Oracle® Spatial User's Guide and Reference 10g Release 1 (10.1) Part Number B10826-01

# 6 Coordinate Systems (Spatial Reference Systems)

This chapter describes in greater detail the Oracle Spatial coordinate system support, which was introduced in Section 1.5.4. You can store and manipulate SDO_GEOMETRY objects in a variety of coordinate systems.

For reference information about coordinate system transformation functions and procedures, see Chapter 15.

This chapter contains the following major sections:

## 6.1 Terms and Concepts

This section explains important terms and concepts related to coordinate system support in Oracle Spatial.

### 6.1.1 Coordinate System (Spatial Reference 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.

### 6.1.2 Cartesian Coordinates

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.

### 6.1.3 Geodetic Coordinates (Geographic Coordinates)

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 (described in Section 6.1.6). For more information about geodetic coordinate system support, see Section 6.2.

### 6.1.4 Projected 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.

### 6.1.5 Local Coordinates

Local coordinates are Cartesian coordinates in a non-Earth (non-georeferenced) coordinate system. Section 6.3 describes local coordinate system support in Spatial.

### 6.1.6 Geodetic Datum

A geodetic datum is a means of representing the figure of the Earth, usually as an oblate ellipsoid of revolution, that approximates the surface of the Earth locally or globally, and is the reference for the system of geodetic coordinates.

### 6.1.7 Authalic Sphere

An authalic sphere is a sphere that has the same surface area as a particular oblate ellipsoid of revolution representing the figure of the Earth.

### 6.1.8 Transformation

Transformation is the conversion of coordinates from one coordinate system to another coordinate system.

If the coordinate system is georeferenced, transformation can involve datum transformation: the conversion of geodetic coordinates from one geodetic datum to another geodetic datum, usually involving changes in the shape, orientation, and center position of the reference ellipsoid.

## 6.2 Geodetic Coordinate Support

Effective with Oracle9i, Spatial provides a rational and complete treatment of geodetic coordinates. Before Oracle9i, Spatial computations were based solely on flat (Cartesian) coordinates, regardless of the coordinate system specified for the layer of geometries. Consequently, computations for data in geodetic coordinate systems were inaccurate, because they always treated the coordinates as if they were on a flat surface, and they did not consider the curvature of the surface.

Effective with release 9.2, ellipsoidal surface computations consider the curvatures of arcs in the specified geodetic coordinate system and return correct, accurate results. In other words, Spatial queries return the right answers all the time.

### 6.2.1 Geodesy and Two-Dimensional Geometry

A two-dimensional geometry is a surface geometry, but the important question is: What is the surface? A flat surface (plane) is accurately represented by Cartesian coordinates. However, Cartesian coordinates are not adequate for representing the surface of a solid. A commonly used surface for spatial geometry is the surface of the Earth, and the laws of geometry there are different than they are in a plane. For example, on the Earth's surface there are no parallel lines: lines are geodesics, and all geodesics intersect. Thus, closed curved surface problems cannot be done accurately with Cartesian geometry.

Spatial provides accurate results regardless of the coordinate system or the size of the area involved, without requiring that the data be projected to a flat surface. The results are accurate regardless of where on the Earth's surface the query is focused, even in "special" areas such as the poles. Thus, you can store coordinates in any datum and projections that you choose, and you can perform accurate queries regardless of the coordinate system.

### 6.2.2 Choosing a Geodetic or Projected Coordinate System

For applications that deal with the Earth's surface, the data can be represented using a geodetic coordinate system or a projected plane coordinate system. In deciding which approach to take with the data, consider any needs related to accuracy and performance:

• Accuracy

For many spatial applications, the area is sufficiently small to allow adequate computations on Cartesian coordinates in a local projection. For example, the New Hampshire State Plane local projection provides adequate accuracy for most spatial applications that use data for that state.

However, Cartesian computations on a plane projection will never give accurate results for a large area such as Canada or Scandinavia. For example, a query asking if Stockholm, Sweden and Helsinki, Finland are within a specified distance may return an incorrect result if the specified distance is close to the actual measured distance. Computations involving large areas or requiring very precise accuracy must account for the curvature of the Earth's surface.

• Performance

Spherical computations use more computing resources than Cartesian computations, and take longer to complete. In general, a Spatial operation using geodetic coordinates will take two to three times longer than the same operation using Cartesian coordinates.

### 6.2.3 Geodetic MBRs

To create a query window for certain operations on geodetic data, use an MBR (minimum bounding rectangle) by specifying an SDO_ETYPE value of 1003 or 2003 and an SDO_INTERPRETATION value of 3, as described in Table 2-2 in Section 2.2.4. A geodetic MBR can be used with the following operators: SDO_FILTER, SDO_RELATE with the `ANYINTERACT` mask, SDO_ANYINTERACT, and SDO_WITHIN_DISTANCE.

Example 6-1 requests the names of all cola markets that are likely to interact spatially with a geodetic MBR.

Example 6-1 Using a Geodetic MBR

```SELECT c.name FROM cola_markets_cs c WHERE
SDO_FILTER(c.shape,
SDO_GEOMETRY(
2003,
8307,    -- SRID for WGS 84 longitude/latitude
NULL,
SDO_ELEM_INFO_ARRAY(1,1003,3),
SDO_ORDINATE_ARRAY(6,5, 10,10))
) = 'TRUE';

```

Example 6-1 produces the following output (assuming the data as defined in Example 6-4 in Section 6.8):

```NAME
--------------------------------
cola_c
cola_b
cola_d

```

The following considerations apply to the use of geodetic MBRs:

• Do not use a geodetic MBR with spatial objects stored in the database. Use it only to construct a query window.

• The lower-left Y coordinate (minY) must be less than the upper-right Y coordinate (maxY). If the lower-left X coordinate (minX) is greater than the upper-right X coordinate (maxX), the window is assumed to cross the date line meridian (that is, the meridian "opposite" the prime meridian, or both 180 and -180 longitude). For example, an MBR of (-10,10, -100, 20) with longitude/latitude data goes three-fourths of the way around the Earth (crossing the date line meridian), and goes from latitude lines 10 to 20.

