421:, because for any point in space, each criterion is either present or not present, and the point is either in the final habitat area or it is not (acknowledging that the criteria may be vague, but this requires more complex fuzzy suitability analysis methods). That is, which vegetation polygon the point is in is not important, only whether it is suitable or not suitable. This means that the criteria can be expressed as a Boolean logic expression, in this case, H = A and B and not C.
176:
252:
167:(LCGU), the area where a pair of polygons overlapped, with attributes inherited from the original polygons. Chrisman and James Dougenik implemented this strategy in the WHIRLPOOL program, released in 1979 as part of the Odyssey project to develop a general-purpose GIS. This system implemented several improvements over the earlier approaches in CGIS and PIOS, and its algorithm became part of the core of GIS software for decades to come.
432:(consisting of one or more disjoint polygons but no adjacent polygons) representing the region that meets the criterion. With these inputs, each of the operators of Boolean logic corresponds exactly to one of the polygon overlay operators: intersect = AND, union = OR, subtract = AND NOT, exclusive or = XOR. Thus, the above habitat region would be generated by computing the intersection of A and B, and subtracting C from the result.
163:, in part to develop GIS as a digital tool to implement McHarg's methods. In 1975, Thomas Peucker and Nicholas Chrisman of the Harvard Lab introduced the POLYVRT data model, one of the first to explicitly represent topological relationships and attributes in vector data. They envisioned a system that could handle multiple "polygon networks" (layers) that overlapped by computing
409:, also known as a suitability model or multi-criteria evaluation. The task is to find the region that meets a set of criteria, each of which can be represented by a region. For example, the habitat of a species of wildlife might need to be A) within certain vegetation cover types, B) within a threshold distance of a water source (computed using a
379:
most common use is when the two layers represent the same theme, but one represents recent changes (e.g., new parcels) that need to replace the older ones in the same location. It can be replicated by subtracting one layer from the other, then computing the union of that result with the original first layer.
481:
Clip: While the primary input can be points or lines, the clipping layer is usually required to be polygons, producing the same geometry as the primary input, but only including those features (or parts of lines) that are within the clipping polygons. This operation might also be considered a form of
392:
in ArcGIS and
Manifold; not in QGIS, TNTmips, or GRASS): The result includes all of the LCGUs that cover one of the input layers, excluding those that are only in the other layer. It is called "divide" because it has the appearance of one layer being used to divide the polygons of the other layer. It
346:
in GRASS; missing from
Manifold): The result includes the portions of polygons in both layers that do not overlap; that is, all LCGUs that have one parent. This could also be achieved by computing the intersection and the union, then subtracting the intersection from the union, or by subtracting each
73:
The basic approach of a vector overlay operation is to take in two or more layers composed of vector shapes, and output a layer consisting of new shapes created from the topological relationships discovered between the input shapes. A range of specific operators allows for different types of input,
378:
in TNTmips; not in QGIS or GRASS): The result includes one layer intact, with the portions of the polygons of the other layer only where the two layers do not intersect. It is called "cover" because the result looks like one layer is covering the other; it is called "update" in ArcGIS because the
225:: Create an attribute table that includes the columns from both inputs. For each LCGU, determine its parent polygon from each input layer, and copy its attributes into the LCGU's row the new table; if was not in any of the polygons for one of the input layers, leave the values as null.
455:
Vector overlay is most commonly performed using two polygon layers as input and creating a third polygon layer. However, it is possible to perform the same algorithm (parts of it at least) on points and lines. The following operations are typically supported in GIS software:
290:
in GRASS): The result includes only the LCGUs where the two input layers intersect (overlap); that is, those with both "parents." This is identical to the set theoretic intersection of the input layers. Intersect is probably the most commonly used operator in this list.
466:, as it merges the attribute tables of the two layers analogous to a table join. An example of this would be allocating students to school districts. Because it is rare for a point to exactly fall on a line or another point, the fuzzy tolerance is often used here.
511:
in 1982. Each generation of Esri software (ARC/INFO, ArcGIS, ArcGIS Pro) has included a set of separate tools for each of the overlay operators (Intersect, Union, Clip, etc.). The current implementation in ArcGIS Pro recently added an alternative set of
141:(CGIS), developed during the 1960s and completed in 1971, was based on a rudimentary vector data model, and one of the earliest functions was polygon overlay. Another early vector GIS, the Polygon Information Overlay System (PIOS), developed by
360:
in TNTmips): The result includes the portions of polygons of one layer where they intersect the other layer. The outline is the same as the intersection, but the interior only includes the polygons of one layer rather than computing the LCGUs.
