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### Spatial Analysis (3D)

CS 128/ES 228 - Lecture 12b

Putting it all together (again)

- 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)

CS 128/ES 228 - Lecture 12b

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 6.5, pp. 187-88

CS 128/ES 228 - Lecture 12b

On to 3-D

CS 128/ES 228 - Lecture 12b

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 12b

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 12b

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 12b

Image from: http://www.ian-ko.com/resources/triangulated_irregular_network.htm

Surface ApproximationsWith 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 12b

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 12b

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 12b

Display “by point”

- Notice the (very) large number of data points
- This is not always feasible
- “Draw” the dot

Image from: http://www.csc.noaa.gov/products/nchaz/htm/lidtut.htm

CS 128/ES 228 - Lecture 12b

Display “by contour”

- More feasible, but granularity is an issue
- Consider the ocean…
- “Connect” the dots

Image from: http://www.csc.noaa.gov/products/nchaz/htm/lidtut.htm

CS 128/ES 228 - Lecture 12b

Display “by surface”

- Involves interpolation of data
- Better picture, but is it more accurate?
- “Paint” the connected dots

Image from: http://www.csc.noaa.gov/products/nchaz/htm/lidtut.htm

CS 128/ES 228 - Lecture 12b

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

CS 128/ES 228 - Lecture 12b

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 12b

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 12b

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 12b

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 12b

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 12b

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 12b

Our friend calculus

- Slope is essentially a first derivative
- Second derivatives are also useful for…

convexity computations

CS 128/ES 228 - Lecture 12b

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 12b

Matt Hartloff, ‘2000

- Delaunay “Sweep” algorithm uses Voronoi diagram as first step

CS 128/ES 228 - Lecture 12b

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 12b

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 12b

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 most people would think it’s “standard” to have it and if you don’t, you are likely to wish you had the “luxury”.

CS 128/ES 228 - Lecture 12b

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