• When Spatial constructs the MBR internally for the query, lines along latitude lines are densified by adding points at one-degree intervals. This might affect results for objects within a few meters of the edge of the MBR (especially objects near the North and South Poles).

The following additional examples show special or unusual cases, to illustrate how a geodetic MBR is interpreted with longitude/latitude data:

• (10,0, -110,20) crosses the date line meridian and goes most of the way around the world, and goes from the equator to latitude 20.

• (10,-90, 40,90) is a band from the South Pole to the North Pole between longitudes 10 and 40.

• (10,-90, 40,50) is a band from the South Pole to latitude 50 between longitudes 10 and 40.

• (-180,-10, 180,5) is a band that wraps the equator from 10 degrees south to 5 degrees north.

• (-180,-90, 180,90) is the whole Earth.

• (-180,-90, 180,50) is the whole Earth below latitude 50.

• (-180,50, 180,90) is the whole Earth above latitude 50.

### 6.2.4 Other Considerations and Requirements with Geodetic Data

The following geometries are not permitted if a geodetic coordinate system is used:

• Circles

• Circular arcs

Geodetic coordinate system support is provided only for geometries that consist of points or geodesics (lines on the ellipsoid). If you have geometries containing circles or circular arcs in a projected coordinate system, you can densify them using the SDO_GEOM.SDO_ARC_DENSIFY function (documented in Chapter 13) before transforming them to geodetic coordinates, and then perform Spatial operations on the resulting geometries.

The following size limits apply with geodetic data:

• No polygon element can have an area larger than one-half the surface of the Earth.

• No line element can have a length longer than half the perimeter (a great circle) of the Earth.

If you need to work with larger elements, first break these elements into multiple smaller elements and work with them. For example, you cannot create an element representing the entire ocean surface of the Earth; however, you can create multiple elements, each representing part of the overall ocean surface.

To take full advantage of Spatial features, you must index geodetic data layers using a geodetic R-tree index. (You can create a non-geodetic R-tree or quadtree index on geodetic data by specifying `'geodetic=FALSE'` in the PARAMETERS clause of the CREATE INDEX statement; however, this is not recommended. See the Usage Notes for the CREATE INDEX statement in Chapter 10 for more information.) In addition, for Spatial release 9.0.1 and higher you must delete (DROP INDEX) and re-create all spatial indexes on geodetic data from a release before 9.0.1.

Tolerance is specified as meters for geodetic layers. If you use tolerance values that are typical for non-geodetic data, these values are interpreted as meters for geodetic data. For example, if you specify a tolerance value of 0.005 for geodetic data, this is interpreted as precise to 5 millimeters. If this value is more precise than your applications need, performance may be affected because of the internal computational steps taken to implement the specified precision. (For more information about tolerance, see Section 1.5.5.)

For geodetic layers, you must specify the dimensional extents in the index metadata as -180,180 for longitude and -90,90 for latitude. The following statement (from Example 6-4 in Section 6.8) specifies these extents (with a 10-meter tolerance value in each dimension) for a geodetic data layer:

```INSERT INTO USER_SDO_GEOM_METADATA
VALUES (
'cola_markets_cs',
'shape',
SDO_DIM_ARRAY(
SDO_DIM_ELEMENT('Longitude', -180, 180, 10),  -- 10 meters tolerance
SDO_DIM_ELEMENT('Latitude', -90, 90, 10)  -- 10 meters tolerance
),
8307   -- SRID for 'Longitude / Latitude (WGS 84)' coordinate system
);

```

See Section 6.7 for additional notes and restrictions relating to geodetic data.

## 6.3 Local Coordinate Support

Spatial provides a level of support for local coordinate systems. Local coordinate systems are often used in CAD systems, and they can also be used in local surveys where the relationship between the surveyed site and the rest of the world is not important.

Several local coordinate systems are predefined and included with Spatial in the MDSYS.CS_SRS table (described in Section 6.4.1). These supplied local coordinate systems, whose names start with Non-Earth, define non-Earth Cartesian coordinate systems based on different units of measurement (Meter, Millimeter, Inch, and so on). In the current release, you can use these local coordinate systems only to convert coordinates in a local coordinate system from one unit of measurement to another (for example, inches to millimeters) by transforming a geometry or a layer of geometries.

## 6.4 Coordinate Systems Data Structures

The coordinate systems functions and procedures use information provided in the following tables supplied with Oracle Spatial:

• MDSYS.CS_SRS (see Section 6.4.1) defines the valid coordinate systems. It associates each coordinate system with its well-known text description, which is in conformance with the standard published by the Open GIS Consortium (`http://www.opengis.org`).

• MDSYS.SDO_ANGLE_UNITS (see Section 6.4.2) defines the valid angle units. The angle unit is part of the well-known text description.

• MDSYS.SDO_DIST_UNITS (see Table 2-6 in Section 2.6) defines the valid distance units. The distance unit is included in the well-known text description.

• MDSYS.SDO_DATUMS (see Section 6.4.3) defines the valid datums. The datum is part of the well-known text description.

• MDSYS.SDO_ELLIPSOIDS (see Section 6.4.4) defines the valid ellipsoids. The ellipsoid (SPHEROID specification) is part of the well-known text description.

• MDSYS.SDO_PROJECTIONS (see Section 6.4.5) defines the valid map projections. The map projection is part of the well-known text description.

 Note: You should not modify or delete any Oracle-supplied information in any of the tables that are used for coordinate system support. You should not add any information to the MDSYS.CS_SRS table unless you are creating a user-defined coordinate system. (Do not add information to the MDSYS.SDO_DATUMS, MDSYS.SDO_ELLIPSOIDS, or MDSYS.PROJECTIONS tables.) Section 6.5 describes how to create a user-defined coordinate system.

### 6.4.1 MDSYS.CS_SRS Table

The MDSYS.CS_SRS reference table contains over 900 rows, one for each valid coordinate system.