114:
As far as possible maps should be drawn on transparent paper, so that when completed the maps to the same scale can be ‘sieved’—i.e., placed one on top of another in turn so that correlations or their absence can be noted.
46:
in GIS since its early development. Some overlay operations, especially
Intersect and Union, are implemented in all GIS software and are used in a wide variety of analytical applications, while others are less common.
477:
Subtract: The output will be of the same dimension as the primary input, with the subtraction layer being of the same or lesser dimension: Points - {Points, Lines, Polygons} = Points, Lines - {Lines, Polygons} =
491:
Union: Normally, both input layers are expected to be of the same dimensionality, producing an output layer including both sets of features. ArcGIS and GRASS do not allow this option with points or lines.
325:
in GRASS; missing from
Manifold): The result includes only the portions of polygons in one layer that do not overlap with the other layer; that is, the LCGUs that have no parent from the other layer.
219:: Find each minimal closed ring of lines, and use it to create a polygon. Each of these will be a least common geographic unit (LCGU), with at most one "parent" polygon from each of the two inputs.
522:(open source), although it was originally raster-based, has included overlay as part of its vector system since GRASS 3.0 (1988). Most of the polygon overlay operators are collected into a single
460:
Intersect: The output will be of the same dimension as the lower of the inputs: Points * {Points, Lines, Polygons} = Points, Lines * {Lines, Polygons} = Lines. This is often used as a form of
200:: In each layer, identify edges shared between polygons. Break each line at the junction of shared edges and remove duplicates to create a set of topologically planar connected lines.
500:
Vector
Overlay is included in some form in virtually every GIS software package that supports vector analysis, although the interface and underlying algorithms vary significantly.
304:
in GRASS): The result includes all of the LCGUs, both those where the inputs intersect and where they do not. This is identical to the set theoretic union of the input layers.
190:
Since the original implementation, the basic strategy of the polygon overlay algorithm has remained the same, although the vector data structures that are used have evolved.
160:
187:
both the geometry and the attributes of the inputs. Usually, both inputs are polygon layers, but lines and points are allowed in many operations, with simpler processing.
263:
are used to answer a variety of questions, although some are far more commonly implemented and used than others. The most common are closely analogous to operators in
740:
866:
55:
213:
from the two inputs. At each intersection, split both lines. Then merge the two line layers into a single set of topologically planar connected lines.
58:, in which different topics (say, climate, topography, and agriculture) can be directly compared based on a common location. It is also based on the
202:
In early topological data structures such as POLYVRT and the ARC/INFO coverage, the data was natively stored this way, so this step was unnecessary.
513:
425:
42:
are often used synonymously, although they are not identical in the range of operations they include. Overlay has been one of the core elements of
233:, a threshold distance. Any pair of lines that stay within this distance of each other are collapsed into a single line, avoiding unwanted narrow
156:
424:
In a task such as this, the overlay procedure can be simplified because the individual polygons within each layer are not important, and can be
259:
The basic algorithm can be modified in a number of ways to return different forms of integration between the two input layers. These different
82:
Prior to the advent of GIS, the overlay principle had developed as a method of literally superimposing different thematic maps (typically an
847:
393:
can be replicated by computing the intersection, then subtracting one layer from the other, then computing the union of these two results.
919:
557:
Javascript API includes the most common overlay methods, although these operate on individual input polygon objects, not on entire layers.
536:(open source) originally incorporated GRASS as its analytical engine, but has gradually developed its own processing framework, including
229:
Parameters are usually available to allow the user to calibrate the algorithm for a particular situation. One of the earliest was the
142:
94:) to see the interactions and find locations with specific combinations of characteristics. The technique was largely developed by
958:
153:
algorithm to find intersections quickly. Unfortunately, the results of overlay in these early systems was often prone to error.
138:
931:
537:
804:
647:
821:
585:
Steinitz, Carl; Parker, Paul; Jordan, Lawrie (1976). "Hand-Drawn
Overlays: Their History and Prospective Uses".
