EN ISO 19107:2005

SLOVENSKI STANDARD
01-april-2005
Geografske informacije - Prostorska shema (ISO 19107:2003)
Geographic information - Spatial schema (ISO 19107:2003)
Geoinformation - Raumbezugsschema
Information géographique - Schéma spatial (ISO 19107:2003)
Ta slovenski standard je istoveten z: EN ISO 19107:2005
ICS:
07.040 Astronomija. Geodezija. Astronomy. Geodesy.
Geografija Geography
35.240.70 Uporabniške rešitve IT v IT applications in science
znanosti
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 19107
NORME EUROPÉENNE
EUROPÄISCHE NORM
January 2005
ICS 35.240.70
English version
Geographic information - Spatial schema (ISO 19107:2003)
Information géographique - Schéma spatial (ISO Geoinformation - Raumbezugsschema
19107:2003)
This European Standard was approved by CEN on 24 December 2004.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the Central Secretariat or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the official
versions.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia,
Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
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EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2005 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 19107:2005: E
worldwide for CEN national Members.

Foreword
The text of ISO 19107:2003 has been prepared by Technical Committee ISO/TC 211
"Geographic information/Geomatics” of the International Organization for Standardization (ISO)
and has been taken over as EN ISO 19107:2005 by Technical Committee CEN/TC 287
"Geographic Information", the secretariat of which is held by NEN.

This European Standard shall be given the status of a national standard, either by publication of
an identical text or by endorsement, at the latest by July 2005, and conflicting national standards
shall be withdrawn at the latest by July 2005.

According to the CEN/CENELEC Internal Regulations, the national standards organizations of
the following countries are bound to implement this European Standard: Austria, Belgium,
Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary,
Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland,
Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.

Endorsement notice
The text of ISO 19107:2003 has been approved by CEN as EN ISO 19107:2005 without any
modifications.
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
ISO 19107:2003(E)
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ii © ISO 2003 — All rights reserved

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 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

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 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 .41
Figure 11 — GM_Curve .43
Figure 12 — GM_Surface.45
Figure 13 — GM_Solid.46
Figure 14 — DirectPosition .48
Figure 15 — Curve segment classes .50
Figure 16 — Linear, arc and geodesic interpolation .56
Figure 17 — Arcs.59
Figure 18 — Conics and placements .65
Figure 19 — Spline and specialty curves.69
Figure 20 — Surface patches.76
Figure 21 — Polygonal surface.79
Figure 22 — TIN construction .81
Figure 23 — GM_ParametricCurveSurface and its subtypes .83
Figure 24 — GM_Aggregate .90
Figure 25 — GM_Complex.94
Figure 26 — GM_Composite.95
Figure 27 — GM_CompositePoint .96
Figure 28 — GM_CompositeCurve.96
Figure 29 — GM_CompositeSurface .97
Figure 30 — GM_CompositeSolid.98
Figure 31 — Topology packages, class content and internal dependencies.99
Figure 32 — Topological class diagram .100
Figure 33 — Relation between geometry and topology.101
Figure 34 — TP_Object.102
Figure 35 — Boundary and coboundary operation represented as associations .103
Figure 36 — Important classes in topology.104
Figure 37 — Boundary relation data types.106
Figure 38 — TP_Primitive .108
Figure 39 — TP_DirectedTopo subclasses.110
Figure 40 — TP_DirectedTopo .110
vi © ISO 2003 — All rights reserved

ISO 19107:2003(E)
Figure 41 — TP_Node . 113
Figure 42 — TP_Edge . 114
Figure 43 — TP_Face. 116
Figure 44 — TP_Solid. 117
Figure 45 — TP_Expression. 119
Figure 46 — TP_Complex. 122
Figure C.1 — A data set composed of the GM_Primitives . 149
Figure C.2 — Simple cartographic representation of sample data. 151
Figure C.3 — A 3D Geometric object with labeled coordinates. 152
Figure C.4 — Surface example. 153
Figure D.1 — Packages and classes for simple topology . 155
Figure D.2 — Topology and geometry classes in simple topology. 156
Figure D.3 — Feature components in simple topology. 157
Figure D.4 — Theme based feature topology. 159
Figure D.5 — Geometric example of MiniTopo topology structure. 160
Figure D.6 — MiniTopo . 161
Figure D.7 — Classic MiniTopo record illustration. 163
Tables
Table 1 — Conformance classes for geometric primitives . 3
Table 2 — Conformance classes for geometric complexes . 3
Table 3 — Conformance classes for topological complexes . 3
Table 4 — Conformance classes for topological complexes with geometric realizations . 3
Table 5 — Conformance classes for Boolean operators . 3
Table 6 — Package and classes. 21
Table 7 — Various types of parametric curve surfaces . 84
Table 8 — Meaning of Boolean intersection pattern matrix. 124
Table 9 — Meaning of Egenhofer intersection pattern matrix . 125
Table 10 — Meaning of full topological intersection pattern matrix . 126
Table D.1 — Correspondence between original MiniTopo pointers and the current model. 164

ISO 19107:2003(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 19107 was prepared by Technical Committee ISO/TC 211, Geographic information/Geomatics.
viii © ISO 2003 — All rights reserved

ISO 19107:2003(E)
Introduction
This International Standard provides conceptual schemas for describing and manipulating the spatial
characteristics of geographic features. Standardization in this area will be the cornerstone for other
geographic information standards.
A feature is an abstraction of a real world phenomenon; it is a geographic feature if it is associated with a
location relative to the Earth. Vector data consists of geometric and topological primitives used, separately or
in combination, to construct objects that express the spatial characteristics of geographic features. Raster
data is based on the division of the extent covered into small units according to a tessellation of the space and
the assignment to each unit of an attribute value. This International Standard
...