 Note: You should probably not modify, delete, or add any information in the MDSYS.CS_SRS table. If you do plan to modify this table, you should connect to the database as the MDSYS user. If you plan to add any user-defined coordinate systems, be sure to use SRID values of 1000000 (1 million) or higher, and follow the guidelines in Section 6.5.

The MDSYS.CS_SRS table contains the columns shown in Table 6-1.

Table 6-1 MDSYS.CS_SRS Table

Column Name Data Type Description
CS_NAME VARCHAR2(68) A well-known name, often mnemonic, by which a user can refer to the coordinate system.
SRID NUMBER(38) The unique ID number (Spatial Reference ID) for a coordinate system. Currently, SRID values 1-999999 are reserved for use by Oracle Spatial, and values 1000000 (1 million) and higher are available for user-defined coordinate systems.
AUTH_SRID NUMBER(38) An optional ID number that can be used to indicate how the entry was derived; it might be a foreign key into another coordinate table, for example.
AUTH_NAME VARCHAR2(256) An authority name for the coordinate system. Contains 'Oracle' in the supplied table. Users can specify any value in any rows that they add.
WKTEXT VARCHAR2(2046) The well-known text (WKT) description of the SRS, as defined by the Open GIS Consortium. For more information, see Section 6.4.1.1.
CS_BOUNDS SDO_GEOMETRY An optional SDO_GEOMETRY object that is a polygon with WGS 84 longitude and latitude vertices, representing the spheroidal polygon description of the zone of validity for a projected coordinate system. Must be null for a geographic or non-Earth coordinate system. Is null in all supplied rows.

#### 6.4.1.1 Well-Known Text (WKT)

The WKTEXT column of the MDSYS.CS_SRS table contains the well-known text (WKT) description of the SRS, as defined by the Open GIS Consortium.

The following is the WKT EBNF syntax. All user-defined coordinate systems must strictly comply with this syntax.

```<coordinate system> ::=
<horz cs> | <local cs>

<horz cs> ::=
<geographic cs> | <projected cs>

<projected cs> ::=
PROJCS [ "<name>", <geographic cs>, <projection>,
{<parameter>,}* <linear unit> ]

<projection> ::=
PROJECTION [ "<name>" ]

<parameter> ::=
PARAMETER [ "<name>", <number> ]

<geographic cs> ::=
GEOGCS [ "<name>", <datum>, <prime meridian>, <angular unit> ]

<datum> ::=
DATUM [ "<name>", <spheroid>
{, <shift-x>, <shift-y>, <shift-z>
]

<spheroid> ::=
SPHEROID ["<name>", <semi major axis>, <inverse flattening> ]

<prime meridian> ::=
PRIMEM ["<name>", <longitude> ]

<longitude> ::=
<number>

<semi-major axis> ::=
<number>

<inverse flattening> ::=
<number>

<angular unit> ::= <unit>

<linear unit> ::= <unit>

<unit> ::=
UNIT [ "<name>", <conversion factor> ]

<local cs> ::=
LOCAL_CS [ "<name>", <local datum>, <linear unit>,
<axis> {, <axis>}* ]

<local datum> ::=
LOCAL_DATUM [ "<name>", <datum type>
{, <shift-x>, <shift-y>, <shift-z>
]

<datum type> ::=
<number>

<axis> ::=
AXIS [ "<name>", NORTH | SOUTH | EAST |
WEST | UP | DOWN | OTHER ]

```

The prime meridian (PRIMEM) must be specified in decimal degrees of longitude.

An example of the WKT for a geodetic (geographic) coordinate system is:

```'GEOGCS [ "Longitude / Latitude (Old Hawaiian)", DATUM ["Old Hawaiian", SPHEROID
["Clarke 1866", 6378206.400000, 294.978698]], PRIMEM [ "Greenwich", 0.000000 ],
UNIT ["Decimal Degree", 0.01745329251994330]]'

```

The WKT definition of the coordinate system is hierarchically nested. The Old Hawaiian geographic coordinate system (GEOGCS) is composed of a named datum (DATUM), a prime meridian (PRIMEM), and a unit definition (UNIT). The datum is in turn composed of a named spheroid and its parameters of semi-major axis and inverse flattening.

An example of the WKT for a projected coordinate system (a Wyoming State Plane) is:

```'PROJCS["Wyoming 4901, Eastern Zone (1983, meters)", GEOGCS [ "GRS 80", DATUM
["GRS 80", SPHEROID ["GRS 80", 6378137.000000, 298.257222]], PRIMEM [
"Greenwich", 0.000000 ], UNIT ["Decimal Degree", 0.01745329251994330]],
PROJECTION ["Transverse Mercator"], PARAMETER ["Scale_Factor", 0.999938],
PARAMETER ["Central_Meridian", -105.166667], PARAMETER ["Latitude_Of_Origin",
40.500000], PARAMETER ["False_Easting", 200000.000000], UNIT ["Meter",
1.000000000000]]'

```

The projected coordinate system contains a nested geographic coordinate system as its basis, as well as parameters that control the projection.

Oracle Spatial supports all common geodetic datums and map projections.

An example of the WKT for a local coordinate system is:

```LOCAL_CS [ "Non-Earth (Meter)", LOCAL_DATUM ["Local Datum", 0], UNIT ["Meter", 1.0], AXIS ["X", EAST], AXIS["Y", NORTH]]

```

You can use the SDO_CS.VALIDATE_WKT function, described in Chapter 15, to validate the WKT of any coordinate system defined in the MDSYS.CS_SRS table.

### 6.4.2 MDSYS.SDO_ANGLE_UNITS Table

The MDSYS.SDO_ANGLE_UNITS reference table contains one row for each valid UNIT specification in the well-known text (WKT) description in the coordinate system definition. The WKT is described in Section 6.4.1.1.

The MDSYS.SDO_ANGLE_UNITS table contains the columns shown in Table 6-2.

