Combining data layers - Spatial Data Analysis: An Introduction for GIS Users - page 66

intersection (Burrough and McDonnell, 1998). For properties (e.g. areas) A and B,
the two can be dei ned as follows:
Inclusion Is A contained within B? Operators transfer attributes to the features con-
tained or that contain other features. For example, if point A is contained within poly-
gon B, then the point is labelled as belonging to area B and attribute information from
B is transferred to A.
Intersection Do A and B overlap? h is leads to the creation of new spatial features.
For example, if two areas overlap then at the points where the edges overlap new nodes
are created and overlapping areas in the output contain the attributes of both input
layers (in this example, they have type A AND type B). Inclusion and intersection are
both illustrated below.
Overlay operators can be used for polygon overlay, line-in-polygon overlay, point-in-
polygon overlay, and to identify overlapping lines. Polygon overlay is a spatial opera-
tion that overlays one polygon layer on another to create a new polygon layer. h e
spatial features of each set of polygons (or a subset) and their polygon attributes are
joined in the output layer. Joining polygons enables the use of operations requiring
new polygon combinations (e.g. all areas that are both highly populated and highly
polluted). Line-in-polygon operations allow the line features to take the attributes of
the polygon in which they lie (e.g. identii cation of which census areas a road passes
through). Point-in-polygon overlay transfers the attributes of the polygon in which the
point lies to the point (e.g. labelling a house with the administrative region it is con-
tained by). h ese operations (including point-in-polygon overlay) necessitate identi-
i cation of line intersections. A means of identifying line intersections is outlined in
Appendix D.
5.2.1 Point in polygon
Ascertaining which polygon a point falls in is a frequent problem in GIS contexts and
questions such as 'Which disease events are in which administrative areas?' are ot en
posed. h ere are various ways in which this can be resolved. Laurini and h ompson
(1992) outline one approach. h e essence of this algorithm is that a line (the 'half line')
is drawn from the point to the edge of the map and the number of intersections with
lines that are part of the current polygon is counted. h e number of intersections will
only be odd if the point falls within the boundary of the current polygon. h is proce-
dure is illustrated in Figure 5.1. In this example the half line crosses the boundary of
the polygon in which it sits three times, coni rming that is where it is located. h e
search process can be accelerated through the use of a minimum enclosing rectangle
(MER, as dei ned in Appendix D) to ascertain if the point can possibly be contained
within a given polygon (i.e. if the point is within the MER then it may also be within
the polygon contained by the MER). Once polygons are excluded in this way, the
remaining candidates can be tested using the line segments (see Appendix D for a test-
ing procedure) until the relevant polygon is identii ed. Heywood et al. (2006) detail
problem cases, for example where the point lies on a polygon boundary or the half line