ISO 19107:2003

Geographic information — Spatial schema

ISO 19107:2003 specifies conceptual schemas for describing the spatial characteristics of geographic features, and a set of spatial operations consistent with these schemas. It treats vector geometry and topology up to three dimensions. It defines standard spatial operations for use in access, query, management, processing, and data exchange of geographic information for spatial (geometric and topological) objects of up to three topological dimensions embedded in coordinate spaces of up to three axes.

Information géographique — Schéma spatial

Geografske informacije - Prostorska shema

General Information

• Status: Withdrawn
• Publication Date: 07-May-2003
• Withdrawal Date: 07-May-2003
• ICS: 35.240.70 - IT applications in science
• Technical Committee: ISO/TC 211 - Geographic information/Geomatics
• Drafting Committee: ISO/TC 211 - Geographic information/Geomatics
• Current Stage: 9599 - Withdrawal of International Standard
• Completion Date: 28-Oct-2019
• Ref Project: SIST ISO 19107:2003 - Geographic information -- Spatial schema

Relations

• Revised: ISO 19107:2019 - Geographic information — Spatial schema
• Effective Date: 01-Mar-2014

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 19107
First edition
2003-05-01

Geographic information — Spatial
schema
Information géographique — Schéma spatial




Reference number
ISO 19107:2003(E)
©
ISO 2003

---------------------- Page: 1 ----------------------
ISO 19107:2003(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.


©  ISO 2003
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail [e-mail]
Web www.iso.org
Published in Switzerland

ii © ISO 2003 — All rights reserved

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ISO 19107:2003(E)
Contents Page
Foreword. viii
Introduction . ix
1 Scope. 1
2 Conformance . 1
2.1 Overview . 1
2.2 Conformance classes. 3
3 Normative references . 4
4 Terms and definitions. 4
5 Symbols, notation and abbreviated terms . 14
5.1 Presentation and notation. 14
5.1.1 Unified Modeling Language (UML) concepts. 14
5.1.2 Attributes, operations, and associations . 14
5.1.3 Stereotypes. 17
5.1.4 Data types and collection types . 18
5.1.5 Strong substitutability. 19
5.2 Organization . 20
5.3 Abbreviated terms. 22
6 Geometry packages . 22
6.1 Semantics . 22
6.2 Geometry root package. 24
6.2.1 Semantics . 24
6.2.2 GM_Object . 25
6.3 Geometric primitive package. 32
6.3.1 Semantics . 32
6.3.2 GM_Boundary. 33
6.3.3 GM_ComplexBoundary . 34
6.3.4 GM_PrimitiveBoundary . 34
6.3.5 GM_CurveBoundary . 34
6.3.6 GM_Ring. 34
6.3.7 GM_SurfaceBoundary . 34
6.3.8 GM_Shell. 35
6.3.9 GM_SolidBoundary. 35
6.3.10 GM_Primitive . 35
6.3.11 GM_Point. 38
6.3.12 Bearing. 39
6.3.13 GM_OrientablePrimitive . 40
6.3.14 GM_OrientableCurve . 42
6.3.15 GM_OrientableSurface . 42
6.3.16 GM_Curve . 43
6.3.17 GM_Surface . 44
6.3.18 GM_Solid. 46
6.4 Coordinate geometry package . 47
6.4.1 DirectPosition. 47
6.4.2 GM_PointRef. 48
6.4.3 GM_Envelope . 48
6.4.4 TransfiniteSet . 49
6.4.5 GM_Position . 49
6.4.6 GM_PointArray, GMPointGrid. 49
6.4.7 GM_GenericCurve. 49
6.4.8 GM_CurveInterpolation . 53
© ISO 2003 — All rights reserved iii