Table 6-2 MDSYS.SDO_ANGLE_UNITS Table

Column Name Data Type Description
SDO_UNIT VARCHAR2(32) (Reserved for future use by Oracle Spatial.)
UNIT_NAME VARCHAR2(100) Name of the angle unit. Specify a value from this column in the UNIT specification of the WKT for any user-defined coordinate system. Examples: Decimal Degree, Radian, Decimal Second, Decimal Minute, Gon, Grad.
CONVERSION_FACTOR NUMBER The ratio of the specified unit to one Radian. For example, the ratio of Decimal Degree to Radian is 0.017453293.

### 6.4.3 MDSYS.SDO_DATUMS Table

The MDSYS.SDO_DATUMS reference table contains one row for each valid DATUM specification in the well-known text (WKT) description in the coordinate system definition. The WKT is described in Section 6.4.1.1.

The MDSYS.SDO_DATUMS table contains the columns shown in Table 6-3.

Table 6-3 MDSYS.SDO_DATUMS Table

Column Name Data Type Description
NAME VARCHAR2(64) Name of the datum. Specify a value (Oracle-supplied or user-defined) from this column in the DATUM specification of the WKT for any user-defined coordinate system. Examples: Adindan, Afgooye, Ain el Abd 1970, Anna 1 Astro 1965, Arc 1950, Arc 1960, Ascension Island 1958.
SHIFT_X NUMBER Number of meters to shift the ellipsoid center relative to the center of the WGS 84 ellipsoid on the x-axis.
SHIFT_Y NUMBER Number of meters to shift the ellipsoid center relative to the center of the WGS 84 ellipsoid on the y-axis.
SHIFT_Z NUMBER Number of meters to shift the ellipsoid center relative to the center of the WGS 84 ellipsoid on the z-axis.
ROTATE_X NUMBER Number of arc-seconds of rotation about the x-axis.
ROTATE_Y NUMBER Number of arc-seconds of rotation about the y-axis.
ROTATE_Z NUMBER Number of arc-seconds of rotation about the z-axis.
SCALE_ADJUST NUMBER A value to be used in adjusting the X, Y, and Z values after any shifting and rotation, according to the formula: 1.0 + (SCALE_ADJUST * 10-6)

The following are the names (in tabular format) of the supported datums:

 Adindan Afgooye Ain el Abd 1970 Anna 1 Astro 1965 Arc 1950 Arc 1960 Ascension Island 1958 Astro B4 Sorol Atoll Astro Beacon E Astro DOS 71/4 Astronomic Station 1952 Australian Geodetic 1966 Australian Geodetic 1984 Belgium Hayford Bellevue (IGN) Bermuda 1957 Bogota Observatory CH 1903 (Switzerland) Campo Inchauspe Canton Astro 1966 Cape Cape Canaveral Carthage Chatham 1971 Chua Astro Corrego Alegre DHDN (Potsdam/Rauenberg) DOS 1968 Djakarta (Batavia) Easter Island 1967 European 1950 European 1979 European 1987 GRS 67 GRS 80 GUX 1 Astro Gandajika Base Geodetic Datum 1949 Guam 1963 Hito XVIII 1963 Hjorsey 1955 Hong Kong 1963 Hu-Tzu-Shan ISTS 073 Astro 1969 Indian (Bangladesh, etc.) Indian (Thailand/Vietnam) Ireland 1965 Johnston Island 1961 Kandawala Kerguelen Island Kertau 1948 L.C. 5 Astro Liberia 1964 Lisboa (DLx) Luzon (Mindanao Island) Luzon (Philippines) Mahe 1971 Marco Astro Massawa Melrica 1973 (D73) Merchich Midway Astro 1961 Minna NAD 27 (Alaska) NAD 27 (Bahamas) NAD 27 (Canada) NAD 27 (Canal Zone) NAD 27 (Caribbean) NAD 27 (Central America) NAD 27 (Continental US) NAD 27 (Cuba) NAD 27 (Greenland) NAD 27 (Mexico) NAD 27 (Michigan) NAD 27 (San Salvador) NAD 83 NTF (Greenwich meridian) NTF (Paris meridian) NWGL 10 Nahrwan (Masirah Island) Nahrwan (Saudi Arabia) Nahrwan (Un. Arab Emirates) Naparima, BWI Netherlands Bessel Observatorio 1966 Old Egyptian Old Hawaiian Oman Ordinance Survey Great Brit Pico de las Nieves Pitcairn Astro 1967 Provisional South American Puerto Rico Pulkovo 1942 Qatar National Qornoq RT 90 (Sweden) Reunion Rome 1940 Santo (DOS) Sao Braz Sapper Hill 1943 Schwarzeck South American 1969 South Asia Southeast Base Southwest Base Timbalai 1948 Tokyo Tristan Astro 1968 Viti Levu 1916 WGS 60 WGS 66 WGS 72 WGS 84 Wake-Eniwetok 1960 Yacare Zanderij

### 6.4.4 MDSYS.SDO_ELLIPSOIDS Table

The MDSYS.SDO_ELLIPSOIDS reference table contains one row for each valid SPHEROID specification in the well-known text (WKT) description in the coordinate system definition. The WKT is described in Section 6.4.1.1.

The MDSYS.SDO_ELLIPSOIDS table contains the columns shown in Table 6-4.

Table 6-4 MDSYS.SDO_ELLIPSOIDS Table

Column Name Data Type Description
NAME VARCHAR2(64) Name of the ellipsoid (spheroid). Specify a value from this column in the SPHEROID specification of the WKT for any user-defined coordinate system. Examples: Clarke 1866, WGS 72, Australian, Krassovsky, International 1924.
SEMI_MAJOR_AXIS NUMBER Radius in meters along the semi-major axis (one-half of the long axis of the ellipsoid).
INVERSE_FLATTENING NUMBER Inverse flattening of the ellipsoid. That is, `1/f`, where `f = (a-b)/a`, and `a` is the semi-major axis and `b` is the semi-minor axis.

