# Spatial Concepts<?xml:namespace prefix = o ns = “urn:schemas-microsoft-com:office:office” />

Oracle Spatial is an integrated set of functions and procedures that enables spatial

data to be stored, accessed, and analyzed quickly and efficiently in an Oracle9i

database.

Spatial data represents the essential location characteristics of real or conceptual

objects as those objects relate to the real or conceptual space in which they exist.

**1.1 What Is Oracle Spatial?**

Oracle Spatial, often referred to as Spatial, provides a SQL schema and functions

that facilitate the storage, retrieval, update, and query of collections of spatial

features in an Oracle9i database. Spatial consists of the following components:

A schema (MDSYS) that prescribes the storage, syntax, and semantics of

supported geometric data types

A spatial indexing mechanism

A set of operators and functions for performing area-of-interest queries, spatial

join queries, and other spatial analysis operations

Administrative utilities

The spatial component of a spatial feature is the geometric representation of its

shape in some coordinate space. This is referred to as its geometry.

**1.2 Object-Relational Model**

Spatial supports the object-relational model for representing geometries. The

object-relational model uses a table with a single column of MDSYS.SDO_

GEOMETRY and a single row per geometry instance. The object-relational model

corresponds to a “SQL with Geometry Types” implementation of spatial feature

tables in the OpenGIS ODBC/SQL specification for geospatial features.

The benefits provided by the object-relational model include:

n Support for many geometry types, including arcs, circles, compound polygons,

compound line strings, and optimized rectangles

n Ease of use in creating and maintaining indexes and in performing spatial

queries

n Index maintenance by the Oracle9i database server

n Geometries modeled in a single row and single column

n Optimal performance

**1.3 Introduction to Spatial Data**

Oracle Spatial is designed to make spatial data management easier and more

natural to users of location-enabled applications and Geographic Information

System (GIS) applications. Once this data is stored in an Oracle database, it can be

easily manipulated, retrieved, and related to all the other data stored in the

database.

A common example of spatial data can be seen in a road map. A road map is a

two-dimensional object that contains points, lines, and polygons that can represent

cities, roads, and political boundaries such as states or provinces. A road map is a

visualization of geographic information. The location of cities, roads, and political

boundaries that exist on the surface of the Earth are projected onto a

two-dimensional display or piece of paper, preserving the relative positions and

relative distances of the rendered objects.

The data that indicates the Earth location (latitude and longitude, or height and

depth) of these rendered objects is the spatial data. When the map is rendered, this

spatial data is used to project the locations of the objects on a two-dimensional piece

of paper. A GIS is often used to store, retrieve, and render this Earth-relative spatial

data.

Types of spatial data that can be stored using Spatial other than GIS data include

data from computer-aided design (CAD) and computer-aided manufacturing

(CAM) systems. Instead of operating on objects on a geographic scale, CAD/CAM

systems work on a smaller scale, such as for an automobile engine or printed circuit

boards.

The differences among these systems are only in the relative sizes of the data, not

the data’s complexity. The systems might all actually involve the same number of

data points. On a geographic scale, the location of a bridge can vary by a few tenths

of an inch without causing any noticeable problems to the road builders, whereas if

the diameter of an engine’s pistons are off by a few tenths of an inch, the engine will

not run. A printed circuit board is likely to have many thousands of objects etched

on its surface that are no bigger than the smallest detail shown on a road builder’s

blueprints.

These applications all store, retrieve, update, or query some collection of features

that have both nonspatial and spatial attributes. Examples of nonspatial attributes

are name, soil_type, landuse_classification, and part_number. The spatial attribute

is a coordinate geometry, or vector-based representation of the shape of the feature.

**1.4 Geometry Types**

A geometry is an ordered sequence of vertices that are connected by straight line

segments or circular arcs. The semantics of the geometry are determined by its type.

Spatial supports several primitive types and geometries composed of collections of

these types, including 2-dimensional:

n Points and point clusters

n Line strings

n n-point polygons

n Arc line strings (All arcs are generated as circular arcs.)

n Arc polygons

n Compound polygons

n Compound line strings

n Circles

n Optimized rectangles

2-dimensional points are elements composed of two ordinates, X and Y, often

corresponding to longitude and latitude. Line strings are composed of one or more

pairs of points that define line segments. Polygons are composed of connected line

strings that form a closed ring and the interior of the polygon is implied.