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ISO 19107:2003(E)
6.4.9 GM_CurveSegment .54
6.4.10 GM_LineString.55
6.4.11 GM_LineSegment .56
6.4.12 GM_GeodesicString .57
6.4.13 GM_Geodesic.58
6.4.14 GM_ArcString .58
6.4.15 GM_Arc.60
6.4.16 GM_Circle.62
6.4.17 GM_ArcStringByBulge.62
6.4.18 GM_ArcByBulge .63
6.4.19 GM_Conic.64
6.4.20 GM_Placement.66
6.4.21 GM_AffinePlacement .67
6.4.22 GM_Clothoid .67
6.4.23 GM_OffsetCurve .68
6.4.24 GM_Knot.70
6.4.25 GM_KnotType .71
6.4.26 GM_SplineCurve.71
6.4.27 GM_PolynomialSpline.71
6.4.28 GM_CubicSpline.72
6.4.29 GM_SplineCurveForm.73
6.4.30 GM_BSplineCurve .73
6.4.31 GM_Bezier .74
6.4.32 GM_SurfaceInterpolation.75
6.4.33 GM_GenericSurface .75
6.4.34 GM_SurfacePatch.77
6.4.35 GM_PolyhedralSurface .78
6.4.36 GM_Polygon.78
6.4.37 GM_TriangulatedSurface.80
6.4.38 GM_Triangle.80
6.4.39 GM_Tin .81
6.4.40 GM_ParametricCurveSurface.82
6.4.41 GM_GriddedSurface.85
6.4.42 GM_Cone.86
6.4.43 GM_Cylinder .86
6.4.44 GM_Sphere.86
6.4.45 GM_BilinearGrid .87
6.4.46 GM_BicubicGrid .87
6.4.47 GM_BSplineSurfaceForm .87
6.4.48 GM_BSplineSurface .88
6.5 Geometric aggregate package.89
6.5.7 Semantics.89
6.5.8 GM_Aggregate.89
6.5.9 GM_MultiPrimitive .89
6.5.10 GM_MultiPoint .90
6.5.11 GM_MultiCurve .91
6.5.12 GM_MultiSurface .91
6.5.13 GM_MultiSolid.91
6.6 Geometric complex package.92
6.6.7 Semantics.92
6.6.8 GM_Complex.93
6.6.9 GM_Composite .94
6.6.10 GM_CompositePoint .95
6.6.11 GM_CompositeCurve.96
6.6.12 GM_CompositeSurface.97
6.6.13 GM_CompositeSolid .97
7 Topology packages.98
7.4 Semantics.98
7.5 Topology root package.100
iv © ISO 2003 — All rights reserved

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ISO 19107:2003(E)
7.5.1 Semantics . 100
7.5.2 TP_Object. 101
7.6 Topological primitive package . 105
7.6.1 Semantics . 105
7.6.2 TP_Boundary. 105
7.6.3 TP_ComplexBoundary. 105
7.6.4 TP_PrimitiveBoundary. 105
7.6.5 TP_EdgeBoundary . 106
7.6.6 TP_FaceBoundary. 107
7.6.7 TP_SolidBoundary . 107
7.6.8 TP_Ring. 107
7.6.9 TP_Shell . 107
7.6.10 TP_Primitive . 108
7.6.11 TP_DirectedTopo . 109
7.6.12 TP_Node. 112
7.6.13 TP_DirectedNode . 113
7.6.14 TP_Edge. 114
7.6.15 TP_DirectedEdge . 115
7.6.16 TP_Face. 115
7.6.17 TP_DirectedFace . 117
7.6.18 TP_Solid. 117
7.6.19 TP_DirectedSolid . 118
7.6.20 TP_Expression . 118
7.7 Topological complex package. 121
7.7.1 Semantics . 121
7.7.2 TP_Complex . 121
8 Derived topological relations. 123
8.1 Introduction . 123
8.2 Boolean or set operators. 124
8.2.1 Form of the Boolean operators . 124
8.2.2 Boolean Relate . 124
8.2.3 Relation to set operations. 125
8.3 Egenhofer operators. 125
8.3.1 Form of the Egenhofer operators. 125
8.3.2 Egenhofer relate. 125
8.3.3 Relation to set operations. 126
8.4 Full topological operators. 126
8.4.1 Form of the full topological operators . 126
8.4.2 Full topological relate . 126
8.5 Combinations . 126
Annex A (normative) Abstract test suite. 127
A.1 Geometric primitives . 127
A.2 Geometric complexes. 130
A.3 Topological complexes . 132
A.4 Topological complexes with geometric realization. 134
A.5 Boolean operators . 136
Annex B (informative) Conceptual organization of terms and definitions . 138
B.1 Introduction . 138
B.2 General terms . 138
B.3 Collections and related terms. 139
B.4 Modelling terms. 139
B.5 Positioning terms. 140
B.6 Geometric terms. 140
B.7 Topological terms . 143
B.8 Relationship of geometric and topological complexes . 146
Annex C (informative) Examples of spatial schema concepts . 148
C.1 Geometry. 148
© ISO 2003 — All rights reserved v

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ISO 19107:2003(E)
Annex D (informative) Examples for application schemata .154
D.1 Introduction.154
D.2 Simple Topology.154
D.3 Feature Topology .158
D.4 MiniTopo.159
Bibliography.165

Figures
Figure 1 — UML example association .16
Figure 2 — UML example package dependency.20
Figure 3 — Normative clause as UML package dependencies .21
Figure 4 — Geometry package: Class content and internal dependencies.23
Figure 5 — Geometry basic classes with specialization relations .24
Figure 6 — GM_Object.26
Figure 7 — GM_Boundary .33
Figure 8 — GM_Primitive .36
Figure 9 — GM_Point.38
Figure 10 — GM_OrientablePrimitive .
...

