Spatial Analysis (3D)

1. Spatial Analysis (3D) CS 128/ES 228 - Lecture 13b

2. Some (More) GIS Queries • How steep is the road? • Which direction does the hill face? • What does the horizon look like? • What is that object over there? • Where will the waste flow? • What’s the fastest route home? CS 128/ES 228 - Lecture 13b

3. Types of queries • Aspatial – make no reference to spatial data • 2-D Spatial – make reference to spatial data in the plane • 3-D Spatial – make reference to “elevational” data • Network – involve analyzing a network in the GIS (yes, it’s spatial) CS 128/ES 228 - Lecture 13b

4. 1984 technology 1997 technology 3-D Computational Complexity CS 128/ES 228 - Lecture 13b

5. Approximations • In the vector model, each object represents exactly one feature; it is “linked” to its complete set of attribute data • In the raster model, each cell represents exactly one piece of data; the data is specifically for that cell • THE DATA IS DISCRETE!!! CS 128/ES 228 - Lecture 13b

6. Image from: http://www.ian-ko.com/resources/triangulated_irregular_network.htm Surface Approximations With a surface, only a few points have “true data” The “values” at other points are only an approximation The are determined (somehow) by the neighboring points The surface is CONTINUOUS CS 128/ES 228 - Lecture 13b

7. Types of approximation • GLOBAL or LOCAL • Does the approximation function use all points or just “nearby” ones? • EXACT or APPROXIMATE • At the points where we do have data, is the approximation equal to that data? CS 128/ES 228 - Lecture 13b

8. Types of approximation • GRADUAL or ABRUPT • Does the approximation function vary continuously or does it “step” at boundaries? • DETERMINISTIC or STOCHASTIC • Is there a randomness component to the approximation? CS 128/ES 228 - Lecture 13b

9. Display “by point” Image from: http://www.csc.noaa.gov/products/nchaz/htm/lidtut.htm CS 128/ES 228 - Lecture 13b

10. Display “by contour” Image from: http://www.csc.noaa.gov/products/nchaz/htm/lidtut.htm CS 128/ES 228 - Lecture 13b

11. Display “by surface” Image from: http://www.csc.noaa.gov/products/nchaz/htm/lidtut.htm CS 128/ES 228 - Lecture 13b

12. Voronoi (Theissen) polygons • Points on the surface are approximated by giving them the value of the nearest data point • Exact, abrupt, deterministic CS 128/ES 228 - Lecture 13b

13. Matt Hartloff, ‘2000 • Delaunay “Sweep” algorithm CS 128/ES 228 - Lecture 13b

14. Matt Hartloff, continued • Jackson Hole CS 128/ES 228 - Lecture 13b

15.  1- X w y W = *y + (1-)*x Smooth Shading • Standard (linear) interpolation leads to smooth shaded images • Local, exact, gradual, deterministic CS 128/ES 228 - Lecture 13b

16. or Image from: http://www.ian-ko.com/resources/triangulated_irregular_network.htm TINs – Triangulated Irregular Networks • Connect “adjacent” data points via lines to form triangles, then interpolate • Local, exact, gradual, possibly stochastic CS 128/ES 228 - Lecture 13b

17. Simple Queries? • The descriptions thus far represent “simple” queries, in the same sense that length, area, etc. did for 2-D. • A more complex query would involve comparing the various data points in some way CS 128/ES 228 - Lecture 13b

18. slope aspect Slope and aspect • A natural question with elevational data is to ask how rapidly that data is changing, e.g. “What is the gradient?” • Another natural question is to ask what direction the slope is facing, i.e. “What is the normal?” CS 128/ES 228 - Lecture 13b

19. What is slope? • The slope of a curve (or surface) is represented by a linear approximation to a data set. • Can be solved for using algebra and/or calculus Image from: http://oregonstate.edu/dept/math/CalculusQuestStudyGuides/vcalc/tangent/tangent.html CS 128/ES 228 - Lecture 13b

20. Solving for slope • In a raster world, we use the equation for a plane: z = a*x + b*y + c and we solve for a “best fit” • In a vector world, it is usually computed as the TIN is formed (viz. the way area is pre-computed for polygons) CS 128/ES 228 - Lecture 13b

21. Our friend calculus • Slope is essentially a first derivative • Second derivatives are also useful for… convexity computations CS 128/ES 228 - Lecture 13b

22. Image from: http://www.friends-of-fpc.org/tutorials/graphics/dlx_ogl/teil12_6.gif What is aspect? • Aspect is what mathematicians would call a “normal” • Computed arithmetically from equation of plane Shows what direction the surface “faces” CS 128/ES 228 - Lecture 13b

23. Visibility • What can I see from where? • Tough to compute! CS 128/ES 228 - Lecture 13b

24. What is an elevation? • It could be an ELEVATION, i.e. an altitude • BUT, it could be rainfall, income, or any other scalar measurement • Bottom Line: It’s one more dimension on top of the geographic data CS 128/ES 228 - Lecture 13b

25. 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 13b

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

27. Conclusions • A GIS without spatial analysis is like a car without a gas pedal. • 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”. CS 128/ES 228 - Lecture 13b