Information technology —
Spatial Reference Model (SRM)
Contents
1 Scope
3 Terms, definitions, symbols, and abbreviated terms
3.2 Notation, symbols and abbreviated terms
4 Concepts
4.1 Introduction
4.2 Spatial objects and object-space
4.3 Position-space and normal embeddings
4.4 Reference datums
4.6.1 Abstract coordinate systems
4.6.2 Temporal coordinate systems
4.6.3 Spatial coordinate systems
4.8 Designated spatial surfaces and vertical offsets
4.9 Spatial reference frame operations
4.10 Application program interface
4.11 SRM units
4.12 Profiles
4.13 Registration
5.1 Introduction
5.2 Preliminaries
5.3 Abstract CS
5.4 CS types
5.5 Coordinate surfaces, induced surface CSs, and coordinate curves
5.5.1 Introduction
5.5.2 Coordinate-component surfaces and induced surface CSs
5.5.3 Coordinate-component curves
5.6 CS properties
5.6.1 Linearity
5.6.2 Orthogonality
5.6.3 Linear CS properties: Cartesian, and orthonormal
5.6.4 CS right-handedness and coordinate-component ordering
5.7 CS localization
5.8 Map projection coordinate systems
5.8.1 Map projections
5.8.2 Map projection as a surface CS
5.8.3 Map projection geometry
5.8.4 Relationship to projection functions
5.8.5 Map projection CS common parameters
5.8.6 Augmented map projections
5.9.1 Specification table elements and common functions and parameters
5.9.2 Euclidean 3D CS specification
5.9.3 Lococentric Euclidean 3D CS specification
5.9.4 Spherical CS specification
5.9.5 Lococentric spherical CS specification
5.9.6 Azimuthal spherical CS specification
5.9.7 Lococentric azimuthal spherical CS specification
5.9.8 Geodetic 3D CS specification
5.9.9 Planetodetic 3D specification
5.9.10 Cylindrical CS specification
5.9.11 Lococentric cylindrical CS specification
5.9.12 Mercator CS specification
5.9.13 Oblique Mercator spherical CS specification
5.9.14 Transverse Mercator CS specification
5.9.15 Lambert conformal conic CS specification
5.9.16 Polar stereographic CS specification
5.9.17 Equidistant cylindrical CS specification
5.9.18 Surface geodetic CS specification
5.9.19 Surface planetodetic CS specification
5.9.20 Lococentric surface Euclidean CS specification
5.9.21 Lococentric surface azimuthal CS specification
5.9.22 Lococentric surface polar CS specification
5.9.23 Euclidean 2D CS specification
5.9.24 Lococentric Euclidean 2D CS specification
5.9.25 Azimuthal CS specification
5.9.26 Lococentric azimuthal CS specification
5.9.27 Polar CS specification
5.9.28 Lococentric polar CS specification
5.9.29 Euclidean 1D CS specification
6.1 Introduction
6.2 Temporal coordinate systems
6.2.1 Integrated and dynamic temporal coordinate systems
6.2.2 Universal time
6.2.3 International atomic time
6.2.4 Coordinated universal time
6.3 Specified temporal coordinate systems
6.4 Registered temporal coordinate systems
7 Reference datums, embeddings, and object reference models
7.1 Introduction
7.2 Reference datums
7.2.1 Introduction
7.2.2 Reference datums
7.2.3 Ellipsoidal RDs
7.2.4 RDs associated with physical objects
7.2.5 RD binding
7.3 Normal embeddings of position-space into object-space
7.3.1 Normal embeddings
7.3.2 Specification of 3D similarity transformations
7.3.3 Specification of 2D similarity transformations
7.4.1 Introduction
7.4.2 ORM
7.4.3 Binding constraint
7.4.4 ORM template
7.4.5 Standardized ORMs
7.5 Object binding rules for ORMT BI_AXIS_ORIGIN_3D realizations
7.5.1 Object binding rule set
7.5.2 Equatorial inertial
7.5.3 Solar ecliptic
7.5.4 Solar equatorial
7.5.5 Heliocentric Aries ecliptic
7.5.6 Heliocentric planet ecliptic
7.5.7 Heliocentric planet equatorial