SLOVENSKI STANDARD
SIST ISO 19107:2003
01-november-2003
Geografske informacije - Prostorska shema
Geographic information -- Spatial schema
Information géographique -- Schéma spatial
Ta slovenski standard je istoveten z: ISO 19107:2003
ICS:
07.040 Astronomija. Geodezija. Astronomy. Geodesy.
Geografija Geography
35.240.70 Uporabniške rešitve IT v IT applications in science
znanosti
SIST ISO 19107:2003 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST ISO 19107:2003

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SIST ISO 19107:2003

INTERNATIONAL ISO
STANDARD 19107
First edition
2003-05-01

Geographic information — Spatial
schema
Information géographique — Schéma spatial




Reference number
ISO 19107:2003(E)
©
ISO 2003

---------------------- Page: 3 ----------------------

SIST ISO 19107:2003
ISO 19107:2003(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.


©  ISO 2003
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail [e-mail]
Web www.iso.org
Published in Switzerland

ii © ISO 2003 — All rights reserved

---------------------- Page: 4 ----------------------

SIST ISO 19107:2003
ISO 19107:2003(E)
Contents Page
Foreword. viii
Introduction . ix
1 Scope. 1
2 Conformance . 1
2.1 Overview . 1
2.2 Conformance classes. 3
3 Normative references . 4
4 Terms and definitions. 4
5 Symbols, notation and abbreviated terms . 14
5.1 Presentation and notation. 14
5.1.1 Unified Modeling Language (UML) concepts. 14
5.1.2 Attributes, operations, and associations . 14
5.1.3 Stereotypes. 17
5.1.4 Data types and collection types . 18
5.1.5 Strong substitutability. 19
5.2 Organization . 20
5.3 Abbreviated terms. 22
6 Geometry packages . 22
6.1 Semantics . 22
6.2 Geometry root package. 24
6.2.1 Semantics . 24
6.2.2 GM_Object . 25
6.3 Geometric primitive package. 32
6.3.1 Semantics . 32
6.3.2 GM_Boundary. 33
6.3.3 GM_ComplexBoundary . 34
6.3.4 GM_PrimitiveBoundary . 34
6.3.5 GM_CurveBoundary . 34
6.3.6 GM_Ring. 34
6.3.7 GM_SurfaceBoundary . 34
6.3.8 GM_Shell. 35
6.3.9 GM_SolidBoundary. 35
6.3.10 GM_Primitive . 35
6.3.11 GM_Point. 38
6.3.12 Bearing. 39
6.3.13 GM_OrientablePrimitive . 40
6.3.14 GM_OrientableCurve . 42
6.3.15 GM_OrientableSurface . 42
6.3.16 GM_Curve . 43
6.3.17 GM_Surface . 44
6.3.18 GM_Solid. 46
6.4 Coordinate geometry package . 47
6.4.1 DirectPosition. 47
6.4.2 GM_PointRef. 48
6.4.3 GM_Envelope . 48
6.4.4 TransfiniteSet . 49
6.4.5 GM_Position . 49
6.4.6 GM_PointArray, GMPointGrid. 49
6.4.7 GM_GenericCurve. 49
6.4.8 GM_CurveInterpolation . 53
© ISO 2003 — All rights reserved iii

