FREEFORM DATA TYPES IN SPATIAL DATABASE

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FREEFORM DATA TYPES IN SPATIAL DATABASE

CONVERSI0N FUNCTIONS

Several functions are created on the new data types. The first group of functions relates to basic transformation functions: 'translation', 'rotation', 'scale'. Because of the projective invariant property of Bezier/Bspline/ NURBS, the transformation of these curves and surfaces can be just done by applying the transformation to their control points. No further change is needed.

The second group is cocalled conversion functions. Because NURBS are the generalization of B-spline and Bezier, it is rather simple to convert from B-spline and Bezier to NURBS. Furthermore, because GIS doesn't support freeform geometry, the conversions from Bezier/Bspline/ NURBS to simple shapes are necessary. We have implemented two such functions in this research; they are a drop function to convert a NURBS curve to line strings, and a mesh function to convert a NURBS surface to polygons and triangles.

Third group of functions provide allow for creation of new geometry types such as centroid, convex hull and bounding box. Another group of functions compute a distance and check for intersection between two geometries (the function anyintersect is implemented on the convex hull of the geometries). Currently, some of the functions return approximation results instead of accurate results, because this way the algorithms are easier and computation are faster. Calculation of accurate centroid of freeform geometry, or accurate intersection between freeform geometry, could be very complex and heavy, therefore the accurate calculation functions are excluded from database as discussed earlier. Some examples of such functions are listed below:

SQL> select id, VALIDATION(A.geom)

from test_table A;

ID A.GEOM.VALIDATION()

---------- ------------------

1 0 --- Correct entry
2 -1 --- Storage invalid
3 -2 --- Geometry invalid
SQL> select distance(A.geom,B.geom) from test_table A, test_table B where A.id=3 and B.id=5; DISTANCE(A.GEOM,B.GEOM)

---------------------

558.859116

Figure 3.A building cluster (left: CAD model in MicroStation; right: GIS model in ArcGIS)

VISUALIZATION

Using these data types complex models containing freeform curves and surfaces can be created and edited in a CAD application and stored in DBMS. The transformation function to simple geometry allows for conversion into simple geometries (i.e. freeforms are converted in triangulated surfaces) and concequently visualization in a GIS application. Generally this approach allows for integration of complex and simple shapes at database level. Points, lines and polygons of a model are stored in the simple geometry column with SDO_Geometry, and freeform shapes are stored in the complex geometry column with our new data type. Various other attributes such as ID, name, colour, owner, etc. can be also appropriately organized the same database.

When CAD applications request model data from DBMS, simple shapes from the simple geometry column and freeform shapes from the freeform column are retrieved and visualized directly according to their geometry type, as CAD applications supports all these geometry types. All the import and export operations can be implemented in the development environments provided by CAD applications. If a GIS application access the data, it uses only the simple data types. The complex geometry types are converted by the corresponding function to simple object (lines and triangles). Note this operation can not be reversed. Therefore the freeform geometries can be only visualized in GIS application but not edited.

Figure 2 and 3 shows complex freeform curves and surfaces in CAD and GIS application. The CAD model contains on Figure 3 contains line strings, polygons and some NURBS surfaces. Note the two roofs in Figure 3 left are two NURBS surfaces, and in right are actually several polygons.

CONCLUSIONS AND RECOMMENDATIONS

We have shown that NURBS is a very general representation of freeform shapes, and we recommend considering its inclusion in the Implementation specifications of OGC. NURBS, Bézier and Bsplines are already recognized in the CAD domain as flexible geometries for modelling complex shapes and it is not difficult to be supported by DBMS. Tests have convincingly demonstrated that appropriate data types for efficient management of freeform curves and surfaces can be created at DBMS level. Oracle Spatial 11g already allows storage of such shapes but none of the geometric functions support them.

This research is only the first step toward managing freeform data types in a spatial DBMS and GIS. Many issues have to be investigated further. For example, the validation rules for freeform curves and surfaces have to be specified in more detail. The current implementation of validation functions is derived directly from the mathematical definitions. Further research is needed to determine relevant functions for support at DBMS level. The implemented set of prototype functions is relatively basic and not sufficient. For example, the function AnyIntersect uses the convex hulls of the control points of two shapes to investigate possible intersections. More accurate conclusions on the intersection of the shapes would require exhaustive computations. Separate data type for error messages would be very valuable, since the freeform shapes are much more complex than the simple features. It can be included as an error number attribute and an error message attribute within the data type.

Although NURBS can represent conic sections (circle, ellipse, hyperbola, parabola), separate data types still have to be designed to represent these simple shapes in their simplest form. The parameters needed to store, for example, a circle as a NURBS shape are considerable. This research did not consider indexing of freeform shapes. As is well known, a spatial index can make spatial queries much more efficient.

The current DBMS spatial indexing mechanism works on existing simple geometries and cannot be used for prototype data types. Further investigations are needed to develop. The data types do not yet resolve the problems of modelling of freeform shapes in GIS applications. Currently, the only possibility is to approximate freeform shapes with simple features (sets of lines and polygons) for visualization with 3D GIS models. Alternatively, the traditional GIS models stored in DBMS can be integrated with CAD freeform models and further explored (and modelled) in CAD applications. In this manner, the first real integration of typical CAD shapes with GIS shapes can be realized.