7.5.8 Celestiomagnetic
7.5.9 Solar magnetic ecliptic
7.5.10 Solar magnetic dipole
8.1 Introduction
8.2 Spatial coordinate systems
8.3.1 Specification
8.3.2 SRF specification elements
8.4 SRF induced surface spatial reference frame
8.5 SRF templates
8.5.1 Introduction
8.5.2 Celestiocentric SRFT
8.5.3 Local space rectangular 3D SRFT
8.5.4 Celestiodetic SRFT
8.5.5 Planetodetic SRFT
8.5.6 Local tangent space Euclidean SRFT
8.5.7 Local tangent space azimuthal spherical SRFT
8.5.8 Local tangent space cylindrical SRFT
8.5.9 Lococentric Euclidean 3D SRFT
8.5.10 Celestiomagnetic SRFT
8.5.11 Equatorial inertial SRFT
8.5.12 Solar ecliptic SRFT
8.5.13 Solar equatorial SRFT
8.5.14 Solar magnetic ecliptic SRFT
8.5.15 Solar magnetic dipole SRFT
8.5.16 Heliospheric Aries ecliptic SRFT
8.5.17 Heliospheric Earth ecliptic SRFT
8.5.18 Heliospheric Earth equatorial SRFT
8.5.19 Mercator SRFT
8.5.20 Oblique Mercator spherical SRFT
8.5.21 Transverse Mercator SRFT
8.5.22 Lambert conformal conic SRFT
8.5.23 Polar stereographic SRFT
8.5.24 Equidistant cylindrical SRFT
8.5.25 Local space rectangular 2D SRFT
8.5.26 Local space azimuthal 2D SRFT
8.5.27 Local space polar 2D SRFT
8.6.1 Introduction
8.6.2 British national grid
8.6.3 UK ordnance survey GRS80 grid
8.6.4 Delaware (US) state plane coordinate system
8.6.5 Geocentric WGS 1984
8.6.6 Geodetic Australia 1984
8.6.7 Geodetic WGS 1984
8.6.8 Geodetic north american 1983
8.6.9 Irish grid
8.6.10 Irish transverse Mercator
8.6.11 Lambert-93
8.6.12 Lambert II étendu (Lambert II wide)
8.6.13 Mars planetocentric
8.6.14 Mars planetographic
8.6.15 Maryland (US) state plane coordinate system
8.7.1 Introduction
8.7.2 Alabama (US) state plane coordinate system
8.7.3 GTRS global coordinate system (GCS)
8.7.4 Japan plane coordinate system
8.7.5 Lambert NTF
8.7.6 Universal polar stereographic
8.7.7 Universal transverse Mercator
8.7.8 Wisconsin (US) state plane coordinate system
9 Designated spatial surfaces and vertical offsets
9.1 Introduction
9.2 Designated spatial surface
9.5 Vertical offset height and elevation
9.6 Use of vertical offset height in spatial referencing
9.7 Other vertical measurements
9.8 Geoidal and equipotential DSS specifications
10.1 Introduction
10.3 Operations on ORMs
10.3.1 Introduction
10.3.2 ORMs for a single object
10.3.3 Relating ORMs for different objects
10.4 Operations to change spatial coordinates between SRFs
10.4.1 Introduction
10.4.2 Change coordinate SRF operation
10.4.3 The matched normal embeddings case
10.4.4 Map projection SRF and celestiodetic SRF with matched normal embeddings case
10.4.5 Linear orthonormal 3D SRF to linear orthonormal 3D SRF cases
10.4.6 Changing abstract space linear SRF coordinates to a linear SRF in the space of another object
10.5 Spatial directions and change SRF operations on directions
10.5.1 Introduction
10.5.2 Specification of direction
10.5.3 Changing the reference coordinate of a direction
10.5.4 Changing the SRF representation of a direction
10.6 Euclidean distance
10.7 Geodesic distance and azimuth on an oblate ellipsoid
10.7.1 Introduction
10.7.2 Geodesic distance
10.7.3 Geodetic azimuth
11 Application program interface
11.1 Introduction
11.2.1 Overview
11.2.2 Abbreviations
11.2.3 Numbers
11.2.4 Logicals
11.2.5 Object_Reference
11.2.6 Enumerated data types
11.2.7 Selection data types
11.2.8 Array types
11.2.9 Structured data types
11.3 Object classes
11.3.1 Introduction
11.3.2 Class specification format
11.3.3 LifeCycleObject
11.3.4 Private objects
11.3.5 Abstract classes
11.3.6 SRF concrete subclasses of BaseSRF2D
