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

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

  • 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” http://www.ian-ko.com/resources/triangulated_irregular_network.htm

  • 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” http://www.ian-ko.com/resources/triangulated_irregular_network.htm

  • 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” http://www.ian-ko.com/resources/triangulated_irregular_network.htm

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

  • 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

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

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

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

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

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

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

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

  • 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 http://www.friends-of-fpc.org/tutorials/graphics/dlx_ogl/teil12_6.gif

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

CS 128/ES 228 - Lecture 12b


Jackson hole wy
Jackson Hole, WY http://www.friends-of-fpc.org/tutorials/graphics/dlx_ogl/teil12_6.gif

…then shades result based upon slopes and aspects

CS 128/ES 228 - Lecture 12b


Visibility
Visibility http://www.friends-of-fpc.org/tutorials/graphics/dlx_ogl/teil12_6.gif

  • 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? http://www.friends-of-fpc.org/tutorials/graphics/dlx_ogl/teil12_6.gif

  • 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 http://www.friends-of-fpc.org/tutorials/graphics/dlx_ogl/teil12_6.gif

  • 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 http://www.friends-of-fpc.org/tutorials/graphics/dlx_ogl/teil12_6.gif

All answers learned in CS 232!

CS 128/ES 228 - Lecture 12b


Conclusions
Conclusions http://www.friends-of-fpc.org/tutorials/graphics/dlx_ogl/teil12_6.gif

  • 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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