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SIST ISO 19107:2003
ISO 19107:2003(E)
6.4.9 GM_CurveSegment .54
6.4.10 GM_LineString.55
6.4.11 GM_LineSegment .56
6.4.12 GM_GeodesicString .57
6.4.13 GM_Geodesic.58
6.4.14 GM_ArcString .58
6.4.15 GM_Arc.60
6.4.16 GM_Circle.62
6.4.17 GM_ArcStringByBulge.62
6.4.18 GM_ArcByBulge .63
6.4.19 GM_Conic.64
6.4.20 GM_Placement.66
6.4.21 GM_AffinePlacement .67
6.4.22 GM_Clothoid .67
6.4.23 GM_OffsetCurve .68
6.4.24 GM_Knot.70
6.4.25 GM_KnotType .71
6.4.26 GM_SplineCurve.71
6.4.27 GM_PolynomialSpline.71
6.4.28 GM_CubicSpline.72
6.4.29 GM_SplineCurveForm.73
6.4.30 GM_BSplineCurve .73
6.4.31 GM_Bezier .74
6.4.32 GM_SurfaceInterpolation.75
6.4.33 GM_GenericSurface .75
6.4.34 GM_SurfacePatch.77
6.4.35 GM_PolyhedralSurface .78
6.4.36 GM_Polygon.78
6.4.37 GM_TriangulatedSurface.80
6.4.38 GM_Triangle.80
6.4.39 GM_Tin .81
6.4.40 GM_ParametricCurveSurface.82
6.4.41 GM_GriddedSurface.85
6.4.42 GM_Cone.86
6.4.43 GM_Cylinder .86
6.4.44 GM_Sphere.86
6.4.45 GM_BilinearGrid .87
6.4.46 GM_BicubicGrid .87
6.4.47 GM_BSplineSurfaceForm .87
6.4.48 GM_BSplineSurface .88
6.5 Geometric aggregate package.89
6.5.7 Semantics.89
6.5.8 GM_Aggregate.89
6.5.9 GM_MultiPrimitive .89
6.5.10 GM_MultiPoint .90
6.5.11 GM_MultiCurve .91
6.5.12 GM_MultiSurface .91
6.5.13 GM_MultiSolid.91
6.6 Geometric complex package.92
6.6.7 Semantics.92
6.6.8 GM_Complex.93
6.6.9 GM_Composite .94
6.6.10 GM_CompositePoint .95
6.6.11 GM_CompositeCurve.96
6.6.12 GM_CompositeSurface.97
6.6.13 GM_CompositeSolid .97
7 Topology packages.98
7.4 Semantics.98
7.5 Topology root package.100
iv © ISO 2003 — All rights reserved

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SIST ISO 19107:2003
ISO 19107:2003(E)
7.5.1 Semantics . 100
7.5.2 TP_Object. 101
7.6 Topological primitive package . 105
7.6.1 Semantics . 105
7.6.2 TP_Boundary. 105
7.6.3 TP_ComplexBoundary. 105
7.6.4 TP_PrimitiveBoundary. 105
7.6.5 TP_EdgeBoundary . 106
7.6.6 TP_FaceBoundary. 107
7.6.7 TP_SolidBoundary . 107
7.6.8 TP_Ring. 107
7.6.9 TP_Shell . 107
7.6.10 TP_Primitive . 108
7.6.11 TP_DirectedTopo . 109
7.6.12 TP_Node. 112
7.6.13 TP_DirectedNode . 113
7.6.14 TP_Edge. 114
7.6.15 TP_DirectedEdge . 115
7.6.16 TP_Face. 115
7.6.17 TP_DirectedFace . 117
7.6.18 TP_Solid. 117
7.6.19 TP_DirectedSolid . 118
7.6.20 TP_Expression . 118
7.7 Topological complex package. 121
7.7.1 Semantics . 121
7.7.2 TP_Complex . 121
8 Derived topological relations. 123
8.1 Introduction . 123
8.2 Boolean or set operators. 124
8.2.1 Form of the Boolean operators . 124
8.2.2 Boolean Relate . 124
8.2.3 Relation to set operations. 125
8.3 Egenhofer operators. 125
8.3.1 Form of the Egenhofer operators. 125
8.3.2 Egenhofer relate. 125
8.3.3 Relation to set operations. 126
8.4 Full topological operators. 126
8.4.1 Form of the full topological operators . 126
8.4.2 Full topological relate . 126
8.5 Combinations . 126
Annex A (normative) Abstract test suite. 127
A.1 Geometric primitives . 127
A.2 Geometric complexes. 130
A.3 Topological complexes . 132
A.4 Topological complexes with geometric realization. 134
A.5 Boolean operators . 136
Annex B (informative) Conceptual organization of terms and definitions . 138
B.1 Introduction . 138
B.2 General terms . 138
B.3 Collections and related terms. 139
B.4 Modelling terms. 139
B.5 Positioning terms. 140
B.6 Geometric terms. 140
B.7 Topological terms . 143
B.8 Relationship of geometric and topological complexes . 146
Annex C (informative) Examples of spatial schema concepts . 148
C.1 Geometry. 148
© ISO 2003 — All rights reserved v

---------------------- Page: 7 ----------------------

SIST ISO 19107:2003
ISO 19107:2003(E)
Annex D (informative) Examples for application schemata .154
D.1 Introduction.154
D.2 Simple Topology.154
D.3 Feature Topology .158
D.4 MiniTopo.159
Bibliography.165

Figures
Figure 1 — UML example association .16
Figure 2 — UML example package dependency.20
Figure 3 — Normative clause as UML package dependencies .21
Figure 4 — Geometry package: Class content and internal dependencies.23
Figure 5 — Geometry basic classes with specialization relations .
...