Vector overlay is an operation (or class of operations) in a geographic information system (GIS) for integrating two or more vector spatial data sets. Terms such as polygon overlay, map overlay, and topological overlay 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 spatial analysis 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. Overlay is based on the fundamental principle of geography known as areal integration, in which different topics (say, climate, topography, and agriculture) can be directly compared based on a common location. It is also based on the mathematics of set theory and point-set topology. 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, and different choices in what to include in the output.
History Prior to the advent of GIS, the overlay principle had developed as a method of literally superimposing different thematic maps (typically an isarithmic map or a chorochromatic map) drawn on transparent film (e.g., cellulose acetate) to see the interactions and find locations with specific combinations of characteristics. The technique was largely developed by landscape architects. Warren Manning appears to have used this approach to compare aspects of Billerica, Massachusetts, although his published accounts only reproduce the maps without explaining the technique. Jacqueline Tyrwhitt published instructions for the technique in an English textbook in 1950, including:
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. (p.157) Ian McHarg was perhaps most responsible for widely publicizing this approach to planning in Design with Nature (1969), in which he gave several examples of projects on which he had consulted, such as transportation planning and land conservation. The first true GIS, the Canada Geographic Information System (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 ESRI for San Diego County, California in 1971, also supported polygon overlay. It used the Point in polygon algorithm to find intersections quickly. Unfortunately, the results of overlay in these early systems was often prone to error. Carl Steinitz, a landscape architect, helped found the Harvard Laboratory for Computer Graphics and Spatial Analysis, 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 Least Common Geographic Units (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.
Algorithm
The goal of all overlay operations is to take in vector layers, and create a layer that integrates 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. 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.
Given the two input polygon layers, extract the boundary lines. Cracking part A: 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. 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. Cracking part B: Find any intersections between lines 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. Assembling part A: 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. Assembling part B: 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. Parameters are usually available to allow the user to calibrate the algorithm for a particular situation. One of the earliest was the snapping or fuzzy tolerance, a threshold distance. Any pair of lines that stay within this distance of each other are collapsed into a single line, avoiding unwanted narrow sliver polygons that can occur when lines that should be coincident (for example, a river and a boundary that should follow it de jure) are digitized separately with slightly different vertices.
Operators
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