1. CS 128/ES 228 - Lecture 12b1 Spatial Analysis (3D)

2. CS 128/ES 228 - Lecture 12b2 When last we visited…

3. CS 128/ES 228 - Lecture 12b3 Buffering – another tool Buffering (building a neighborhood around a feature) is a common aid in GIS analysis

4. CS 128/ES 228 - Lecture 12b4 Using Buffers to Select Select the features Save the features as a layer (Export)

5. CS 128/ES 228 - Lecture 12b5 Putting it all together Siting a nuclear waste dump Build Layer A by selecting only those areas with “good” geology (good geology layer) Build Layer B by taking a population density layer and reclassifying it in a boolean (2- valued) way to select only areas with a low population density (low population layer) Build Layer C by selecting those areas in A that intersect with features in B (good geology AND low population layer) Build Layer D by selecting “major” roads from a standard roads layer (major roads layer)

6. CS 128/ES 228 - Lecture 12b6 Siting the Dump, Part Deux Build Layer E by buffering Layer D at a suitable distance (major roads buffer layer) Build Layer F by selecting those features from C that are not in any region of E (good geology, low population and not near major roads layer) Build Layer G by selecting regions that are “conservation areas” (no development layer) Build Layer H by selecting those features from F that are not in any region of G (suitable site layer) See also: Figure 6.9, p. 121

7. CS 128/ES 228 - Lecture 12b7 On to 3-D

8. CS 128/ES 228 - Lecture 12b8 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?

9. CS 128/ES 228 - Lecture 12b9 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)

10. CS 128/ES 228 - Lecture 12b10 3-D Computational Complexity 1984 technology 1997 technology

11. CS 128/ES 228 - Lecture 12b11 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!!!

12. CS 128/ES 228 - Lecture 12b12 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 Image from: http://www.ian-ko.com/resources/triangulated_irregular_network.htm

13. CS 128/ES 228 - Lecture 12b13 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?

14. CS 128/ES 228 - Lecture 12b14 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?

15. CS 128/ES 228 - Lecture 12b15 Display “by point” Image from: http://www.csc.noaa.gov/products/nchaz/htm/lidtut.htm Notice the (very) large number of data points This is not always feasible “Draw” the dot

16. CS 128/ES 228 - Lecture 12b16 Display “by contour” Image from: http://www.csc.noaa.gov/products/nchaz/htm/lidtut.htm More feasible, but granularity is an issue Consider the ocean… “Connect” the dots

17. CS 128/ES 228 - Lecture 12b17 Display “by surface” Image from: http://www.csc.noaa.gov/products/nchaz/htm/lidtut.htm Involves interpolation of data Better picture, but is it more accurate? “Paint” the connected dots

18. CS 128/ES 228 - Lecture 12b18 Voronoi (Theissen) polygons as a painting tool Points on the surface are approximated by giving them the value of the nearest data point Exact, abrupt, deterministic

19. CS 128/ES 228 - Lecture 12b19 Smooth Shading Standard (linear) interpolation leads to smooth shaded images Local, exact, gradual, deterministic Xyw 1- W = *y + (1-)*x

20. CS 128/ES 228 - Lecture 12b20 TINs – Triangulated Irregular Networks Connect “adjacent” data points via lines to form triangles, then interpolate Local, exact, gradual, possibly stochastic or Image from: http://www.ian-ko.com/resources/triangulated_irregular_network.htm

21. CS 128/ES 228 - Lecture 12b21 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

22. CS 128/ES 228 - Lecture 12b22 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?” slope aspect

23. CS 128/ES 228 - Lecture 12b23 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

24. CS 128/ES 228 - Lecture 12b24 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)

25. CS 128/ES 228 - Lecture 12b25 Our friend calculus Slope is essentially a first derivative Second derivatives are also useful for… convexity computations

26. CS 128/ES 228 - Lecture 12b26 What is aspect? Aspect is what mathematicians would call a “normal” Computed arithmetically from equation of plane Image from: http://www.friends-of-fpc.org/tutorials/graphics/dlx_ogl/teil12_6.gif Shows what direction the surface “faces”

27. CS 128/ES 228 - Lecture 12b27 Matt Hartloff, ‘2000 Delaunay “Sweep” algorithm uses Voronoi diagram as first step

28. CS 128/ES 228 - Lecture 12b28 Jackson Hole, WY …then shades result based upon slopes and aspects

29. CS 128/ES 228 - Lecture 12b29 Visibility What can I see from where? Tough to compute!

30. CS 128/ES 228 - Lecture 12b30 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

31. CS 128/ES 228 - Lecture 12b31 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

32. CS 128/ES 228 - Lecture 12b32 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!

33. CS 128/ES 228 - Lecture 12b33 Conclusions A GIS without spatial analysis is like a car without a gas pedal. It is okay to look at, but you can’t do anything with it. 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”.