The following are the names (in tabular format) of the supported ellipsoids:

 Airy 1930 Airy 1930 (Ireland 1965) Australian Bessel 1841 Bessel 1841 (NGO 1948) Bessel 1841 (Schwarzeck) Clarke 1858 Clarke 1866 Clarke 1866 (Michigan) Clarke 1880 Clarke 1880 (Arc 1950) Clarke 1880 (IGN) Clarke 1880 (Jamaica) Clarke 1880 (Merchich) Clarke 1880 (Palestine) Everest Everest (Kalianpur) Everest (Kertau) Everest (Timbalai) Fischer 1960 (Mercury) Fischer 1960 (South Asia) Fischer 1968 GRS 67 GRS 80 Hayford Helmert 1906 Hough IAG 75 Indonesian International 1924 Krassovsky MERIT 83 NWL 10D NWL 9D New International 1967 OSU86F OSU91A Plessis 1817 South American 1969 Sphere (6370997m) Struve 1860 WGS 60 WGS 66 WGS 72 WGS 84 Walbeck War Office

### 6.4.5 MDSYS.SDO_PROJECTIONS Table

The MDSYS.SDO_PROJECTIONS reference table contains one row for each valid PROJECTION specification in the well-known text (WKT) description in the coordinate system definition. The WKT is described in Section 6.4.1.1.

The MDSYS.SDO_PROJECTIONS table contains the column shown in Table 6-5.

Table 6-5 MDSYS.SDO_PROJECTIONS Table

Column Name Data Type Description
NAME VARCHAR2(64) Name of the map projection. Specify a value from this column in the PROJECTION specification of the WKT for any user-defined coordinate system. Examples: Geographic (Lat/Long), Universal Transverse Mercator, State Plane Coordinates, Albers Conical Equal Area.

The following are the names (in tabular format) of the supported projections:

 Alaska Conformal Albers Conical Equal Area Azimuthal Equidistant Bonne Cassini Cylindrical Equal Area Eckert IV Eckert VI Equidistant Conic Equirectangular Gall General Vertical Near-Side Perspective Geographic (Lat/Long) Gnomonic Hammer Hotine Oblique Mercator Interrupted Goode Homolosine Interrupted Mollweide Lambert Azimuthal Equal Area Lambert Conformal Conic Lambert Conformal Conic (Belgium 1972) Mercator Miller Cylindrical Mollweide New Zealand Map Grid Oblated Equal Area Orthographic Polar Stereographic Polyconic Robinson Sinusoidal Space Oblique Mercator State Plane Coordinates Stereographic Swiss Oblique Mercator Transverse Mercator Transverse Mercator Danish System 34 Jylland-Fyn Transverse Mercator Danish System 45 Bornholm Transverse Mercator Finnish KKJ Transverse Mercator Sjaelland Universal Transverse Mercator Van der Grinten Wagner IV Wagner VII

## 6.5 Creating a User-Defined Coordinate System

To create a user-defined coordinate system, add a row to the MDSYS.CS_SRS table. See Section 6.4.1 for information about this table, including the requirements for values in each column.

To specify the WKTEXT column in the MDSYS.CS_SRS table, follow the syntax specified in Section 6.4.1.1. See also the examples in that section.

When you specify the WKTEXT column entry, use valid values from several Spatial reference tables:

• MDSYS.SDO_ANGLE_UNITS (see Section 6.4.2) in a UNIT specification for angle units

• MDSYS.SDO_DIST_UNITS (see Table 2-6 in Section 2.6) in a UNIT specification for distance units

• MDSYS.SDO_DATUMS (see Section 6.4.3) in the DATUM specification, or a user-defined datum not in MDSYS.SDO_DATUMS

If you supply a user-defined datum, the datum name must be different from any datum name in the MDSYS.SDO_DATUMS table, and the WKT must specify at least the datum name and the spheroid (or ellipsoid) information listed in Section 6.4.1.1. If the shift, rotation, and scale parameters are all zero, you can omit them; however, if any of these parameter values are nonzero, you must specify them all.

• MDSYS.SDO_ELLIPSOIDS (see Section 6.4.4) in the SPHEROID specification

If you supply a user-defined ellipsoid, the ellipsoid name must be different from any ellipsoid name in the MDSYS.SDO_ELLIPSOIDS table. You must also specify the semi-major axis and inverse flattening for a user-defined ellipsoid.

• MDSYS.SDO_PROJECTIONS (see Section 6.4.5) in the PROJECTION specification

The name in each PARAMETER specification must be one of the following, depending on the projection that you use:

• `Standard_Parallel_1` (in decimal degrees)

• `Standard_Parallel_2` (in decimal degrees)

• `Central_Meridian` (in decimal degrees)

• `Latitude_of_Origin` (in decimal degrees)

• `Azimuth` (in decimal degrees)

• `False_Easting` (in meters)

• `False_Northing` (in meters)

• `Perspective_Point_Height` (in meters)

• `Landsat_Number` (must be 1, 2, 3, 4, or 5)

• `Path_Number`

• `Scale_Factor`

Some of these parameters are appropriate for several projections. They are not all appropriate for every projection.

Example 6-2 creates a user-defined projected coordinate system. The first four columns are not the WKT information, but specify other fields in the MSDYD.CS_SRS table. The WKT information starts with PROJCS. This example is similar to an existing coordinate system, but has a different name, SRID, and central meridian.

Example 6-2 Creating a User-Defined Projected Coordinate System

```INSERT INTO mdsys.cs_srs VALUES ('UTM Zone 44.5, Northern Hemisphere (WGS 84)',
1082378, 1082378, 'Oracle',
'PROJCS["UTM Zone 44.5, Northern Hemisphere (WGS 84)",
GEOGCS [ "WGS 84",
DATUM ["WGS 84 ",
SPHEROID ["WGS 84", 6378137.000000, 298.257224]],
PRIMEM [ "Greenwich", 0.000000 ],
UNIT ["Decimal Degree", 0.01745329251994330]],
PROJECTION ["Transverse Mercator"],
PARAMETER ["Scale_Factor", 0.999600],
PARAMETER ["Central_Meridian", 84.000000],
PARAMETER ["False_Easting", 500000.000000],
UNIT ["Meter", 1.000000000000]]',NULL);

```

Example 6-3 creates a user-defined geodetic coordinate system. The first four columns are not the WKT information, but specify other fields in the MSDYD.CS_SRS table. The WKT information starts with GEOGCS. This example includes an ellipsoid (SPHEROID) definition in which the semi-major axis and inverse flattening parameters are slightly changed from the WGS 84 coordinate system, as well as a different datum definition. Because the `shift_x` and `shift_y` parameter values are specified, all the shift, rotation, and scaling values must be specified. There is no projection information included for a geodetic coordinate system.

