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Network and Surface Analysis: Shortest Paths, Flow Dynamics, and Visualization Techniques

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beulah
28 diapositives · 484 Views · Aug 01, 2014

This lecture explores the fundamental concepts of network analysis, focusing on determining the shortest paths, cheapest routes, and maximum flow capacity within given networks. It also delves into surface analysis techniques, such as the use of contour maps and choropleth maps to visually represent various data, including elevation and distribution of resources. The discussion emphasizes the importance of accurate data classification, visualization challenges, and the relevance of advanced modeling techniques for robust surface and network analysis.

#network and surface analysis: shortest paths, flow dynamics, and visualization techniques #network and surface analysis: shortest paths, flow dynamics, and visualization techniques ppt #powerpoint #presentation
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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