Self-crossing polygons are not supported, although self-crossing line strings are

supported. If a line string crosses itself, it does not become a polygon. A

self-crossing line string does not have any implied interior.

**1.5 Data Model**

The Spatial data model is a hierarchical structure consisting of elements, geometries,

and layers, which correspond to representations of spatial data. Layers are

composed of geometries, which in turn are made up of elements.

For example, a point might represent a building location, a line string might

represent a road or flight path, and a polygon might represent a state, city, zoning

district, or city block.

**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 the interior ring of a polygon with holes are considered as two distinct elements

that together make up a complex polygon.

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).

**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.

**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). Each layer’s geometries and associated spatial index are

stored in the database in standard tables.

**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).

Before Oracle Spatial release 8.1.6, geometries (objects of type SDO_GEOMETRY)

were stored as strings of coordinates without reference to any specific coordinate

system. Spatial functions and operators always assumed a coordinate system that

had the properties of an orthogonal Cartesian system, and sometimes did not

provide correct results if Earth-based geometries were stored in latitude and

longitude coordinates. With release 8.1.6, Spatial provided support for many

different coordinate systems, and for converting data freely between different

coordinate systems.

Spatial data can be associated with a Cartesian, geodetic (geographical), projected,

or local coordinate system:

n 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.

n 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.)

n 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.

n 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.

For more information about coordinate system support in Spatial, including

geodetic, projected, and local coordinates and coordinate system transformation,

**1.5.5 Tolerance**

Tolerance is used to associate a level of precision with spatial data. The tolerance

value must be a non-negative number greater than zero. The range of values and

the significance of the value depend on whether or not the spatial data is associated

with a geodetic coordinate system.

n 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 100 indicates a tolerance of 100 meters.

n For non-geodetic data, the tolerance value can be up to 1, referring to the

decimal fraction of the distance unit in use. (If a coordinate system is specified,

the distance unit is the default for that system.) For example, a tolerance value

of 0.005 indicates a tolerance of 0.005 (that is, 1/200) of the distance unit.

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

with the data.

A tolerance value is specified in two cases:

n In the geometry metadata definition for a layer

n As an optional input parameter to certain functions

1.5.5.1 In the Geometry Metadata for a Layer

The dimensional information for a layer includes a tolerance value. Specifically, the

DIMINFOcolumn(described in Section 2.4.3) of the xxx_SDO_GEOM_METADATA

views includes an SDO_TOLERANCE value.

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 Section 2.1, 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:

n If the SDO_TOLERANCE value of the layer is 0.005, this query returns

.846049894.

n 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.

You can therefore take either of two approaches in selecting an SDO_TOLERANCE

value for a layer:

n 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.

n The value can reflect the precision of the values associated with geometries in

the layer. For example, if all the 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

the appropriate value is 0.5. However, if

geometries are defined using numbers up to 4 decimal positions (for example,

31.2587), such as with longitude and latitude values, the appropriate value is

0.00005.

**1.5.5.2 As an Input Parameter**

Many Spatial functions accept an optional tolerance parameter, which (if specified)

overrides the default tolerance value for the layer (explained in Section 1.5.5.1). 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.

**1.6 Query Model**

Spatial uses a two-tier query model to resolve spatial queries and spatial joins. The

term is used to indicate that two distinct operations are performed to resolve

queries. The output of the two combined operations yields the exact result set.

The two operations are referred to as primary and secondary filter operations.

n The primary filter permits fast selection of candidate records to pass along to

the secondary filter. The primary filter compares geometry approximations to

reduce computation complexity and is considered a lower-cost filter. Because

the primary filter compares geometric approximations, it returns a superset of

the exact result set.

n The secondary filter applies exact computations to geometries that result from

the primary filter. The secondary filter yields an accurate answer to a spatial

query. The secondary filter operation is computationally expensive, but it is

only applied to the primary filter results, not the entire data set.

