Open Geospatial Consortium
Submission Date: 2018-03-20
Approval Date: 2018-08-27
Publication Date: 2018-12-19
External identifier of this OGC® document: http://www.opengis.net/doc/BP/CDB-SRF/1.1
Internal reference number of this OGC® document: 16-011r4
Version: 1.1
Category: OGC® Best Practice
Editor: Carl Reed

Volume 8: CDB Spatial and Coordinate Reference
Systems Guidance
Copyright notice
Copyright © 2018 Open Geospatial Consortium
To obtain additional rights of use, visit http://www.opengeospatial.org/legal/.

Warning
This document defines an OGC Best Practices on a particular technology or approach
related to an OGC standard. This document is not an OGC Standard and may not bereferred to as an OGC Standard. It is subject to change without notice. However, thisdocument is an official position of the OGC membership on this particular technology
topic.

Document type:
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OGC® Best PracticeApproved
EnglishCopyright © 2018 Open Geospatial Consortium

1

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Copyright © 2018 Open Geospatial Consortium2

Contents
1.

Scope ........................................................................................................................... 52.

Conformance ............................................................................................................... 6

3.

References ................................................................................................................... 6

4.

Terms and Definitions................................................................................................. 6

5.

Conventions ................................................................................................................ 7
5.1

6.

CDB Approach............................................................................................................ 7
6.1

7.

Identifiers ............................................................................................................. 7

CDB Spatial Reference Systems .......................................................................... 7

The Three Systems...................................................................................................... 8
7.1

Geographic Coordinate System (Geodetic).......................................................... 9

7.1.1

Earth-Centered SRS (aka Rectangular Geocentric SRS) ............................ 10

7.1.2

General Cartesian SRS................................................................................ 10

7.1.3

Local Vertical SRS ..................................................................................... 10

7.2

Geodetic to Geocentric transformation .............................................................. 11

7.3

Geocentric to Geodetic Transformation ............................................................. 12

7.4

Geodetic to LVCS Coordinate Transformation ................................................. 13

7.5

Angular Displacements to Linear Displacement ................................................ 14

7.6

3D Model Coordinate System ............................................................................ 15

Copyright © 2018 Open Geospatial Consortium3i.

Abstract

Volume 8 of the CDB standard defines the conceptual model and the methodologies thatallow the description, and transformation or conversion, of geometric properties within aset of spatial reference frames supported by the CDB standard. The CDB Spatial
Reference Model (SRM) supports an unambiguous specification of the positions,directions, and distances associated with spatial information. This document also defines
algorithms for precise transformation of positions, directions and distances among
different spatial reference frames.
In previous versions of the CDB standard, this CDB volume was Appendix K in CDB
Version 3.2 as submitted to the OGC.

ii.

Keywords
The following are keywords to be used by search engines and document catalogues.
ogcdoc, OGC document, cdb, spatial reference model, srm, coordinate systems, crs, srsiii.

Preface
Attention is drawn to the possibility that some of the elements of this document may be
the subject of patent rights. The Open Geospatial Consortium shall not be held
responsible for identifying any or all such patent rights.
Recipients of this document are requested to submit, with their comments, notification of
any relevant patent claims or other intellectual property rights of which they may beaware that might be infringed by any implementation of the standard set forth in thisdocument, and to provide supporting documentation.

iv.

Submitting organizations

The following organizations submitted this Document to the Open Geospatial
Consortium (OGC):CAE Inc.
Carl Reed, OGC Individual Member
Envitia, Ltd
Glen Johnson, OGC Individual Member
KaDSci, LLC
Laval University
Open Site Plan
University of Calgary
UK Met Office
The OGC CDB standard is based on and derived from an industry developed andmaintained specification, which has been approved and published as OGC Document 15003: OGC Common DataBase Volume 1 Main Body. An extensive listing ofcontributors to the legacy industry-led CDB specification is at Chapter 11, pp 475-476 in

Copyright © 2018 Open Geospatial Consortium4

that OGC Best Practices Document(https://portal.opengeospatial.org/files/?artifact_id=61935 ).

v.

Submitters
All questions regarding this submission should be directed to the editor or the submitters:

vi.

