## 7 Digital Boundaries that contain holes

In the first case the polygon associated with the 35UCGC0004 Output Area is a torus (doughnut) polygon. This might represent a rural situation where we have a small village surrounded by an unpopulated region of land. In order to represent the geometry of this feature, the polygon needs to be built from a pair of 2 rings. The first ring represents the outside edge of the polygon. The second ring representing the interior edge of the polygon. The geospatial data has to hold an outer ring that hold the sequence of points that define the exterior edge of the polygon plus an inner ring that holds the sequence of points that define the interior edge of the polygon. The green area that occupies the hole is a separate Output Area features and will have it`s geometry defined as a distinct and separate polygon. We know that a GIS is able to construct a polygon from rings and that the ring in turn can be constructed from a linear sequence of points that start and end in the same location, but how does the GIS deal with the situation where the polygon is made up from more that 1 ring and construct holes within the extent of the feature. The answer lies in the ordering of the points from the start to the end point. Shown below is the pair of point sequences for the 2 rings that make up our polygon. The big blue circles mark the start and end points and the numbers show the index number of the point in the linear sequence.

Look at the ordering of the numbers and you will see that the index of the outer edge of the polygon increases clockwise (left to right) from the start point to the end point whereas the index of the inner edge of the polygon increases counter-clockwise (right to left) from the start point to the end point. The GIS can use this difference in the order of the point sequence to correctly construct the geometry of the Output Area polygon and ensure that the hole is included.