Information technology —
Spatial Reference Model (SRM)

 

Contents


                Foreword

 

0              Introduction

 

1              Scope

 

2              Normative references

 

3              Terms, definitions, symbols, and abbreviated terms

3.1           Terms and definitions

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

4.5           Object reference models

4.6           Coordinate systems

4.6.1        Abstract coordinate systems

4.6.2        Temporal coordinate systems

4.6.3        Spatial coordinate systems

4.7           Spatial reference frames

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              Abstract coordinate systems

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           CS specifications

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             Temporal coordinate systems

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          Object reference model

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            Spatial reference frames

8.1         Introduction

8.2         Spatial coordinate systems

8.3         Spatial reference frame

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         Standardized SRFs

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         Standardized SRF sets

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

9.3         Vertical offset surface

9.4         Geoidal separation

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          SRF operations

10.1       Introduction

10.2       Notation and terminology

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       Non-object data types

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       Data storage structures

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

12.2      Profile specification

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.2      Rn as a real vector space

A.3      The point set topology of Rn

A.4      Smooth functions on Rn

A.5      Functional composition

A.6      Smooth surfaces in R3

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      Special functions

A.8.1   Double argument arctangent function

A.8.2   Jacobian elliptic functions

A.9      Projection function

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      General observations

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      Practical considerations

B.5.1   Distortion considerations

B.5.2   Validity checking

B.6      The Bursa-Wolfe equation

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

C.2      Hierarchical diagrams

 

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.2       Computational error

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

I.8       Level of conformance

 

Annex J    Deprecated SRM concept instances

J.1      Introduction

J.2      RDs

J.3      ORMs

J.4      DSSs

 

          Bibliography

 

          Index


 

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