Data Model

1.5.1 Element

An element is the basic building block of a geometry. The supported spatial element types are points, line strings, and polygons. For example, elements might model star constellations (point clusters), roads (line strings), and county boundaries (polygons). Each coordinate in an element is stored as an X,Y pair. The exterior ring and zero or more interior rings (holes) of a complex polygon are considered a single element.

Point data consists of one coordinate. Line data consists of two coordinates representing a line segment of the element. Polygon data consists of coordinate pair values, one vertex pair for each line segment of the polygon. Coordinates are defined in order around the polygon (counterclockwise for an exterior polygon ring, clockwise for an interior polygon ring).

Parent topic: Data Model

1.5.2 Geometry

A geometry (or geometry object) is the representation of a spatial feature, modeled as an ordered set of primitive elements. A geometry can consist of a single element, which is an instance of one of the supported primitive types, or a homogeneous or heterogeneous collection of elements. A multipolygon, such as one used to represent a set of islands, is a homogeneous collection. A heterogeneous collection is one in which the elements are of different types, for example, a point and a polygon.

An example of a geometry might describe the buildable land in a town. This could be represented as a polygon with holes where water or zoning prevents construction.

Parent topic: Data Model

1.5.3 Layer

A layer is a collection of geometries having the same attribute set. For example, one layer in a GIS might include topographical features, while another describes population density, and a third describes the network of roads and bridges in the area (lines and points). The geometries and associated spatial index for each layer are stored in the database in standard tables.

Parent topic: Data Model

1.5.4 Coordinate System

A coordinate system (also called a spatial reference system) is a means of assigning coordinates to a location and establishing relationships between sets of such coordinates. It enables the interpretation of a set of coordinates as a representation of a position in a real world space.

Any spatial data has a coordinate system associated with it. The coordinate system can be georeferenced (related to a specific representation of the Earth) or not georeferenced (that is, Cartesian, and not related to a specific representation of the Earth). If the coordinate system is georeferenced, it has a default unit of measurement (such as meters) associated with it, but you can have Spatial automatically return results in another specified unit (such as miles).

Spatial data can be associated with a Cartesian, geodetic (geographical), projected, or local coordinate system:

Cartesian coordinates are coordinates that measure the position of a point from a defined origin along axes that are perpendicular in the represented two-dimensional or three-dimensional space.

If a coordinate system is not explicitly associated with a geometry, a Cartesian coordinate system is assumed.
Geodetic coordinates (sometimes called geographic coordinates) are angular coordinates (longitude and latitude), closely related to spherical polar coordinates, and are defined relative to a particular Earth geodetic datum. (A geodetic datum is a means of representing the figure of the Earth and is the reference for the system of geodetic coordinates.)
Projected coordinates are planar Cartesian coordinates that result from performing a mathematical mapping from a point on the Earth's surface to a plane. There are many such mathematical mappings, each used for a particular purpose.
Local coordinates are Cartesian coordinates in a non-Earth (non-georeferenced) coordinate system. Local coordinate systems are often used for CAD applications and local surveys.

When performing operations on geometries, Spatial uses either a Cartesian or curvilinear computational model, as appropriate for the coordinate system associated with the spatial data.

Related Topics

Parent topic: Data Model

1.5.5 Tolerance

Tolerance is used to associate a level of precision with spatial data. Tolerance reflects the distance that two points can be apart and still be considered the same (for example, to accommodate rounding errors). The tolerance value must be a positive number greater than zero. The significance of the value depends on whether or not the spatial data is associated with a geodetic coordinate system. (Geodetic and other types of coordinate systems are described in Coordinate System.)

For geodetic data (such as data identified by longitude and latitude coordinates), the tolerance value is a number of meters. For example, a tolerance value of 10 indicates a tolerance of 10 meters.
For non-geodetic data, the tolerance value is a number of the units that are associated with the coordinate system associated with the data. For example, if the unit of measurement is miles, a tolerance value of 0.005 indicates a tolerance of 0.005 (that is, 1/200) mile (approximately 26 feet or 7.9 meters), and a tolerance value of 2 indicates a tolerance of 2 miles.