Name

Affiliation

Carl Reed
David Graham

Carl Reed & Associates
CAE Inc.

Document Organization

For ease of editing and review, the standard has been separated into 12 Volumes and aschema repository.
● Volume 0: OGC CDB Companion Primer for the CDB standard. (Best Practice)● Volume 1: OGC CDB Core Standard: Model and Physical Data Store Structure.
The main body (core) of the CBD standard (Normative).
• Volume 2: OGC CDB Core Model and Physical Structure Annexes (BestPractice).
● Volume 3: OGC CDB Terms and Definitions (Normative).
● Volume 4: OGC CDB Use of Shapefiles for Vector Data Storage (Best Practice).
● Volume 5: OGC CDB Radar Cross Section (RCS) Models (Best Practice).
● Volume 6: OGC CDB Rules for Encoding Data using OpenFlight (Best Practice).
● Volume 7: OGC CDB Data Model Guidance (Best Practice).
● Volume 8: OGC CDB Spatial Reference System Guidance (Best Practice).
● Volume 9: OGC CDB Schema Package: provides the normative schemas for key
features types required in the synthetic modelling environment. Essentially, theseschemas are designed to enable semantic interoperability within the simulation
context. (Normative)● Volume 10: OGC CDB Implementation Guidance (Best Practice).
● Volume 11: OGC CDB Core Standard Conceptual Model (Normative)● Volume 12: OGC CDB Navaids Attribution and Navaids Attribution
Enumeration Values (Best Practice)

1. Scope
The handling of spatial data requires a good deal of rigor to accurately describe theposition of points in space. Furthermore, it requires the ability to define directions anddistances. Generally, this is accomplished through the use of coordinate systems.
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.

Copyright © 2018 Open Geospatial Consortium

5Specifying a coordinate reference system enables the interpretation of a set of coordinates
as a representation of a position in a real world space.
In the CDB standard, these terms can be used interchangeably. However, for consistency
with previous versions of the CDB standard, the term spatial reference system (SRS) is
used.
There is often the requirement to represent position in several different spatial reference
systems. Each spatial reference system provides a particular way of defining positions
within its domain. This level of abstraction also permits spatial reference systems to be
decomposed into a series of, or even a hierarchy of reference, each relative to anotherreference system. This mechanism permits objects to be independently defined(positioned, oriented, and scaled) with respect to a local SRS and then be later
incorporated into other reference systems. The reference systems can be abstract
mathematical constructs or they can be bound to real world objects (e.g., a flap locateddefined in a flap reference system which in turn is bound to an aircraft wing reference
system).

2. Conformance
There are no conformance classes in this document

3. References
The following normative documents contain provisions that, through reference in thistext, constitute provisions of this document. For dated references, subsequent
amendments to, or revisions of, any of these publications do not apply. For undated
references, the latest edition of the normative document referred to applies.
ISO: ISO 19111:2007, Geographic information ― Spatial referencing by coordinates,
2007

4. Terms and Definitions
This document uses the terms defined in Sub-clause 5.3 of [OGC 06-121r8], which isbased on the ISO/IEC Directives, Part 2, Rules for the structure and drafting ofInternational Standards. In particular, the word “shall” (not “must”) is the verb form used
to indicate a requirement to be strictly followed to conform to this standard.
Any terms and definitions for this CDB document may be found in Volume 3: CDB
Terms and Definitions (http://www.opengeospatial.org/standards/cdb).

Copyright © 2018 Open Geospatial Consortium

6

5. Conventions
This sections provides details and examples for any conventions used in the document.
Examples of conventions are symbols, abbreviations, use of XML schema, or special
notes regarding how to read the document.
5.1 Identifiers
There are no normative provisions in this document.