Example 6-3 Creating a User-Defined Geodetic Coordinate System

```INSERT INTO mdsys.cs_srs  VALUES
( 'Longitude / Latitude (WGS 90)', 1008307, 1008307, 'Oracle',
'GEOGCS [ "Longitude / Latitude (WGS 90)",
DATUM ["WGS 90",
SPHEROID ["WGS 90", 6378137.032499, 298.257236], 100, 100, 0, 0, 0, 0, 0],
PRIMEM [ "Greenwich", 0.000000 ],
UNIT ["Decimal Degree", 0.01745329251994330]]',NULL);
```

## 6.6 Coordinate System Transformation Functions

The current release of Oracle Spatial includes the following functions and procedures for data transformation using coordinate systems:

• SDO_CS.TRANSFORM function: Transforms a geometry representation using a coordinate system (specified by SRID or name).

• SDO_CS.TRANSFORM_LAYER procedure: Transforms an entire layer of geometries (that is, all geometries in a specified column in a table).

• SDO_CS.VALIDATE_WKT function: Validates the well-known text (WKT) description associated with a specified SRID.

• SDO_CS.VIEWPORT_TRANSFORM function: Transforms an optimized rectangle into a valid polygon for use with Spatial operators and functions.

Reference information about these functions and procedures is in Chapter 15.

Support for additional functions and procedures is planned for future releases of Oracle Spatial.

## 6.7 Notes and Restrictions with Coordinate Systems Support

The following notes and restrictions apply to coordinate systems support in the current release of Spatial.

### 6.7.1 Different Coordinate Systems for Geometries with Operators and Functions

For Spatial operators (described in Chapter 12) that take two geometries as input parameters, if the geometries are based on different coordinate systems, the query window (the second geometry) is transformed to the coordinate system of the first geometry before the operation is performed. This transformation is a temporary internal operation performed by Spatial; it does not affect any stored query-window geometry.

For SDO_GEOM package geometry functions (described in Chapter 13) that take two geometries as input parameters, both geometries must be based on the same coordinate system.

### 6.7.2 Functions Not Supported with Geodetic Data

In the current release, the following functions are not supported with geodetic data:

### 6.7.3 Functions Supported by Approximations with Geodetic Data

In the current release, the following functions are supported by approximations with geodetic data:

When these functions are used on data with geodetic coordinates, they internally perform the operations in an implicitly generated local-tangent-plane Cartesian coordinate system and then transform the results to the geodetic coordinate system. For SDO_GEOM.SDO_BUFFER, generated arcs are approximated by line segments before the back-transform.

## 6.8 Example of Coordinate System Transformation

This section presents a simplified example that uses coordinate system transformation functions and procedures. It refers to concepts that are explained in this chapter and uses functions documented in Chapter 15.

Example 6-4 uses mostly the same geometry data (cola markets) as in Section 2.1, except that instead of null SDO_SRID values, the SDO_SRID value 8307 is used. That is, the geometries are defined as using the coordinate system whose SRID is 8307 and whose well-known name is "Longitude / Latitude (WGS 84)". This is probably the most widely used coordinate system, and it is the one used for global positioning system (GPS) devices. The geometries are then transformed using the coordinate system whose SRID is 8199 and whose well-known name is "Longitude / Latitude (Arc 1950)".

Example 6-4 uses the geometries illustrated in Figure 2-1 in Section 2.1, except that `cola_d` is a rectangle (here, a square) instead of a circle, because arcs are not supported with geodetic coordinate systems.

Example 6-4 does the following:

• Creates a table (COLA_MARKETS_CS) to hold the spatial data

• Inserts rows for four areas of interest (`cola_a`, `cola_b`, `cola_c`, `cola_d`), using the SDO_SRID value 8307

• Updates the USER_SDO_GEOM_METADATA view to reflect the dimension of the areas, using the SDO_SRID value 8307

• Creates a spatial index (COLA_SPATIAL_IDX_CS)

• Performs some transformation operations (single geometry and entire layer)

Example 6-5 includes the output of the SELECT statements in Example 6-4.