Spatial uses a spatial index to implement the primary filter. Spatial does not require

the use of both the primary and secondary filters. In some cases, just using the

primary filter is sufficient. For example, a zoom feature in a mapping application

queries for data that has any interaction with a rectangle representing visible

boundaries. The primary filter very quickly returns a superset of the query. The

mapping application can then apply clipping routines to display the target area.

The purpose of the primary filter is to quickly create a subset of the data and reduce

the processing burden on the secondary filter. The primary filter therefore should be

as efficient (that is, selective yet fast) as possible. This is determined by the

characteristics of the spatial index on the data.

**1.7 Indexing of Spatial Data**

The introduction of spatial indexing capabilities into the Oracle database engine is a

key feature of the Spatial product. A spatial index, like any other index, provides a

mechanism to limit searches, but in this case based on spatial criteria such as

intersection and containment. A spatial index is needed to:

n Find objects within an indexed data space that interact with a given point or

area of interest (window query)

n Find pairs of objects from within two indexed data spaces that interact spatially

with each other (spatial join)

A spatial index is considered a logical index. The entries in the spatial index are

dependent on the location of the geometries in a coordinate space, but the index

values are in a different domain. Index entries may be ordered using a linearly

ordered domain, and the coordinates for a geometry may be pairs of integer,

floating-point, or double-precision numbers.

Oracle Spatial lets you use R-tree indexing (the default) or quadtree indexing, or

both. Each index type is appropriate in different situations. You can maintain both

an R-tree and quadtree index on the same geometry column, by using the add_index

parameter with the ALTER INDEX statement (described in Chapter 9), and you can

choose which index to use for a query by specifying the idxtab1 and/or idxtab2

parameters with certain Spatial operators, such as SDO_RELATE,

**1.7.1 R-tree Indexing**

A spatial R-tree index can index spatial data of up to 4 dimensions. An R-tree index

approximates each geometry by a single rectangle that minimally encloses the

geometry (called the minimum bounding rectangle, or MBR)

For a layer of geometries, an R-tree index consists of a hierarchical index on the

MBRs of the geometries in the layer,

**1.7.2 Quadtree Indexing**

In the linear quadtree indexing scheme, the coordinate space (for the layer where all

geometric objects are located) is subjected to a process called tessellation, which

defines exclusive and exhaustive cover tiles for every stored geometry. Tessellation

is done by decomposing the coordinate space in a regular hierarchical manner. The

range of coordinates, the coordinate space, is viewed as a rectangle. At the first level

of decomposition, the rectangle is divided into halves along each coordinate

dimension generating four tiles. Each tile that interacts with the geometry being

tessellated is further decomposed into four tiles. This process continues until some

termination criteria, such as size of the tiles or the maximum number of tiles to

cover the geometry, is met.

Spatial can use either fixed-size or variable-sized tiles to cover a geometry:

n Fixed-size tiles are controlled by tile resolution. If the resolution is the sole

controlling factor, then tessellation terminates when the coordinate space has

been decomposed a specific number of times. Therefore, each tile is of a fixed

size and shape.

n Variable-sized tiling is controlled by the value supplied for the maximum

number of tiles. If the number of tiles per geometry, n, is the sole controlling

factor, the tessellation terminates when n tiles have been used to cover the given

geometry.

Indexing of Spatial Data

Fixed-size tile resolution and the number of variable-sized tiles used to cover a

geometry are user-selectable parameters called SDO_LEVEL and SDO_NUMTILES,

respectively. Smaller fixed-size tiles or more variable-sized tiles provides better

geometry approximations. The smaller the number of tiles, or the larger the tiles,

the coarser are the approximations.

Spatial supports two quadtree indexing types, reflecting two valid combinations of

SDO_LEVEL and SDO_NUMTILES values:

n Fixed indexing: a non-null and non-zero SDO_LEVEL value and a null or zero

(0) SDO_NUMTILES value, resulting in fixed-sized tiles. Fixed indexing is

described in Section 1.7.2.2.

n Hybrid indexing: non-null and non-zero values for SDO_LEVEL and SDO_

NUMTILES, resulting in two sets of tiles per geometry. One set contains

fixed-size tiles and the other set contains variable-sized tiles. Hybrid indexing is

not recommended for most spatial applications, and is described in Appendix B.