6. CDB Approach
One of the primary objectives of the CDB standard is to provide the means to represent
the entire earth. As such, a CDB compliant data store must handle spatial data with agood deal of rigor to accurately describe the position of points in space and must do so at
the level of fidelity commensurate with the precision that is now possible in modern
simulators.
The size, content, fidelity and precision of synthetic environments now warrant a
different approach, an approach that entirely avoids the “problem with projections” andother approximations used in the past. To this end, the CDB standard mandates the use ageographic coordinate system (GCS). A GCS uses a three-dimensional sphericalsurface to define locations on the earth. Since no projections are involved, full geometriccoherence is assured without compromise and all four key spatial properties can beachieved simultaneously:
(1)
(2)
(3)
(4)

Preservation of distancePreservation of direction
Preservation of area
Preservation of shape

6.1 CDB Spatial Reference Systems
The CDB standard is based on a surface geodetic coordinate system, i.e., points on theearth surface are specified as geographic latitude -longitude and elevation coordinates.
More specifically, geodetic coordinates (sometimes called geographic coordinates) areangular coordinates (longitude and latitude), closely related to spherical polar
coordinates, and are defined relative to a particular Earth geodetic datum. For the CDB,
this is the WGS 84 datum. The WGS 84 datum surface is an oblate spheroid (ellipsoid)with major (equatorial) radius a = 6378137 m at the equator and flattening f =1/298.257223563.[6] The polar semi-minor axis b then equals a times (1−f), or
6356752.3142 m.

Copyright © 2018 Open Geospatial Consortium

7

The CDB data store embeds modeled point features (e.g., the representation of 3-D
objects, moving and/or static) within a Cartesian Coordinate System1. Its use is generally
constrained to objects that are small in comparison to the earth. As shown below, amodeled point feature can be referenced anywhere on the earth by providing the model’sorientation (the AO1 attribute specified in Chapter 5 of Volume 1: OGC CDB Core
Standard: Model and Physical Database Structure) and the model’s origin using a set oflatitude/longitude/elevation coordinates. Note that the model’s z-axis implicitly points
upward with respect to the earth surface.

Figure 1: Cartesian Model positioned to WGS-84 Coordinates

The earth shape is described by the WGS-84 reference ellipsoid. The CDB standard also
defines three related set of Spatial Reference Systems (and associated coordinate
systems) for use in conjunction with the surface geodetic coordinate system; they are:
(1)
(2)
(3)

Earth-centered Cartesian (Geocentric)
Generic Cartesian
Local Vertical (LVCS)

7. The Three Systems
The following sections detail the normative aspects of the three Spatial Reference
Systems (SRS) supported in the CDB model. We start with a general discussion of theGeographical Coordinate System before addressing the Spatial Reference Systems.
A Cartesian coordinate system is a coordinate system that specifies each point
uniquely in a plane by a pair of numerical coordinates, which are the signed distances tothe point from two fixed perpendicular directed lines, measured in the same unit of length
1 .

Copyright © 2018 Open Geospatial Consortium

87.1 Geographic Coordinate System (Geodetic)
A geographic coordinate system (also called the geodetic coordinate system) is one inwhich the coordinates are expressed as latitude, longitude, and altitude relative to thereference ellipsoid. Geographical latitude f and longitude l are the angles of the normal
on the reference ellipsoid along the point to the equator and zero meridian. The angles arenormally given as degrees, minutes and seconds. Altitude is the distance above andnormal to the reference ellipsoid in meters. The WGS 84 ellipsoid represents the actual
geoid within an accuracy of 100 meters. The prime meridian and the equator are thereference planes used to define latitude and longitude.
In other terms, the geographic latitude – there are many other defined latitudes – of apoint is the angle between the equatorial plane and a line normal to the reference
ellipsoid’s surface. The geographic longitude of a point is the angle between a reference
plane, Greenwich, and a plane passing through the point, both planes being perpendicular
to the equatorial plane. The geographic height at a point is the distance from thereference ellipsoid to the point in a direction normal to the reference ellipsoid.
Table 1: Geographic Coordinate System (Geodetic)

Field

Specification

Properties

Orthogonal.
a: major semi-axis length

CS parameters andconstraints

b: minor semi-axis length
Constraints: a > b: (oblate ellipsoid)

Coordinate componentsl : longitude in radians, andf : geodetic latitude in radians.

