# 6.2 Geodetic Coordinate Support

Effective with Oracle9i, Spatial and Graph 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 the Earth 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 and Graph 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. Some operations using geodetic coordinates may take longer to complete than the same operations using Cartesian coordinates.

It is important that you choose the correct type of coordinate system, because it affects the point at which anomalies related to floating point arithmetic are likely to appear.

## 6.2.3 Choosing Non-Ellipsoidal or Ellipsoidal Height

This section discusses guidelines for choosing the appropriate type of height for three-dimensional data: non-ellipsoidal or ellipsoidal. Although ellipsoidal height is widely used and is the default for many GPS applications, and although ellipsoidal computations incur less performance overhead in many cases, there are applications for which a non-ellipsoidal height may be preferable or even necessary.

Also, after any initial decision, you can change the reference height type, because transformations between different height datums are supported.

### 6.2.3.1 Non-Ellipsoidal Height

Non-ellipsoidal height is measured from some point other than the reference ellipsoid. Some common non-ellipsoidal measurements of height are from ground level, mean sea level (MSL), or the reference geoid.

• Ground level: Measuring height from the ground level is conceptually the simplest approach, and it is common in very local or informal applications. For example, when modeling a single building or a cluster of buildings, ground level may be adequate.

Moreover, if you ever need to integrate local ground height with a global height datum, you can achieve this with a transformation (EPSG method 9616) adding a local constant reference height. If you need to model local terrain undulations, you can achieve this with a transformation using an offset matrix (EPSG method 9635), just as you can between the geoid and the ellipsoid.

• Mean sea level (MSL): MSL is a common variation of sea level that provides conceptual simplicity, ignoring local variations and changes over time in sea level. It can also be extrapolated to areas covered by land.

Height relative to MSL is useful for a variety of applications, such as those dealing with flooding risk, gravitational potential, and how thin the air is. MSL is commonly used for the heights of aircraft in flight.

• Geoid: The geoid, the equipotential surface closest to MSL, provides the most precise measurements of height in terms of gravitational pull, factoring in such things as climate and tectonic changes. The geoid can deviate from MSL by approximately 2 meters (plus or minus).

If an application is affected more by purely gravitational effects than by actual local sea level, you may want to use the geoid as the reference rather than MSL. To perform transformations between MSL, geoid, or ellipsoid, you can use EPSG method 9635 and the appropriate time-stamped offset matrix.

Because most non-ellipsoidal height references are irregular and undulating surfaces, transformations between them are more complicated than with ellipsoidal heights. One approach is to use an offset grid file to define the transformation. This approach is implemented in EPSG method 9635. The grid file has to be acquired (often available publicly from government websites). Moreover, because most such non-ellipsoidal height datums (including the geoid, sea level, and local terrain) change over time, the timestamp of an offset matrix may matter, even if not by much. (Of course, the same principle applies to ellipsoids as well, since they are not static in the long term. After all, they are intended to approximate the changing geoid, MSL, or terrain.)

Regarding performance and memory usage with EPSG method 9635, at runtime the grid must be loaded before the transformation of a dataset. This load operation temporarily increases the footprint in main memory and incurs one-time loading overhead. If an entire dataset is transformed, the overhead can be relatively insignificant; however, if frequent transformations are performed on single geometries, the cumulative overhead can become significant.

### 6.2.3.2 Ellipsoidal Height

Ellipsoidal height is measured from a point on the reference ellipsoid. The ellipsoid is a convenient and relatively faithful approximation of the Earth. Although using an ellipsoid is more complex than using a sphere to represent the Earth, using an ellipsoid is, for most applications, simpler than using a geoid or local heights (although with some sacrifice in precision). Moreover, geoidal and sea-level heights are often not well suited for mathematical analysis, because the undulating and irregular shapes would make certain computations prohibitively complex and expensive.

GPS applications often assume ellipsoidal height as a reference and use it as the default. Because the ellipsoid is chosen to match the geoid (and similar sea level), ellipsoidal height tends not to deviate far from MSL height. For example, the geoid diverges from the NAD83 ellipsoid by only up to 50 meters. Other ellipsoids may be chosen to match a particular country even more closely.

Even if different parties use different ellipsoids, a WKT can conveniently describe such differences. A simple datum transformation can efficiently and accurately perform transformations between ellipsoids. Because no offset matrix is involved, no loading overhead is required. Thus, interoperability is simplified with ellipsoidal height, although future requirements or analysis might necessitate the use of MSL, a geoid, or other non-ellipsoidal height datums.

## 6.2.4 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 (optimized rectangle) and an SDO_INTERPRETATION value of 3, as described in Table 2-2 in SDO_ELEM_INFO. 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 6-17 in Example of Coordinate System Transformation):

```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 and Graph 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 in the middle latitudes in both hemispheres).

• When an optimized rectangle spans more than 119 degrees in longitude, it is internally divided into three rectangles; and as a result, these three rectangles share an edge that is the common boundary between them. If you validate the geometry of such an optimized rectangle, error code 13351 is returned because the internal rectangles have a shared edge. You can use such an optimized rectangle for queries with only the following: SDO_ANYINTERACT operator, SDO_RELATE operator with the ANYINTERACT mask, or SDO_GEOM.RELATE function with the ANYINTERACT mask. (Any other queries on such an optimized rectangle may return incorrect results.)

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.

## 6.2.5 Other Considerations and Requirements with Geodetic Data

The following geometries are not permitted if a geodetic coordinate system is used or if any transformation is being performed (even if the transformation is from one projected coordinate system to another projected coordinate system):

• 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 SDO_GEOM Package (Geometry)) 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 or equal to one-half the surface of the Earth. Moreover, if the result of a union of two polygons is greater than one-half the surface of the Earth, the operation will not produce a correct result. For example, if A union B results in a polygon that is greater than one-half of the area of the Earth, the operations A difference B, A intersection B, and A XOR B are not supported, and only a relate operation with the ANYINTERACT mask is supported between those two polygons.

• In a line, the distance between two adjacent coordinates cannot be greater than or equal to one-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 a geometry representing the entire ocean surface of the Earth; however, you can create multiple geometries, each representing part of the overall ocean surface. To work with a line string that is greater than or equal to one-half the perimeter of the Earth, you can add one or more intermediate points on the line so that all adjacent coordinates are less than one-half the perimeter of the Earth.

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 0.05 for geodetic data, this is interpreted as precise to 5 centimeters. 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 Tolerance.)

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 6-17 in Example of Coordinate System Transformation) specifies these extents (with a 10-meter tolerance value in each dimension) for a geodetic data layer:

```INSERT INTO user_sdo_geom_metadata
(TABLE_NAME,
COLUMN_NAME,
DIMINFO,
SRID)
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 Notes and Restrictions with Coordinate Systems Support for additional notes and restrictions relating to geodetic data.