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Surface Analysis

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?.

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Surface Analysis

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

  2. 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 CS 128/ES 228 - Lecture 13a

  3. Network complexities All answers learned in CS 232! CS 128/ES 228 - Lecture 13a

  4. 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 228 - Lecture 13a

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

  6. Choroplethmaps • 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 228 - Lecture 13a

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

  8. Display issues for choropleths • Classification Type • Number of intervals • Colors CS 128/ES 228 - Lecture 13a

  9. How do we select choroplethregions? • Based on existing polygons • Based on dissolved polygons • Based on nearest points CS 128/ES 228 - Lecture 13a

  10. A Choroplethyou built CS 128/ES 228 - Lecture 13a

  11. 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 228 - Lecture 13a

  12. 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 228 - Lecture 13a

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

  14. Review of surface approximation “dimensions” • Local vs. Gradual • Exact vs. Approximate • Gradual vs. Abrupt • Deterministic vs. Stochastic CS 128/ES 228 - Lecture 13a

  15. Thiessen polygons • Local • Exact • Abrupt • Deterministic CS 128/ES 228 - Lecture 13a

  16. More sophisticated surface generation (trend surface) Use a “least squares”-like technique to fit a surface to the data CS 128/ES 228 - Lecture 13a

  17. Trend Surfaces • Global • Approximate (in most cases) • Gradual • Deterministic • Better quality obtained by using higher order surface, but takes longer CS 128/ES 228 - Lecture 13a

  18. 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 CS 128/ES 228 - Lecture 13a

  19. 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 228 - Lecture 13a

  20. Spatial moving average • Global (but heavily local) • Approximate (but close to exact) • Gradual • Deterministic CS 128/ES 228 - Lecture 13a

  21. “Realistic” surface modeling • Requires approximating • “Show the impression, not the data” • Often involves slope and aspect • Commonly used for shading maps CS 128/ES 228 - Lecture 13a

  22. 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 228 - Lecture 13a

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

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

  25. 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 CS 128/ES 228 - Lecture 13a

  26. More complex models • To compute the irradiance, I, use the following formula I = [cos0cos + sin0sincos(0-A)]S0 x exp(-T0/cos0) where S0 is the exatmospheric solar flux, 0 is the solar zenith angle, etc. CS 128/ES 228 - Lecture 13a

  27. 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 228 - Lecture 13a

  28. 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 CS 128/ES 228 - Lecture 13a

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