Domain of thegenerating function or
mapping equations-p < f < p2
2-p < l £ p

Domain of the inverseof the generating
function or mapping
equationsx 2 y 2 z2++
= 1 and z ¹ ± b.
a2 a2 b2

Copyright © 2018 Open Geospatial Consortium

9

FieldSpecification

Notes(1) The CS surface is the oblate ellipsoid (or sphere)
surface excluding the pole points.
(2) The geodetic 3D CS induces this CS on the 3rd
coordinate surface at any point for which h = 0.
(3) If a = b, the geodetic latitude f coincides with thespherical latitude q.
(4) For WGS-84 a= 6,378,137 m and b = 6,356,752 m.
The inverse flattening ratio f-1 is 298.257223563.

7.1.1 Earth-Centered SRS (aka Rectangular Geocentric SRS)
The earth-centered SRS defines a three-dimensional Euclidian space with respect to thegeometric center of the reference ellipsoid, the center of the earth. The reference datumof the Earth-centered SRS is based on the WGS-84 ellipsoid reference model. In this
SRS, the z-axis is pointing at the North Pole, the x-axis is pointing at the intersection of
the equator and the Greenwich meridian, the prime meridian, and the y-axis is pointing at
the intersection of the equator and 90o east longitude. The associated coordinate system
is called the World Coordinate System and its units are meters. The world coordinate
system is used to specify the 3D position of objects with respect to the earth-centered
SRS. This coordinate system is used as an intermediate system to convert geodetic
coordinates to LVCS and vice versa
7.1.2 General Cartesian SRS
The Cartesian spatial reference frame defines a three-dimensional Euclidian space withrespect to an arbitrary origin. The reference datum specifying the origin and theorientation of the SRS is arbitrary, i.e. the reference datum can be specified within ageocentric SRS, a LVCS SRS or any other SRS. The SRS is right-handed andorthonormal. In this SRS system, the z-axis is pointing up and both the x-axis and y-axis
lie in the horizontal plane. The associated coordinate system is called the General
Cartesian Coordinate System; coordinates are specified in meters. This coordinate
system is used for the representation of 3-D objects, moving and/or static. Its use isgenerally constrained to objects that are small in comparison to the earth2.
7.1.3 Local Vertical SRS
The Local Vertical SRS (LVCS) spatial reference frame defines a three-dimensional
Euclidian space. It is a SRF similar to the Geocentric SRF except that the origin of the
SRF is translated and rotated to a point on the surface of the WGS-84 ellipsoid. At thatpoint, the x-y plane is tangent to the surface of the earth and the z-axis is normal to theellipsoid. The associated coordinate system is called the local vertical coordinate system;
the coordinates are specified in meters. In this coordinate system, the z-axis is pointing

2 To ensure that the object preserves its shape, size, orientation, and relative geometry.

Copyright © 2018 Open Geospatial Consortium

10

up, the y-axis is pointing north and the x-axis is pointing east. Its use is generally
constrained to a surface that is small in comparison to the earth3.
7.2 Geodetic to Geocentric transformation4
The following equations are used to transform geodetic information to geocentric informationaccording to the following:(1)

If <j, l, h> represents the geodetic coordinates to be transformed,
where j is the latitude, l is the longitude, and h is the WGS84 height
above the reference ellipsoid; and(2)

If <x, y, z> represents the geocentric coordinates; then using the
WGS84 ellipsoid equatorial radius, a, of 6,378,137.0m and the
WGS84 ellipsoid polar radius, b, of 6,356,752.314245m, the flattening
f, the eccentricity e and the radius of curvature as a function of latitude
N(j) are given by equation eq. A-1:

f = (a - b) ae2 = 2 f - f 2(eq. A-1)

N (j ) = a 1 - e 2 sin 2 j

From these equations, we define the transformation of each geodetic coordinate as:

x = (N (j ) + h) cosj cos ly = (N (j ) + h) cosj sin l((eq. A-2))

z = N (j )(1 - e 2 ) + h sin j

3 To ensure that the object preserves its shape, size, orientation, and direction
4 There are many excellent references. A recent one is: http://www.oc.nps.edu/oc2902w/coord/coordcvt.pdf

