u34-THE POLYGON OVERLAY OPERATION

u34-THE POLYGON OVERLAY OPERATION - UNIT 34 - THE POLYGON...

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Sheet1 Page 1 UNIT 34 - THE POLYGON OVERLAY OPERATION <toc.html#UNIT34> UNIT 34 - THE POLYGON OVERLAY OPERATION Compiled with assistance from Denis White, Environmental Protection Agency, Corvallis, OR * A. INTRODUCTION <#SEC34.1> o Traditions of polygon overlay use <#SEC34.1.1> * B. GENERAL CONCEPTS OF POLYGON OVERLAY OPERATIONS <#SEC34.2> o Operations requiring polygon overlay <#SEC34.2.1> * C. OVERLAY ALGORITHMS <#SEC34.3> o Objective <#SEC34.3.1> o Given <#SEC34.3.2> o Procedure <#SEC34.3.3> * D. COMPUTATIONAL COMPLEXITY <#SEC34.4> * E. INTERSECTION PROBLEMS <#SEC34.5> o 1. Adjacent lines <#SEC34.5.1> o 2. Sliver polygons <#SEC34.5.2> o Removing slivers during overlay <#SEC34.5.3> o Removing slivers after overlay <#SEC34.5.4> * REFERENCES <#SEC34.6> * DISCUSSION AND EXAM QUESTIONS <#SEC34.7> * NOTES <#SEC34.8> UNIT 34 - THE POLYGON OVERLAY OPERATION Compiled with assistance from Denis White, Environmental Protection Agency, Corvallis, OR A. INTRODUCTION <#OUT34.1> * the simple algorithms discussed previously form the basis for one of the most complex operations of vector GIS systems - polygon overlay Traditions of polygon overlay use <#OUT34.1.1> * the three traditions of polygon overlay are: 1. Landscape planning o superimposing layers of geographical data (e.g. environmental and social factors) so that their spatial
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Sheet1 Page 2 relationships can be used in making land use decisions o a key reference is McHarg, 1969, Design with Nature 2. Set theoretic o a polygon can be thought of as representing a set o when two sets (polygons) A and B are overlaid, we have a graphic interpretation of the set concepts of intersection and union diagram + the area of overlap of A and B is A.AND.B (intersection) + the combined area is A.OR.B (union) overhead/handout Sixteen combinations of Boolean operations o it is possible to identify 16 such combinations, or Boolean expressions including e.g. + A.AND.(NOT.B), i.e. all of the area of A which is not overlapped by B + NOT.(A.OR.B), i.e. the outside world (= (NOT.A).AND.(NOT.B) o in most polygon overlay operations it is the intersection which is of most interest, i.e. the area which is common to A and B 3. Area interpolation Given: the population of area A and the fact that areas A and B overlap Estimate: the population of area B diagram * this problem can be solved by apportioning the population of A so that the amount in the area covered by B is proportional to the area of overlap * this is a simple way of estimating the population of areas from statistics based on other areal units o e.g. estimating populations of voting districts from populations of census tracts * this method assumes that density is uniform within A, but more realistic versions of the technique exist o see Unit 41 B. GENERAL CONCEPTS OF POLYGON OVERLAY OPERATIONS <#OUT34.2> * in GIS, the normal case of polygon overlay takes two map layers and overlays them o each map layer is covered with non-overlapping polygons * if we think of one layer as "red" and the other as "blue", the
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u34-THE POLYGON OVERLAY OPERATION - UNIT 34 - THE POLYGON...

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