In both cases, the smaller the tolerance value, the more precision is to be associated with the data.

For geodetic and projected data, the tolerance value should be less than 10. In addition, ensure that geometries are valid at the specified tolerance.

For geometries that have 16 or more digits of precision, Spatial boolean operations (such as SDO_GEOM.SDO_UNION and SDO_GEOM.SDO_INTERSECTION) and the SDO_GEOM.RELATE function might produce inconsistent results due to the loss of precision in floating point arithmetic. The number of digits of precision is calculated as in the following example: if the tolerance is set to 0.0000000005 and the coordinates have 6 digits to the left of decimal (for example, 123456.4321), the precision is 10 + 6 digits (16). In such cases, it is better to use a larger tolerance value (fewer leading zeros after the decimal) to get consistent results using spatial operations.

Note:

Floating point operations tend to lose precision when the number of digits used in the computation is more than 15, so make sure the number of digits specified for computations is less than 15. For example, if the number is 123456.789 and the tolerance is 10E-10, then this effectively means 16 (10+6) digits of precision, which is more than the recommended 15.

A tolerance value is specified in two cases:

In the geometry metadata definition for a layer
As an input parameter to certain functions

Related Topics

Tolerance Values with LRS Functions

Parent topic: Data Model

1.5.5.1 Tolerance in the Geometry Metadata for a Layer

The dimensional information for a layer includes a tolerance value. Specifically, the DIMINFO column (described in DIMINFO) of the xxx_SDO_GEOM_METADATA views includes an SDO_TOLERANCE value for each dimension, and the value should be the same for each dimension.

If a function accepts an optional tolerance parameter and this parameter is null or not specified, the SDO_TOLERANCE value of the layer is used. Using the non-geodetic data from the example in Simple Example: Inserting, Indexing, and Querying Spatial Data, the actual distance between geometries cola_b and cola_d is 0.846049894. If a query uses the SDO_GEOM.SDO_DISTANCE function to return the distance between cola_b and cola_d and does not specify a tolerance parameter value, the result depends on the SDO_TOLERANCE value of the layer. For example:

If the SDO_TOLERANCE value of the layer is 0.005, this query returns .846049894.
If the SDO_TOLERANCE value of the layer is 0.5, this query returns 0.

The zero result occurs because Spatial first constructs an imaginary buffer of the tolerance value (0.5) around each geometry to be considered, and the buffers around cola_b and cola_d overlap in this case. (If the two geometries being considered have different tolerance values, the higher value is used for the imaginary buffer.)

You can, therefore, take either of two approaches in selecting an SDO_TOLERANCE value for a layer:

The value can reflect the desired level of precision in queries for distances between objects. For example, if two non-geodetic geometries 0.8 units apart should be considered as separated, specify a small SDO_TOLERANCE value such as 0.05 or smaller.
The value can reflect the precision of the values associated with geometries in the layer. For example, if all geometries in a non-geodetic layer are defined using integers and if two objects 0.8 units apart should not be considered as separated, an SDO_TOLERANCE value of 0.5 is appropriate. To have greater precision in any query, you must override the default by specifying the tolerance parameter.

With non-geodetic data, the guideline to follow for most instances of the second case (precision of the values of the geometries in the layer) is: take the highest level of precision in the geometry definitions, and use .5 at the next level as the SDO_TOLERANCE value. For example, if geometries are defined using integers (as in the simplified example in Simple Example: Inserting, Indexing, and Querying Spatial Data), the appropriate value is 0.5; however, if geometries are defined using numbers up to four decimal positions (for example, 31.2587), the appropriate value is 0.00005.

Note:

This guideline should not be used if the geometries include any polygons that are so narrow at any point that the distance between facing sides is less than the proposed tolerance value. Be sure that the tolerance value is less than the shortest distance between any two sides in any polygon.