Copyright © 2018 Open Geospatial Consortium

117.3 Geocentric to Geodetic Transformation
Geocentric coordinates cannot be transformed to the geodetic coordinate system directly.
Instead, a successive approximation approach is used to compute the new coordinates.
The following describes the algorithm to convert geocentric coordinates <x, y, z> togeodetic coordinates <j, l, h>, where j is the latitude, l is the longitude, and h is the
WGS84 height above the reference ellipsoid. First, using the WGS84 ellipsoid equatorial
radius, a = 6,378,137.0 m and the WGS84 ellipsoid polar radius, b = 6,356,752.314245
m, the flattening f and the eccentricity e of the ellipsoid are given by equation A-3:

f = (a - b) ae2 = 2 f - f 2(eq. A-3)

We first compute the longitude l with equation A-4:

æyöl = tan -1 ç ÷èxø(eq. A-4)

We then compute a first approximation of the latitude assuming a spherical earth modelwith equation A-5:æöz÷j = tan -1 çç x2 + y2 ÷èø(eq. A-5)

Then, we iteratively compute the radius of curvature as a function of latitude N(j) and, asa result we iteratively converge to a new, more accurate latitude j’ with equation A-6:

N (j ) = a 1 - e 2 sin 2 j

Copyright © 2018 Open Geospatial Consortium

(eq.
A-6)

12

æ z + N (j ) e 2 sin j ö÷
j ' = tan -1 ç
2
2
ç
÷
x +y
è
ø

For each iteration, j is replaced with j’, until the difference between the two values isless than a preset allowable error. The resulting latitude error will be less than e. Finally,
we compute the height above the reference ellipsoid h with equation A-7h=x2 + y2- N (j )
cos j

(eq.
A-7)

7.4 Geodetic to LVCS Coordinate Transformation
The transformation of a geodetic coordinate into an LVCS coordinate is decomposed into
two parts:
1. Apply a coordinate transformation to each coordinate of an object
from the geodetic coordinate system to the rectangular geocentric
coordinate system.
2. Then apply a second transformation to go from the geocentric
coordinate system to LVCS.
The first transformation, from geodetic to rectangular geocentric is described in section
Error! Reference source not found.. The transformation is applied to the origin of theobject. The result of this transformation is the origin x0 of the object in the geocentric
coordinate system. Then for each coordinate x of the object, we apply the geodetic togeocentric transformation to coordinate x and we then compute the translation vector t
between x and x0 in the geocentric coordinate system with equation A-8

t = x - x0

(eq. A-8)

The second transformation, from geocentric to LVCS is presented here as an algorithm totransform all coordinates of an object from the geodetic coordinate system to LVCS. The
transformation from geodetic to LVCS first requires the assembly of a 3x3 rotation
matrix M with equation A-9:

Copyright © 2018 Open Geospatial Consortium13

cos l00 ù
é - sin l0ê
M = ê - sin j0 cos l0 - sin j0 sin l0 cos j0 úúêë cos j0 cos l0 cos j0 sin l0 sin j0 úû

(eq.
A-9)

Where: j0 and l0 = the latitude and longitude of the origin of the object.
Finally, the rotation matrix M is applied to the translation vector t to obtain eachcoordinate xL in the local vertical coordinate system with equation A-10:

xL = Mt(eq. A-10)

7.5 Angular Displacements to Linear Displacement
For WGS84, which is an elliptical representation of the earth, the transformation fromangular displacements to equivalent linear displacements in a tangential plane is slightly
different than that for a spherical earth.
For WGS84 we get…

dX = r t cos(lat )dlon
dY = r mdlat… as opposed to for a spherical earth

dX = r cos(lat )dlon
dY = rdlat

where…
dX , dY

are the linear displacements along the x and y axes.

r m , rtare the meridional and transverse radiuses of curvature.

ris the radius of the spherical earth.

dlat , dlon

are small displacements at location lat/lon

Copyright © 2018 Open Geospatial Consortium14

we have…

rm =
rt =

(

a 1 - e2)

[1 - e sin (lat )]
2

2

3

2

a

1 - e sin 2 (lat )2b2
e = 1- 2aa -bÞ b = a (1 - f )f =a2

where…
e2a,bf

is the square of the eccentricity
are the semi-major and the minor axes of the earth
is the flattening

This section describes the transformations required to go to-and-from the DIS/HLA andthe CDB moving model coordinate systems.
7.6 3D Model Coordinate System
The CDB 3D model coordinate system conventions are presented earlier in the OGC
CDB Rules for Encoding Data using OpenFlight Best Practice.