Example 6-4 Simplified Example of Coordinate System Transformation

```-- Create a table for cola (soft drink) markets in a
-- given geography (such as city or state).

CREATE TABLE cola_markets_cs (
mkt_id NUMBER PRIMARY KEY,
name VARCHAR2(32),
shape SDO_GEOMETRY);

-- Note about areas of interest: cola_a (rectangle) and
-- cola_b (four-sided polygon) are side by side (share one border).
-- cola_c is a small four-sided polygon that overlaps parts of
-- cola_a and cola_b. A rough sketch:
--     ---------+
--     |    a   |  b   \
--     |     +------+     |
--     |   /___c____|     |
--     |        |         |
--     ---------+---------|

-- The next INSERT statement creates an area of interest for
-- Cola A. This area happens to be a rectangle.
-- The area could represent any user-defined criterion: for
-- example, where Cola A is the preferred drink, where
-- Cola A is under competitive pressure, where Cola A
-- has strong growth potential, and so on.

INSERT INTO cola_markets_cs VALUES(
1,
'cola_a',
SDO_GEOMETRY(
2003,  -- two-dimensional polygon
8307,  -- SRID for 'Longitude / Latitude (WGS 84)' coordinate system
NULL,
SDO_ELEM_INFO_ARRAY(1,1003,1), -- polygon
SDO_ORDINATE_ARRAY(1,1, 5,1, 5,7, 1,7, 1,1) -- All vertices must
-- be defined for rectangle with geodetic data.
)
);

-- The next two INSERT statements create areas of interest for
-- Cola B and Cola C. These areas are simple polygons (but not
-- rectangles).

INSERT INTO cola_markets_cs VALUES(
2,
'cola_b',
SDO_GEOMETRY(
2003,  -- two-dimensional polygon
8307,
NULL,
SDO_ELEM_INFO_ARRAY(1,1003,1), -- one polygon (exterior polygon ring)
SDO_ORDINATE_ARRAY(5,1, 8,1, 8,6, 5,7, 5,1)
)
);

INSERT INTO cola_markets_cs VALUES(
3,
'cola_c',
SDO_GEOMETRY(
2003,  -- two-dimensional polygon
8307,
NULL,
SDO_ELEM_INFO_ARRAY(1,1003,1), --one polygon (exterior polygon ring)
SDO_ORDINATE_ARRAY(3,3, 6,3, 6,5, 4,5, 3,3)
)
);

-- Insert a rectangle (here, square) instead of a circle as in the original,
-- because arcs are not supported with geodetic coordinate systems.
INSERT INTO cola_markets_cs VALUES(
4,
'cola_d',
SDO_GEOMETRY(
2003,  -- two-dimensional polygon
8307,  -- SRID for 'Longitude / Latitude (WGS 84)' coordinate system
NULL,
SDO_ELEM_INFO_ARRAY(1,1003,1), -- polygon
SDO_ORDINATE_ARRAY(10,9, 11,9, 11,10, 10,10, 10,9) -- All vertices must
-- be defined for rectangle with geodetic data.
)
);

---------------------------------------------------------------------------
---------------------------------------------------------------------------
-- Update the USER_SDO_GEOM_METADATA view. This is required
-- before the Spatial index can be created. Do this only once for each
-- layer (table-column combination; here: cola_markets_cs and shape).

VALUES (
'cola_markets_cs',
'shape',
SDO_DIM_ARRAY(
SDO_DIM_ELEMENT('Longitude', -180, 180, 10),  -- 10 meters tolerance
SDO_DIM_ELEMENT('Latitude', -90, 90, 10)  -- 10 meters tolerance
),
8307   -- SRID for 'Longitude / Latitude (WGS 84)' coordinate system
);

-------------------------------------------------------------------
-- CREATE THE SPATIAL INDEX --
-------------------------------------------------------------------
CREATE INDEX cola_spatial_idx_cs
ON cola_markets_cs(shape)
INDEXTYPE IS MDSYS.SPATIAL_INDEX;

-------------------------------------------------------------------
-- TEST COORDINATE SYSTEM TRANSFORMATION --
-------------------------------------------------------------------

-- Return the transformation of cola_c using to_srid 8199
-- ('Longitude / Latitude (Arc 1950)')
SELECT c.name, SDO_CS.TRANSFORM(c.shape, m.diminfo, 8199)
WHERE m.table_name = 'COLA_MARKETS_CS' AND m.column_name = 'SHAPE'
AND c.name = 'cola_c';

-- Same as preceding, but using to_srname parameter.
SELECT c.name, SDO_CS.TRANSFORM(c.shape, m.diminfo, 'Longitude / Latitude (Arc 1950)')
WHERE m.table_name = 'COLA_MARKETS_CS' AND m.column_name = 'SHAPE'
AND c.name = 'cola_c';

-- Transform the entire SHAPE layer and put results in the table
-- named cola_markets_cs_8199, which the procedure will create.
CALL SDO_CS.TRANSFORM_LAYER('COLA_MARKETS_CS','SHAPE','COLA_MARKETS_CS_8199',8199);

-- Select all from the old (existing) table.
SELECT * from cola_markets_cs;

-- Select all from the new (layer transformed) table.
SELECT * from cola_markets_cs_8199;

-- Show metadata for the new (layer transformed) table.
DESCRIBE cola_markets_cs_8199;

-- Use a geodetic MBR with SDO_FILTER
SELECT c.name FROM cola_markets_cs c WHERE
SDO_FILTER(c.shape,
SDO_GEOMETRY(
2003,
8307,    -- SRID for WGS 84 longitude/latitude
NULL,
SDO_ELEM_INFO_ARRAY(1,1003,3),
SDO_ORDINATE_ARRAY(6,5, 10,10))
) = 'TRUE';

```

Example 6-5 shows the output of the SELECT statements in Example 6-4. Notice the slight differences between the coordinates in the original geometries (SRID 8307) and the transformed coordinates (SRID 8199) -- for example, (1, 1, 5, 1, 5, 7, 1, 7, 1, 1) and (1.00078604, 1.00274579, 5.00069354, 1.00274488, 5.0006986, 7.00323528, 1.00079179, 7.00324162, 1.00078604, 1.00274579) for `cola_a`.

