Spatial Analysis (3D)
CS 128/ES 228 - Lecture 12b
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When last we visited…
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Buffering – another tool

Buffering (building
a neighborhood
around a feature)
is a common aid
in GIS analysis
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Using Buffers to Select
•Select the
features
•Save the features
as a layer
•(Export)
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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 (2valued) 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)
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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
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On to 3-D
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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?

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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)

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3-D Computational
Complexity
1984
1997
technology
technology
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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!!!
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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
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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?
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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?
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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
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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
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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
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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

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Smooth Shading


Standard (linear)
interpolation
leads to smooth
shaded images
Local, exact,
gradual,
deterministic

X
1-
w
y
W = *y + (1-)*x
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TINs – Triangulated
Irregular Networks


Connect
“adjacent” data
points via lines
to form
triangles, then
interpolate
or
Local, exact,
gradual,
possibly
stochastic
Image from: http://www.ian-ko.com/resources/triangulated_irregular_network.htm
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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
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Slope and aspect
A natural question with elevational
data is to ask how rapidly that data
is changing, e.g. “What is the
gradient?”
slope
 Another natural question is to ask
what direction the slope is facing,
i.e. “What is the normal?”
aspect

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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
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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)
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Our friend calculus

Slope is essentially a first derivative

Second derivatives are also useful
for…
convexity computations
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What is aspect?
Aspect is what
mathematicians
would call a
“normal”
 Computed
arithmetically
Shows what
from equation
direction the
of plane
surface “faces”

Image from: http://www.friends-of-fpc.org/tutorials/graphics/dlx_ogl/teil12_6.gif
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Matt Hartloff, ‘2000

Delaunay “Sweep” algorithm uses
Voronoi diagram as first step
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Jackson Hole, WY
…then shades result based upon slopes and aspects
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Visibility


What can I see from where?
Tough to compute!
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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
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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
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Network complexities
Shortest path
Easy
Cheapest path
Easy
Network flow
Medium
Traveling
salesperson
Exact solution is
IMPOSSIBLY
HARD but can be
approximated
All answers learned in CS 232!
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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”.
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