11.3.7 SRF concrete subclasses of BaseSRF3D
11.3.8 SRF concrete subclasses of BaseSRFwithTangentPlaneSurface
11.3.9 SRF concrete subclass of BaseSRFwithEllipsoidalHeight
11.3.10 SRF concrete subclasses of BaseSRFMapProjection
11.4 Standard SRFs
11.5 SRF set classes
11.6 Implementation support query functions
11.7 Object inheritance hierarchy
11.8 Method precedence for life cycle objects and examples
11.9.1 Introduction
11.9.2 SRFT_Parameters
11.9.3 SRFS_Info
11.9.4 SRF_Parameters_Info_Code
11.9.5 SRF_Parameters_Info
11.9.6 SRF_Reference_Surface_Info
11.9.7 Coordinate structures
11.9.8 Spatial_Coordinate_Code
11.9.9 Coordinate
11.9.10 RD_Code
11.9.11 OBRS_Code
12 Profiles
12.1 Introduction
12.3 Default profile
13 Registration
13.1 Introduction
13.2 Specification elements for SRM registered items
13.2.1 Introduction
13.2.2 Label
13.2.3 Code
13.2.4 Description
13.2.5 References
13.3 Guidelines for specific SRM concepts
13.3.1 Guidelines for registration of abstract CSs
13.3.2 Guidelines for registration of temporal CSs
13.3.3 Guidelines for registration of RDs
13.3.4 Guidelines for registration of ORMTs
13.3.5 Guidelines for registration of ORMs
13.3.6 Guidelines for registration of RTs
13.3.7 Guidelines for registration of OBRSs
13.3.8 Guidelines for registration of SRFTs
13.3.9 Guidelines for registration of SRFs
13.3.10 Guidelines for registration of SRF sets and their members
13.3.11 Guidelines for registration of DSSs
13.3.12 Guidelines for registration of profiles
14 Conformance
14.1 Introduction
14.2 Functional implementation conformance
14.3 Conformance of exchange formats
14.4 Conformance of language bindings of the SRM API
14.5 Conformance of applications that use the SRM API
14.6 Conformance of specifications that reference this International Standard
Annex A Mathematical foundations
A.1 Introduction
A.3 The point set topology of Rn
A.6.1 Implicit definition
A.6.2 Ellipsoid surfaces
A.7 Smooth curves in Rn
A.7.1 Parametric definition
A.7.2 Implicit definition
A.7.3 Arc length and geodesic distance
A.8.1 Double argument arctangent function
A.8.2 Jacobian elliptic functions
A.9.1 Geometric projection functions into a developable surface
A.9.2 Planar projection functions
A.9.3 Cylindrical projection function
A.9.4 Conic projection function
Annex B Implementation notes
B.1 Introduction
B.2.1 Finite precision
B.2.2 Computational efficiency
B.2.3 Approximation
B.3 Guidelines for algorithm development for spatial operations
B.3.1 Introduction
B.3.2 The computational environment
B.3.3 Domain of application
B.3.4 Define a meaningful error measure
B.3.5 Avoid excessive computational accuracy
B.3.6 Determine the acceptable error before starting
B.3.7 Mathematical approaches
B.3.8 Good programming and formulation practices
B.3.9 Design in context
B.3.10 Software verification and computational error testing
B.3.11 Singularities and near singularities
B.3.12 Performance testing
B.4 Spherical reference models
B.5.1 Distortion considerations
B.5.2 Validity checking
B.7 Time dependent reference transformation examples
B.7.1 Introduction
B.7.2 Notation and terminology
B.7.3 Earth equatorial inertial reference transformation
B.7.4 Solar ecliptic reference transformation
Annex C Hierarchical diagrams for SRM concepts
C.1 Introduction
Annex D RDs associated with physical objects
D.1 Introduction
D.2 RDs
Annex E ORM specifications
E.1 Introduction
E.2 ORMs
E.2.1 Reference ORMs
E.2.2 Standardized ORMs
Annex F Abbreviations and acronyms used in the construction of labels
F.1 Introduction
F.2 Tables