Example 6-5 Output of SELECT Statements in Coordinate System Transformation Example

```SQL> -- Return the transformation of cola_c using to_srid 8199
SQL> -- ('Longitude / Latitude (Arc 1950)')
SQL> SELECT c.name, SDO_CS.TRANSFORM(c.shape, m.diminfo, 8199)
2    FROM cola_markets_cs c, user_sdo_geom_metadata m
3    WHERE m.table_name = 'COLA_MARKETS_CS' AND m.column_name = 'SHAPE'
4    AND c.name = 'cola_c';

NAME
--------------------------------
SDO_CS.TRANSFORM(C.SHAPE,M.DIMINFO,8199)(SDO_GTYPE, SDO_SRID, SDO_POINT(X, Y, Z)
--------------------------------------------------------------------------------
cola_c
SDO_GEOMETRY(2003, 8199, NULL, SDO_ELEM_INFO_ARRAY(1, 1003, 1), SDO_ORDINATE_ARR
AY(3.00074114, 3.00291482, 6.00067068, 3.00291287, 6.0006723, 5.00307625, 4.0007
1961, 5.00307838, 3.00074114, 3.00291482))

SQL>
SQL> -- Same as preceding, but using to_srname parameter.
SQL> SELECT c.name, SDO_CS.TRANSFORM(c.shape, m.diminfo, 'Longitude / Latitude (Arc 1950)')
2    FROM cola_markets_cs c, user_sdo_geom_metadata m
3    WHERE m.table_name = 'COLA_MARKETS_CS' AND m.column_name = 'SHAPE'
4    AND c.name = 'cola_c';

NAME
--------------------------------
SDO_CS.TRANSFORM(C.SHAPE,M.DIMINFO,'LONGITUDE/LATITUDE(ARC1950)')(SDO_GTYPE, SDO
--------------------------------------------------------------------------------
cola_c
SDO_GEOMETRY(2003, 8199, NULL, SDO_ELEM_INFO_ARRAY(1, 1003, 1), SDO_ORDINATE_ARR
AY(3.00074114, 3.00291482, 6.00067068, 3.00291287, 6.0006723, 5.00307625, 4.0007
1961, 5.00307838, 3.00074114, 3.00291482))

SQL>
SQL> -- Transform the entire SHAPE layer and put results in the table
SQL> -- named cola_markets_cs_8199, which the procedure will create.
SQL> CALL SDO_CS.TRANSFORM_LAYER('COLA_MARKETS_CS','SHAPE','COLA_MARKETS_CS_8199',8199);

Call completed.

SQL>
SQL> -- Select all from the old (existing) table.
SQL> SELECT * from cola_markets_cs;

MKT_ID NAME
---------- --------------------------------
SHAPE(SDO_GTYPE, SDO_SRID, SDO_POINT(X, Y, Z), SDO_ELEM_INFO, SDO_ORDINATES)
--------------------------------------------------------------------------------
1 cola_a
SDO_GEOMETRY(2003, 8307, NULL, SDO_ELEM_INFO_ARRAY(1, 1003, 1), SDO_ORDINATE_ARR
AY(1, 1, 5, 1, 5, 7, 1, 7, 1, 1))

2 cola_b
SDO_GEOMETRY(2003, 8307, NULL, SDO_ELEM_INFO_ARRAY(1, 1003, 1), SDO_ORDINATE_ARR
AY(5, 1, 8, 1, 8, 6, 5, 7, 5, 1))

3 cola_c

MKT_ID NAME
---------- --------------------------------
SHAPE(SDO_GTYPE, SDO_SRID, SDO_POINT(X, Y, Z), SDO_ELEM_INFO, SDO_ORDINATES)
--------------------------------------------------------------------------------
SDO_GEOMETRY(2003, 8307, NULL, SDO_ELEM_INFO_ARRAY(1, 1003, 1), SDO_ORDINATE_ARR
AY(3, 3, 6, 3, 6, 5, 4, 5, 3, 3))

4 cola_d
SDO_GEOMETRY(2003, 8307, NULL, SDO_ELEM_INFO_ARRAY(1, 1003, 1), SDO_ORDINATE_ARR
AY(10, 9, 11, 9, 11, 10, 10, 10, 10, 9))

SQL>
SQL> -- Select all from the new (layer transformed) table.
SQL> SELECT * from cola_markets_cs_8199;

SDO_ROWID
------------------
GEOMETRY(SDO_GTYPE, SDO_SRID, SDO_POINT(X, Y, Z), SDO_ELEM_INFO, SDO_ORDINATES)
--------------------------------------------------------------------------------
AAABZzAABAAAOa6AAA
SDO_GEOMETRY(2003, 8199, NULL, SDO_ELEM_INFO_ARRAY(1, 1003, 1), SDO_ORDINATE_ARR
AY(1.00078604, 1.00274579, 5.00069354, 1.00274488, 5.0006986, 7.00323528, 1.0007
9179, 7.00324162, 1.00078604, 1.00274579))

AAABZzAABAAAOa6AAB
SDO_GEOMETRY(2003, 8199, NULL, SDO_ELEM_INFO_ARRAY(1, 1003, 1), SDO_ORDINATE_ARR
AY(5.00069354, 1.00274488, 8.00062191, 1.00274427, 8.00062522, 6.00315345, 5.000
6986, 7.00323528, 5.00069354, 1.00274488))

SDO_ROWID
------------------
GEOMETRY(SDO_GTYPE, SDO_SRID, SDO_POINT(X, Y, Z), SDO_ELEM_INFO, SDO_ORDINATES)
--------------------------------------------------------------------------------

AAABZzAABAAAOa6AAC
SDO_GEOMETRY(2003, 8199, NULL, SDO_ELEM_INFO_ARRAY(1, 1003, 1), SDO_ORDINATE_ARR
AY(3.00074114, 3.00291482, 6.00067068, 3.00291287, 6.0006723, 5.00307625, 4.0007
1961, 5.00307838, 3.00074114, 3.00291482))

SDO_GEOMETRY(2003, 8199, NULL, SDO_ELEM_INFO_ARRAY(1, 1003, 1), SDO_ORDINATE_ARR
AY(10.0005802, 9.00337775, 11.0005553, 9.00337621, 11.0005569, 10.0034478, 10.00

SDO_ROWID
------------------
GEOMETRY(SDO_GTYPE, SDO_SRID, SDO_POINT(X, Y, Z), SDO_ELEM_INFO, SDO_ORDINATES)
--------------------------------------------------------------------------------
05819, 10.0034495, 10.0005802, 9.00337775))

SQL>
SQL> -- Show metadata for the new (layer transformed) table.
SQL> DESCRIBE cola_markets_cs_8199;
Name                                      Null?    Type
----------------------------------------- -------- ----------------------------
SDO_ROWID                                          ROWID
GEOMETRY                                           SDO_GEOMETRY

SQL>
SQL> -- Use a geodetic MBR with SDO_FILTER
SQL> SELECT c.name FROM cola_markets_cs c WHERE
2     SDO_FILTER(c.shape,
3         SDO_GEOMETRY(
4             2003,
5             8307,    -- SRID for WGS 84 longitude/latitude
6             NULL,
7             SDO_ELEM_INFO_ARRAY(1,1003,3),
8             SDO_ORDINATE_ARRAY(6,5, 10,10))
9         ) = 'TRUE';

NAME
--------------------------------
cola_c
cola_b
cola_d
```