Figure 1: CDB 3D Model Coordinate System

Copyright © 2018 Open Geospatial Consortium

15

The DIS coordinate system is used on a HLA network and is represented on thefollowing figure.

Figure 2: DIS Entity5 Coordinate System

The two coordinate systems differ in the axis conventions (Z is up in the CDB while Z isdown in DIS). Furthermore, the position of the origin also differs; DIS requires that theorigin of its coordinate system be located at the center of the entity’s bounding box
excluding its articulated and attached parts6. The CDB standard uses a different
convention.
The transformation from the CDB coordinate system to the DIS coordinate system
involves one translation followed by two rotations. The translation represents the offset
to the DIS origin as defined in chapter 6. Assume that P0 represents the coordinate of the
DIS origin.
P0 = ( x0 , y0 , z0 )(eq. A-11)

The two rotations are relatively simple. First, rotate 180° about the X-axis. This rotation
will position the Z-axis in its correct position. Equation A-12 represents this rotation.

5

DIS refers to a 3D model as an entity.

6

This definition can be found on page 3 of IEEE Std 1278.1-1995. Note that the CDB provides the means to store
the DIS origin within the coordinate system space of the model.

Copyright © 2018 Open Geospatial Consortium16

ì1 0 0 üïï
M x = í0 - 1 0 ý
ï0 0 - 1ïîþ(eq. A-12)

Second, rotate -90° about this new Z-axis. This last rotation completes thetransformation and is represented by equation A-13.

ì0 - 1 0üïï
M z = í1 0 0ý
ï0 0 1ïîþ

(eq. A-13)

Now, if we combine equations A-11, A-12 and A-13, we can transform a point P
expressed in the CDB coordinate system into point P’ in the DIS coordinate system.
Equation A-14 presents the complete transformation.

P ' = M z M x ( P - P0 )(eq. A-14)

The combined matrix gives equation A-15 and the resulting individual terms arepresented in A-16.

ì0 1 0 üïï
M zx = í1 0 0 ý
ï0 0 - 1ïîþ(eq. A-15)

x ' = y - y0
y ' = x - x0

(eq. A-16)

z ' = z0 - z

If a single transformation matrix M is preferred then Matrix Mzx and point P0 are
combined to obtain the set of equations A-17.
Copyright © 2018 Open Geospatial Consortium

17

P ' = MP
where...
ì0
ï1
ï
M =í
ï0
ïî0

1
0

0
0

- y0 ü
- x0 ïï
ý
0 - 1 z0 ï
0 0
1 ïþ

(eq. A-17)

and ...
ìxü
ï yï
ï ï
P=í ý
ïzï
ïî 1 ïþ

To convert from the DIS coordinate system back to the CDB coordinate system, theinverse transformation is applied. Knowing that unscaled rotation matrices (the upper 3 x
3 portion of M) have the property that their inverse is their transpose, we obtain the set of
equations A-18.

P = M -1 P 'where...
ì0
ï1
ï
-1
M =í
ï0
ï
î0

Copyright © 2018 Open Geospatial Consortium

1
0

0
0

x0 ü
y0 ï
ï
ý
0 - 1 z0 ï
0 0
1ï
þ

(eq. A-18)

18

Annex A: Revision history
Date

Release

EditorParagraph modified Description

2/5/2016

1.0

C. ReedVariousPrepare as version 1.

3/8/2016

1.0

C. ReedVarious6/22/2016

1.0r2

C.ReedVarious

Modify based on 3/8/2016 SWG
discussions
Correct ambiguity WRT how altitude isdefined.

10/7/2016

R3

C. ReedVarious11/21/2016 1.0

C. Reed12/28/2017 1.1

C. Reed

Copyright © 2018 Open Geospatial Consortium

Final edits for publication
Ready for publication

MinimalUpdate for version 1.1. Very minor edits.

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