CS 128/ES Lecture 13b1 Surface Analysis

CS 128/ES Lecture 13b2 How do we display a map with “elevation”? Chloropleth map Contour map Surface map

CS 128/ES Lecture 13b3 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

CS 128/ES Lecture 13b4 Simple uses of chloropleths Ordinal Population Per capita income Crop yield Categorical Soil type Political party control Primary industry

CS 128/ES Lecture 13b5 Display issues for chloropleths Classification Type Number of intervals Colors

CS 128/ES Lecture 13b6 To dissolve or not to dissolve: That is the question

CS 128/ES Lecture 13b7 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

CS 128/ES Lecture 13b8 Basic model for “computed chloropleths” Use a query to create new attribute data Set the display to use that new data for computation Choose remaining display options

CS 128/ES Lecture 13b9 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.

CS 128/ES Lecture 13b10 Voronoi (Theissen) polygons – An important type of chloropleth Each point is “credited” with the region of points closer to it than to any other point

CS 128/ES Lecture 13b11 Dulaunay Triangulation By testing adjacent regions of the Voronoi diagram, interesting questions can be answered.

CS 128/ES Lecture 13b12 “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)

CS 128/ES Lecture 13b13 Continuous fields Requires approximating Often involves slope and aspect Commonly used for shading maps

CS 128/ES Lecture 13b14 Building “shade” Shaded maps intrinsically include a “camera” and a “direction” For “perspective”, color is determined using the dot product of the value of the normal (aspect) and the camera vector (line of sight)

CS 128/ES Lecture 13b15 Some shaded surfaces Image from: Burrough & McDonnell, Principles of Geographic Information Systems, p. 192

CS 128/ES Lecture 13b16 Where has all the rainfall gone? Image from: Burrough & McDonnell, Principles of Geographic Information Systems, p. 194

CS 128/ES Lecture 13b17 It’s not calculus Much analysis is done through “cellular” computation Conway’s game of Life is an example

CS 128/ES Lecture 13b18 How is it used in GIS? Image from: Burrough & McDonnell, Principles of Geographic Information Systems, p. 199

CS 128/ES Lecture 13b19 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 13b20 Conclusions 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 13b21 Final thoughts There is no pithy thought today