 |
 |
 |
|
 |
|
|
 |
 |
 |
Spatial Object Approximation
Reproduction
A GIS reproduces items of the real world as objects in its data structure and stores them in its database. The geometry of these objects is normally based on the geometric primitives (point, line, surface), which requires some simplification and approximation of the shapes (discretized space) as they are in reality. A higher resolution of the representation requires more processing time as well as considerable storage space and may therefore not be practical.
Reality S.Salvatore by Lugano |
discretized representation DTM of the region of Lugano |
Storage
The approximation of the geometry of spatial objects in GIS is applied for storage purposes as well as for querying. The geometric attribute of each object uses pointers to the corresponding geometric shape and bounding box to store an approximation of its extent. The most elementary approximation of a geometric shape is with its centroid (2 parameters: x and y). The next approximation level adds the radius of a circle that encloses the object (3 parameters). More complex approximation levels are shown in the table below. When for instance the searching algorithm retrieves a set of approximated items corresponding to the query, then those objects are processed using the whole geometric details stored. Through this approximation, the search of complex objects can be done easily.
| Geometry type | |||
|
Approximation level |
Point |
Line |
Polygon |
|
2 parameters |
|
|
|
|
3 parameters |
|
|
|
|
4 parameters |
|
|
|
|
n parameters |
|
|
|
Object approximation by tessellation
The word "tessellate" means to form or arrange small squares in a checkered or mosaic pattern. A regular tessellation means a tessellation made up of congruent regular polygons. With a tessellation of squares, we can easily approximate the geometric representation of an object as shown below:
 |
|
|
|
|
|
|
|