Annex G Change and deprecation plan
G.1 Introduction
G.2 Change
G.3 Deprecation
G.3.1 Introduction
G.3.2 Deprecation of SRM standardized concept instances
G.3.3 Deprecation of SRM registered items
G.4 Reinstatement
G.4.1 Introduction
G.4.2 Reinstatement of SRM standardized concept instances
G.4.3 Reinstatement of SRM registered items
Annex H Templates for registration proposals
H.1 Introduction
H.2 Proposal for the registration of a CS
H.3 Proposal for the registration of a temporal CS
H.4 Proposal for the registration of an RD
H.5 Proposal for the registration of an ORMT
H.6 Proposal for the registration of an ORM
H.7 Proposal for the registration of a reference transformation
H.8 Proposal for the registration of an OBRS
H.9 Proposal for the registration of an SRFT
H.10 Proposal for the registration of an SRF
H.11 Proposal for the registration of an SRF set
H.12 Proposal for the registration of an DSS
H.13 Proposal for the registration of a profile
Annex I Conformance testing for SRF operations
I.1 Introduction
I.3 Spatial reference frame operations baseline
I.4 Implementations
I.5 Fundamental measure of conformance
I.6 Error metrics for spatial reference frame operations
I.7 Computational error evaluated over test data sets
Annex J Deprecated SRM concept instances
J.1 Introduction
J.2 RDs
J.3 ORMs
J.4 DSSs
Tables
Table 3.1 — Mathematical notation
Table 3.2 — Symbols
Table 3.3 — Abbreviated terms
Table 4.1 — Coordinate system types
Table 5.1 — CS types
Table 5.2 — Localization operators
Table 5.3 — Localization inverse operators
Table 5.4 — Localized CS type relationships
Table 5.5 — Coordinate system specification elements
Table 5.6 — Common parameters and functions of an oblate ellipsoid
Table 5.7 — CS specification directory
Table 5.8 — Euclidean 3D CS
Table 5.9 — Lococentric Euclidean 3D CS
Table 5.10 — Spherical CS
Table 5.11 — Lococentric spherical CS
Table 5.12 — Azimuthal spherical CS
Table 5.13 — Lococentric azimuthal spherical CS
Table 5.14 — Geodetic 3D CS
Table 5.15 — Planetodetic CS
Table 5.16 — Cylindrical CS
Table 5.17 — Lococentric cylindrical CS
Table 5.18 — Mercator CS
Table 5.19 — Oblique Mercator spherical CS
Table 5.20 — Transverse Mercator CS
Table 5.21 — Lambert conformal conic CS
Table 5.22 — Polar stereographic CS
Table 5.23 — Equidistant cylindrical CS
Table 5.24 — Surface geodetic CS
Table 5.25 — Surface planetodetic CS
Table 5.26 — Lococentric surface Euclidean CS
Table 5.27 — Lococentric surface azimuthal CS
Table 5.28 — Lococentric surface polar CS
Table 5.29 — Euclidean 2D CS
Table 5.30 — Lococentric Euclidean 2D CS
Table 5.31 — Azimuthal CS
Table 5.32 — Lococentric azimuthal CS
Table 5.33 — Polar CS
Table 5.34 — Lococentric polar CS
Table 5.35 — Euclidean 1D CS
Table 6.1 — Temporal coordinate system specification elements
Table 6.2 — International atomic time (TAI)
Table 6.3 — Coordinated universal time (UTC)
Table 7.1 — RD categories
Table 7.2 — RD specification elements
Table 7.3 — RD specification directory
Table 7.4 — 2D RDs of category point
Table 7.5 — 3D RDs of category point
Table 7.6 — 2D RDs of category directed curve
Table 7.7 — 3D RDs of category directed curve
Table 7.8 — 3D RDs of category oriented surface
Table 7.9 — Physical object RD specification elements
Table 7.10 — Physical RD specification table locations
Table 7.11 — ORMT specification elements
Table 7.12 — ORMT specification directory
Table 7.13 — 2D ORMT specifications
Table 7.14 — 3D ORMT specifications
Table 7.15 — ORM specification elements
Table 7.16 — Reference transformation specification elements