Triangulation of Gradient Polygons: A Spatial Data Model for Categorical Fields

The concept of the categorical gradient field is introduced to encompass spatially continuous fields of probabilities or membership values in a fixed number of categories. Three models for implementing categorical gradient fields are examined: raster grids, epsilon bands and gradient polygons. Of these, the gradient polygon model shows promise but has not been fully specified. A specification of the model is developed via a four-step process: 1) the constrained Delaunay triangulation of the polygon is created, 2) vertices are added to the polygon edge to ensure consistency, 3) a skeleton of the medial axis is produced and flat spurs are identified, and 4) additional vertices are added along each flat spur. The method is illustrated on a hypothetical transition zone between four adjacent regions, and evaluated according to five general criteria. The model is efficient in terms of data storage, moderately flexible and robust, and intuitive to build and visualize.