Managing Freeform Curves and Surfaces in a Spatial DBMS

Specifications The purpose of Abstract Specifications1 is to create and document a conceptual model sufficient enough to allow for the creation of Implementation Specifications. One OGC abstract specification, the Spatial Schema, gives a standard for geographic information by specifying geometry and topology separately as a UML (Unified Modeling Language)2 package dependency tree. The geometry package (Figure 2.7) has several internal packages that separate primitive geometric objects, aggregates and complexes, which have a more elaborate internal structure than simple aggregates [7]. Two representations of freeform curves and surfaces, i.e. Bézier curve/surface and B-spline curve/surface, have been standardized in the geometric package. Figure 2.8 shows the spline curves packages defined in Spatial Schema, where Bézier curve and B-spline curve are specified in the GM BSplineCurve package. Different from the parameters explained in Section 2.1, four parameters: ’degree’, ’curveForm’, ’knotSpec’ and ’isPolynomial’, are required by this package. Their explanations are as follows [7]: • The ’degree’ attribute specifies the algebraic degree of the basis functions; • The ’curveForm’ attribute is used to identify particular types of curve which this spline is being used to approximate, or set to ’NULL’ if no such approximation is intended; • The ’knotSpec’ attribute gives the type of knot distribution used in defining this spline; This abstract specification has also been accepted by ISO and is referred as ISO 19107. See [17] for an explanation of UML.