecture 13a15 “Voronoi” queries Where is the nearest “facility”, e.g. fire house, hospital, Denny’s restaurant? Which is the “second best” facility? What is the largest empty region (to put new store, or toxic dump)?

16. CS 128/ES 228 - Lecture 13a16 Continuous fields Requires approximating Often involves slope and aspect Commonly used for shading maps

17. CS 128/ES 228 - Lecture 13a17 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)

18. CS 128/ES 228 - Lecture 13a18 Some shaded surfaces Image from: Burrough & McDonnell, Principles of Geographic Information Systems, p. 192

19. CS 128/ES 228 - Lecture 13a19 Where has all the rainfall gone? Image from: Burrough & McDonnell, Principles of Geographic Information Systems, p. 194

20. CS 128/ES 228 - Lecture 13a20 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

21. CS 128/ES 228 - Lecture 13a21 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.

22. CS 128/ES 228 - Lecture 13a22 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)

23. CS 128/ES 228 - Lecture 13a23 Conclusions A GIS without any spatial analysis is like a car without a gas pedal. It is okay to look at, but you can’t do anything with it. A GIS without 3-D spatial analysis is like a car without a radio. It may still be useful, but you wish you had the “luxury”.