Overlay and combination operations

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Overlay and combination operations

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Overlay operations involve the placement of one map layer (set of features) A, on top of a second map layer, B, to create a map layer, C, that is some combination of A and B. C is normally a new layer, but may be a modification of B. Layer A in a vector GIS will consist of points, lines and/or polygons, whilst layer B will normally consist of polygons. All objects are generally assumed to have planar enforcement, and the resulting object set or layer must also have planar enforcement. The general term for such operations is topological overlay, although a variety of terminology is used by different GIS suppliers, as we shall see below. In raster GIS layers A and B are both grids, which should have a common origin and orientation — if not, resampling is required.

The process of overlaying map layers has some similarity with point set theory, but a large number of variations have been devised and implemented in different GIS packages. The principal operations have previously been outlined as the spatial analysis component of the OGC simple features specification (Table 4‑2). The open source package, GRASS, is a typical example of a GIS that provides an implementation of polygon overlay which is very similar to conventional point set theory (Figure 4‑15). Functions provided by GRASS include:

Intersection, where the result includes all those polygon parts that occur in both A and B
Union, where the result includes all those polygon parts that occur in either A or B, so is the sum of all the parts of both A and B
Not, where the result includes only those polygon parts that occur in A but not in B (sometimes described as a Difference operation), and
Exclusive or (XOR), which includes polygons that occur in A or B but not both, so is the same as (A Union B) minus (A Intersection B)

TNTMips provides similar functionality and uses much the same terminology as GRASS (AND, OR, SUBTRACT, XOR) under the heading of vector combinations rather than overlay operations, and permits lines as well as polygons as the “operator” layer.

Note: (a) these operations may split up many of the original polygons (and/or lines) to create a new set of features, each with their own (inherited and derived) attributes (lengths, areas, perimeters, centroids, and associated attributes from A and/or B). New composite regions (with associated combined attribute datasets) are often the desired end result, in which case borders between adjacent polygons may be dissolved and datasets merged in order to achieve this end result; (b) operations are not generally symmetric, i.e. A<operation>B is not necessarily the same as B<operation>A, both from a point of view of the geometry and associated attribute data held in tables.

Figure 4‑15 GRASS overlay operations, v.overlay

Input A

Input B

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A Intersection B

A Union B (A AND B, A must be a polygon)

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A NOT B

A XOR B (A must be a polygon)

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In ArcGIS operations of this type are known by the general term “Overlay”, whilst in Manifold the ArcGIS Overlay operations are described as Topological Overlays to distinguish these composite operations from the more component based operations that Manifold describes as Spatial Overlays. Other vector GIS packages use descriptions such as cookie cutters (or EXTRACT operations) and spatial joins, and without doubt the terminology is confusing — the exact consequences of such operations applied using any particular GIS package will be different and should be examined very carefully. The ArcGIS implementation provides four main Overlay functions: Intersection and Union, which are essentially similar to those illustrated in Figure 4‑15, and two additional operations: Identity, which splits up the elements in B based on the position of elements in A; and Update, which amends those parts of B that intersect with A such that in these regions B’s geometry and associated data reflects those of A.

The Manifold GIS generalizes the notion of overlay to include spatial proximity, for example lines that touch areas, and areas that are adjacent to (immediate neighbors of) other areas. The full set of permitted methods is shown in Table 4‑3.

Table 4‑3 Spatial overlay methods, Manifold GIS

 

Contained

Containing

Intersecting

Boundary

Touching

Neighboring

Areas, A

A,L,P

A

A,L

P

A,L

A,L

Lines, L

L,P

A,L

A,L

P

A,L

A,L

Points, P

 

A,L

 

 

P

A,L

Manifold also permits polygons within a layer to be overlapping, which can result in more complex output patterns. In all cases the Manifold Spatial Overlay process transfers data (fields) from a source object (set of features of the same type) to a target object (also a set of features of the same type) according to transfer rules. These rules specify how the data fields are to be transferred (e.g. copied, summed) conditional upon the spatial overlay method. As such they are rather like an SQL "Update table" or "Create table" command, subject to "Where" conditions.

Polygon-on-polygon overlay, which is a relatively common procedure, frequently results in the creation of very small thin polygons known as slivers. These may be the genuine result of an overlay operation (i.e. valid objects and data) or they may be artifacts, created as a result of differences in the original data capture, manipulation or storage process associated with A and B, even though they should exactly match in places. Such slivers may be removed automatically during the overlay operation, usually by setting tolerance levels, or by post-processing, e.g. removing all polygons with a width less than a tolerance value and replacing these with an arc along the sliver centerline or assigning them to the largest adjacent polygon (e.g. in ArcGIS use the ELIMINATE function in ArcToolbox; in Manifold use the Normalize Topology function).

Overlays involve operations where two distinct sets of spatial object are combined in particular manner, visualized as overlaying one upon the other. Many other forms of combination are possible. For example, with a single layer of polygons, boundaries between polygons could be removed (dissolved) if the polygons are adjacent/share a common boundary and meet certain criteria. The attributes of the newly formed polygon will be the sum or some other measure of the component parts. If a new map layer is created by this process rather than an existing layer modified the process is sometimes described as merging rather than dissolving.

Manifold permits the use of the Dissolve operation on lines and points as well as polygons. In the case of lines, multiple line segments are replaced with a single line segment, whilst with points multiple points are replaced by a single center point. The attribute used to guide the dissolve process may be transferred to the new object(s) as: Blank (i.e. do not transfer values for this field); Average; Count; Maximum; Minimum; Sample (randomly chosen value from the original object); or Sum. Other fields are transferred according to transfer rules set for each field.

ArcGIS supports two additional composite operations: Erase and Symmetric difference. In the Erase operation objects in A overlaid on B result in the removal of those parts of B that intersect with A (essentially the NOT operation of GRASS). Symmetric difference is similar to Erase, but those parts of A that do not intersect with B are included in the output set also (essentially the XOR operation we described earlier for GRASS). In addition ArcGIS supports operations such as Split, Append (a merge operation) and Integrate, which combine or separate features according to well-defined rules. Collectively within ArcGIS these various facilities are described as Geoprocessing Tools, and in ArcGIS V8 were available via a “Geoprocessing Wizard” but in ArcGIS V9 are provided in ArcToolbox as separately identified functions.