239:
that can occur when lines that should be coincident (for example, a river and a boundary that should follow it
23:
146:
663:
Tomlinson, Roger (1968). "A Geographic
Information System for Regional Planning". In Stewart, G.A. (ed.).
413:), and C) not within a threshold distance of significant roads. Each of the criteria can be considered
470:
has separate operations for computing a line intersection as lines (to find coincident lines) and as
516:" tools (as of v2.7) that uses parallel processing to more efficiently process very large datasets.
103:
564:
127:
279:(more than two inputs giving the same result regardless of the order in which they are paired).
888:
471:
447:. This enables the use of GIS to solve many spatial tasks that can be reduced to simple logic.
210:
95:
953:
488:, as it retains the features of one layer based on its topological relationship to another.
271:, and have adopted their terms. As in these algebraic systems, the overlay operators may be
106:, although his published accounts only reproduce the maps without explaining the technique.
406:
179:
Illustration of the steps in computing a polygon overlay in a geographic information system
8:
925:
523:
436:
131:
126:(1969), in which he gave several examples of projects on which he had consulted, such as
107:
874:
Proceedings of the
International Symposium on Cartography and Computing (Auto-Carto VII)
183:
The goal of all overlay operations is to take in vector layers, and create a layer that
748:
Proceedings of the
International Symposium on Cartography and Computing (Auto-Carto IV)
87:
67:
937:
527:
800:
643:
547:
110:
published instructions for the technique in an
English textbook in 1950, including:
91:
693:
Goodchild, Michael F. (1978). "Statistical aspects of the polygon overlay problem".
721:
150:
43:
543:
122:
was perhaps most responsible for widely publicizing this approach to planning in
27:
255:
A visualization of the polygon overlay operations available in most GIS software
725:
712:
Peucker, Thomas K.; Chrisman, Nicholas (1975). "Cartographic Data Structures".
235:
99:
947:
484:
444:
418:
268:
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440:
410:
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59:
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layer from the other, then computing the union of the two subtractions.
264:
119:
63:
519:
507:
GIS software has included polygon overlay since the first release of
51:
623:
Tyrwhitt, Jacqueline (1950). "Surveys for Planning". In APRR (ed.).
508:
83:
435:
Thus, this particular use of polygon overlay can be treated as an
560:
767:
GIS Fundamentals: A First Text on Geographic Information Systems
678:
Tomlinson, Roger F.; Calkins, Hugh W.; Marble, Duane F. (1976).
405:
One of the most common uses of polygon overlay is to perform a
194:
Given the two input polygon layers, extract the boundary lines.
243:) are digitized separately with slightly different vertices.
161:
Harvard Laboratory for Computer Graphics and Spatial Analysis
741:"WHIRLPOOL: A geometric processor for polygon coverage data"
533:
504:
467:
867:"ARC/INFO: A geo-relational model for spatial information"
797:
Concepts and Techniques of Geographic Information Systems
102:
appears to have used this approach to compare aspects of
74:
and different choices in what to include in the output.
677:
554:
149:
in 1971, also supported polygon overlay. It used the
584:
275:(giving the same result regardless of order) and/or
604:Manning, Warren (1913). "The Billerica Town Plan".
50:Overlay is based on the fundamental principle of
945:
695:Harvard papers on geographic information systems
711:
896:Proceedings of the FOSS/GRASS Users Conference
880:
813:
22:is an operation (or class of operations) in a
858:
773:
686:
671:
665:Land Evaluation: Papers of a CSIRO Symposium
667:. Macmillan of Australia. pp. 200–210.
886:
705:
400:
159:, a landscape architect, helped found the
864:
769:(3rd ed.). Eider Press. p. 352.
692:
662:
784:(2nd ed.). Wiley. pp. 125–137.
782:Exploring Geographic Information Systems
779:
738:
656:
622:
250:
174:
794:
764:
758:
732:
603:
578:
946:
680:Computer handling of geographical data
637:
795:Lo, C.P.; Yeung, Albert K.W. (2002).
631:
16:GIS analysis operation on vector data
139:Canada Geographic Information System
450:
90:) drawn on transparent film (e.g.,
13:
928:command documentation in GRASS GIS
788:
625:Town and Country Planning Textbook
567:among its vector analysis process.
