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CS 128/ES 228 - Lecture 13a1 Surface Analysis
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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
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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!
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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
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CS 128/ES 228 - Lecture 13a5 How do we display a map with “elevation”? Choropleth map Contour map Surface map
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CS 128/ES 228 - 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
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CS 128/ES 228 - Lecture 13a7 Simple uses of choropleths Ordinal Population Per capita income Crop yield Categorical Soil type Political party control Primary industry
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CS 128/ES 228 - Lecture 13a8 Display issues for choropleths Classification Type Number of intervals Colors
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CS 128/ES 228 - Lecture 13a9 How do we select choropleth regions? Based on existing polygons Based on dissolved polygons Based on nearest points
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CS 128/ES 228 - Lecture 13a10 A Choropleth you built
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CS 128/ES 228 - 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
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CS 128/ES 228 - 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
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CS 128/ES 228 - 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.
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Review of surface approximation “dimensions” Local vs. Gradual Exact vs. Approximate Gradual vs. Abrupt Deterministic vs. Stochastic CS 128/ES 228 - Lecture 13a14
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CS 128/ES 228 - Lecture 13a15 Thiessen polygons Local Exact Abrupt Deterministic
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More sophisticated surface generation (trend surface) CS 128/ES 228 - Lecture 13a16 Use a “least squares”- like technique to fit a surface to the data
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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 13a17
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Inverse distance interpolation CS 128/ES 228 - 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
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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 13a19
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Spatial moving average CS 128/ES 228 - Lecture 13a20 Global (but heavily local) Approximate (but close to exact) Gradual Deterministic
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CS 128/ES 228 - Lecture 13a21 “Realistic” surface modeling Requires approximating “Show the impression, not the data” Often involves slope and aspect Commonly used for shading maps
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CS 128/ES 228 - 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)
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CS 128/ES 228 - Lecture 13a23 Some shaded surfaces Image from: Burrough & McDonnell, Principles of Geographic Information Systems, p. 192
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CS 128/ES 228 - Lecture 13a24 Where has all the rainfall gone? Image from: Burrough & McDonnell, Principles of Geographic Information Systems, p. 194
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CS 128/ES 228 - Lecture 13a25 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
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CS 128/ES 228 - Lecture 13a26 More complex models To compute the irradiance, I, use the following formula I = [cos 0 cos + sin 0 sincos( 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.
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CS 128/ES 228 - 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)
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CS 128/ES 228 - 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
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