ABSTRACT
As previously defined, a mathematical model is a set of rules used to make a conceptual connection between abstract concepts and human experience. A model is judged “good” to the extent it is both simple and appropriate. When working with spatial data, the simplest model is a one-dimensional (1-D) distance. Models of increasing complexity include a 2-D plane coordinate system formed by the perpendicular intersection of the X and Y axes, a generic 3-D X/Y/Z rectangular Cartesian coordinate system having three mutually perpendicular axes, a spherical Earth model, and, finally, the ellipsoidal Earth model. Figure 4.1a shows the standard 2-D X/Y coordinate system, Figure 4.1b shows a right-handed X/Y/Z coordinate system, and Figure 4.1c illustrates the sexagesimal coordinate system of latitude and longitude used to describe the geodetic location of points on the Earth’s ellipsoidal surface. Other choices will be discussed later, but the goal at this point is to identify a variety of geometrical model choices. With regard to working with spatial data, considerations include, but are not necessarily limited to, the following:
Are the observations or subsequently computed measurements 1-D, 2-D, or 3-D? Is a 1-D or 2-D model sufficient, or is a 3-D model required? Is the extent of a given project small enough to use “flat-Earth” relationships, or is a different model needed to accommodate the Earth’s curvature? Is a spherical-Earth model appropriate, or is the ellipsoidal Earth model required? Is the project of such a nature that a local coordinate system is sufficient, or should the data be referenced to the National Spatial Reference System (NSRS)? What issues of compatibility (e.g., units of feet or meters) must be addressed? What is required for new measurements to be compatible with and/or add to the value of existing data? Is there a spatial data model that accommodates all computational concerns? If so, what is it? That decision should be documented specifically for each project. Otherwise subsequent users are forced to infer the model from the way spatial data are used. For example, project datum coordinates (also called surface coordinates) often resemble state plane coordinates, and serious problems may result if project datum coordinates are used as if they were state plane coordinates.