495:
300:(ArcGIS, QGIS, Manifold, TNTmips;
286:(ArcGIS, QGIS, Manifold, TNTmips;
26:(GIS) for integrating two or more
14:
970:
913:
30:spatial data sets. Terms such as
845:
819:
395:Non-commutative, non-associative
381:Non-commutative, non-associative
363:Non-commutative, non-associative
356:(ArcGIS, QGIS, GRASS, Manifold;
327:Non-commutative, non-associative
839:
959:Geographic information systems
799:. Prentice Hall. p. 211.
780:Chrisman, Nicholas R. (2002).
616:
597:
1:
571:
165:Least Common Geographic Units
24:geographic information system
922:documentation in Esri ArcGIS
246:
170:
147:San Diego County, California
7:
563:includes several tools for
231:snapping or fuzzy tolerance
211:intersections between lines
10:
975:
887:Westervelt, James (2004).
726:10.1559/152304075784447289
546:implements overlay in its
77:
940:documentation in Manifold
865:Morehouse, Scott (1985).
714:The American Cartographer
593:(5 (September)): 444–455.
826:ArcGIS Pro Documentation
739:Dougenik, James (1979).
374:in ArcGIS and Manifold;
349:Commutative, associative
306:Commutative, associative
293:Commutative, associative
137:The first true GIS, the
104:Billerica, Massachusetts
852:QGIS 3.16 documentation
401:Boolean overlay algebra
128:transportation planning
822:"Intersect (Analysis)"
765:Bolstad, Paul (2008).
627:. Architectural Press.
606:Landscape Architecture
530:as a separate command.
336:Symmetrical Difference
256:
180:
117:
934:documentation in QGIS
587:Landcape Architecture
254:
178:
112:
848:"Line intersections"
638:McHarg, Ian (1969).
407:suitability analysis
96:landscape architects
920:The Overlay toolset
108:Jacqueline Tyrwhitt
40:topological overlay
640:Design with Nature
257:
181:
124:Design with Nature
88:chorochromatic map
68:point-set topology
938:Topology Overlays
338:in ArcGIS, QGIS;
261:overlay operators
223:Assembling part B
217:Assembling part A
132:land conservation
92:cellulose acetate
56:areal integration
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451:Lines and points
417:in the sense of
151:Point in polygon
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544:Manifold System
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496:Implementations
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403:
340:Exclusive Union
249:
236:sliver polygons
207:Cracking part B
198:Cracking part A
173:
80:
32:polygon overlay
17:
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5:
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932:Vector Overlay
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914:External links
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642:. p. 34.
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548:transformation
541:
538:vector overlay
531:
526:command, with
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479:
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452:
449:
430:boolean region
428:into a single
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365:
358:Extract Inside
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329:
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248:
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100:Warren Manning
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20:Vector overlay
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889:"GRASS Roots"
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806:0-13-080427-4
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954:GIS software
899:. Retrieved
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829:. Retrieved
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720:(1): 55–69.
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332:Exclusive or
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19:
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441:homomorphic
317:in ArcGIS;
277:associative
273:commutative
209:: Find any
60:mathematics
36:map overlay
948:Categories
901:26 October
831:29 October
754:: 304–311.
612:: 108–118.
572:References
319:Difference
313:(TNTmips;
265:set theory
185:integrates
120:Ian McHarg
84:isarithmic
64:set theory
926:v.overlay
524:v.overlay
520:GRASS GIS
426:dissolved
321:in QGIS;
284:Intersect
247:Operators
171:Algorithm
86:map or a
54:known as
52:geography
509:ARC/INFO
439:that is
390:Identity
311:Subtract
565:overlay
561:TNTmips
550:system.
437:algebra
415:boolean
376:Replace
241:de jure
115:(p.157)
78:History
876:: 388.
846:QGIS.
820:Esri.
803:
646:
528:v.clip
472:points
411:buffer
386:Divide
372:Update
38:, and
28:vector
892:(PDF)
870:(PDF)
744:(PDF)
478:Lines
368:Cover
315:Erase
298:Union
903:2021
833:2021
801:ISBN
644:ISBN
555:Turf
553:The
534:QGIS
505:Esri
468:QGIS
354:Clip
267:and
145:for
143:ESRI
130:and
66:and
722:doi
443:to
344:XOR
323:not
288:AND
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62:of
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
