CS 128/ES 228 - Lecture 11b1 Spatial Analysis (3D)

CS 128/ES 228 - Lecture 11b 1

Spatial Analysis (3D)


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?


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)


3-D Computational Complexity

1984

technology

1997

technology


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!!!


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


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?


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?


Display “by point”

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


Display “by contour”



Display “by surface”



Voronoi (Theissen) polygons Points on the

surface are approximated by giving them the value of the nearest data point

Exact, abrupt, deterministic


Smooth Shading Standard (linear)

interpolation leads to smooth shaded images

Local, exact, gradual, deterministic

X yw

1-

W = *y + (1-)*x


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


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


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


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


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)


Our friend calculus Slope is essentially a first derivative

Second derivatives are also useful for…

convexity computations


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”


Visibility

What can I see from where? Tough to compute!


What is an elevation? It could be an ELEVATION, i.e. an

altitude BUT, it could be rainfall, income, or

any other scalar measurement

Bottom Line: It’s one more dimension on top of the geographic data


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


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!


Conclusions A GIS without spatial analysis is like

a car without a gas pedal.

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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CS 128/ES 228 - Lecture 11b1 Spatial Analysis (3D)