GeoWorld December 2011

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VtoR (Pronounced 'V-tore') and Back! BEYONDMAPPING L BY JOSEPH BERRY ast month's "Beyond Mapping" column described considerations and procedures for deriving contour lines from map surfaces (see "Contour Lines vs. Color Gradients for Displaying Spatial Information," GeoWorld, November 2011, page 10). The discussion emphasized the similarities and differences among continu- ous/gradient map surfaces (raster) and discontinuous/discrete spatial objects iden- tifying points, lines and polygons (vector). Keep in mind that although raster data treat geographic space as a con- tinuum, they can store the three basic types of discrete map features: a point as a single grid cell, a line as a series of connecting cells and a polygon as a set of contiguous cells. Similarly, vector data can store generalizations of continuous map surfaces as a series of contour lines or contour-interval polygons. The Rallying Cry Paramount in raster data storage is the concept of a data layer in which all the categories have to be mutu- ally exclusive in space. For example, a given grid cell in a water map layer can't be simultaneously classified as a "spring" (e.g., category 1) and a "wetland" (e.g., category 2) at the same location unless an addi- tional category is specified for the joint condition of "spring and wetland" (e.g., category 12). Another important consideration is that Joseph Berry is a principal in Berry & Associates, consultants in GIS technology. He can be reached via e-mail at 10 each grid cell is assumed to be the same condition/characteristic throughout its entirety. For example, a 30-meter grid cell assigned as a spring doesn't infer a huge bubbling body of water in the shape of a square—rather, it denotes a cell location that contains a spring somewhere within its interior. Similarly, a series of stream cells doesn't imply a 30-meter-wide flow of water that moves in a sawtooth fashion over the landscape—rather, it identifies grid cells that contain a stream somewhere within their interiors. Although raster data tend to generalize/lower the spatial precision GEO W ORLD / D ECEMBE R 2O11 of map-object placement and boundary, vector data tend to generalize/lower the thematic accuracy of classification. For example, the subtle differences in a map-surface continuum of elevation have to be aggregated into broad contour-interval ranges to store the data as discrete polygons. Or, as in the case of contour lines, store a precise constant value, but impart no information for the space between the lines. Hence, the rallying cry of "VtoR and back!" by grid-based GIS modelers echoes from the walls of cubicles everywhere for converting vector-based spatial objects and raster-based grids. This enables them to access the wealth of vector-based data, then utilize the thematic accuracy and analytical power of continuous grid-based data, and, upon completion, push the model results back to vector. Figure 1 depicts the processing steps for a fre- quently used method of converting vector polygons to contiguous groupings of grid cells. It uses a point file of grid centers and "point-in-polygon" processing to assign a value representing a polygon's characteristic/ condition to every corresponding grid cell. Burning for You The top portion of Figure 2 depicts an alternative approach that directly "burns" the vector features into a grid, analogous to a branding iron or wood- burning tool. In the case of a point feature, the cell containing its x,y coordinates is assigned a value representing the feature. The tricky part comes into play if more than one point feature falls into a grid cell. Then users must specify whether to simply note "one or more" for a binary map or utilize a statistical procedure to sum- marize the point values (e.g., #count, sum, average, standard deviation, maximum, minimum, etc.). Figure 1. The basic procedure for centroid-based vector-to-raster (VtoR) conversion is sensitive to cell size and complexity.

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