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Spatial Analysis (3D) . Putting it all together (again). Siting a nuclear waste dump Build Layer A by selecting only those areas with “good” geology ( good geology layer )

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spatial analysis 3d

Spatial Analysis (3D)

CS 128/ES 228 - Lecture 12b

putting it all together again
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
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
On to 3-D

CS 128/ES 228 - Lecture 12b

some more gis queries
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
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

3 d computational complexity

1984

technology

1997

technology

3-D Computational Complexity

CS 128/ES 228 - Lecture 12b

approximations
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

surface approximations

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 12b

types of approximation
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 approximation1
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
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
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
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
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

smooth shading

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

tins triangulated irregular networks

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 12b

simple queries
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

slope and aspect

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 12b

what is slope
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
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
Our friend calculus
  • Slope is essentially a first derivative
  • Second derivatives are also useful for…

convexity computations

CS 128/ES 228 - Lecture 12b

what is aspect

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
Matt Hartloff, ‘2000
  • Delaunay “Sweep” algorithm uses Voronoi diagram as first step

CS 128/ES 228 - Lecture 12b

jackson hole wy
Jackson Hole, WY

…then shades result based upon slopes and aspects

CS 128/ES 228 - Lecture 12b

visibility
Visibility
  • What can I see from where?
  • Tough to compute!

CS 128/ES 228 - Lecture 12b

when is an elevation not an elevation
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
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

network complexities
Network complexities

All answers learned in CS 232!

CS 128/ES 228 - Lecture 12b

conclusions
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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