Moreover, if you encounter "invalid geometry" errors with inserted or updated geometries, and if the geometries are in fact valid, consider increasing the precision of the tolerance value (for example, changing 0.00005 to 0.000005).

Parent topic: Tolerance

1.5.5.2 Tolerance as an Input Parameter

Many spatial functions accept a tolerance parameter, which (if specified) overrides the default tolerance value for the layer (explained in Tolerance in the Geometry Metadata for a Layer). If the distance between two points is less than or equal to the tolerance value, Spatial considers the two points to be a single point. Thus, tolerance is usually a reflection of how accurate or precise users perceive their spatial data to be.

For example, assume that you want to know which restaurants are within 5 kilometers of your house. Assume also that Maria's Pizzeria is 5.1 kilometers from your house. If the spatial data has a geodetic coordinate system and if you ask, Find all restaurants within 5 kilometers and use a tolerance of 100 (or greater, such as 500), Maria's Pizzeria will be included, because 5.1 kilometers (5100 meters) is within 100 meters of 5 kilometers (5000 meters). However, if you specify a tolerance less than 100 (such as 50), Maria's Pizzeria will not be included.

Tolerance values for spatial functions are typically very small, although the best value in each case depends on the kinds of applications that use or will use the data. See also the tolerance guidelines in Tolerance in the Geometry Metadata for a Layer, and ensure that all input geometries are valid. (Spatial functions may not work as expected if the geometry data is not valid.)

If you explicitly want to use the tolerance value from the dimensional information array for the geometry layer, and if a subprogram has separate formats with tolerance (or tol) and dim parameters, use the format with dim. In the following example, the first statement uses the tolerance value from the dimensional information array, and the second statement specifies a numeric tolerance value (0.005):

-- Return the area of the cola_a geometry.
 
SELECT c.name, SDO_GEOM.SDO_AREA(c.shape, m.diminfo) 
  FROM cola_markets c, user_sdo_geom_metadata m 
  WHERE m.table_name = 'COLA_MARKETS' AND m.column_name = 'SHAPE' 
  AND c.name = 'cola_a';
 
SELECT c.name, SDO_GEOM.SDO_AREA(c.shape, 0.005) FROM cola_markets c 
   WHERE c.name = 'cola_a';

Parent topic: Tolerance

1.5.5.3 SDO_TOLERANCE SQL Function

You can use the SDO_TOLERANCE SQL function to find the tolerance value associated with a spatial column in a table. This SQL function has the format:

SQL_TOLERANCE(<schema-name>, <table-name>, <column-name>)

The following example returns the tolerance value for the SHAPE geometry column in the COLA_MARKETS table:

SQL> select SDO_TOLERANCE('SCOTT', 'COLA_MARKETS', 'SHAPE') from dual;

SDO_TOLERANCE('SCOTT','COLA_MARKETS','SHAPE')                                
------------------------------------------------                                
                                        5.0E-003

The value returned by this example matches the "0.005" that was specified for the X and Y dimensions of the SHAPE column when the spatial table was registered in the USER_SDO_GEOM_METADATA view:

INSERT INTO user_sdo_geom_metadata
    (TABLE_NAME,
     COLUMN_NAME,
     DIMINFO,
     SRID)
  VALUES (
  'cola_markets',
  'shape',
  SDO_DIM_ARRAY(   -- 20X20 grid
    SDO_DIM_ELEMENT('X', 0, 20, 0.005),
    SDO_DIM_ELEMENT('Y', 0, 20, 0.005)
     ),
  NULL   -- SRID
);

Note:

For geodetic geometries, the value returned is in unit-spheres, where 1 unit-sphere is a sphere with a radius of 1.0. For example:

1.56961053E-008 = 0.1 / 6371007.2 (0.1 = 0.1 meter; 6371007.2 = Earth's authalic radius in meters)

Parent topic: Tolerance