SIST EN ISO 19107:2020

Geographic information - Spatial schema (ISO 19107:2019)

This document specifies conceptual schemas for describing the spatial characteristics of geographic entities, and a set of spatial operations consistent with these schemas. It treats "vector" geometry and topology. It defines standard spatial operations for use in access, query, management, processing and data exchange of geographic information for spatial (geometric and topological) objects. Because of the nature of geographic information, these geometric coordinate spaces will normally have up to three spatial dimensions, one temporal dimension and any number of other spatially dependent parameters as needed by the applications. In general, the topological dimension of the spatial projections of the geometric objects will be at most three.

Geoinformation - Raumbezugsschema (ISO 19107:2019)

Information géographique - Schéma spatial (ISO 19107:2019)

Le présent document spécifie les schémas conceptuels de description des caractéristiques spatiales des entités géographiques, ainsi qu'un jeu d'opérations spatiales cohérent avec ces schémas. Il traite de géométrie et de topologie vectorielle. Il définit des opérations spatiales normalisées destinées à être utilisées pour accéder aux informations géométriques sur des objets spatiaux (géométriques et topologiques), pour les interroger, les gérer, les traiter et les échanger. Du fait de la nature des informations géographiques, ces espaces de coordonnées géométriques ont normalement jusqu'à trois dimensions spatiales, une dimension temporelle et n'importe quel nombre d'autres paramètres de l'espace, selon les besoins des applications. En général, la dimension topologique des projections spatiales des objets géométriques sera de trois au maximum.

Geografske informacije - Prostorska shema (ISO 19107:2019)

Ta standard določa konceptualne sheme za opisovanje prostorskih značilnosti geografskih entitet in nabor prostorskih operacij, skladnih s temi shemami. Obravnava »vektorsko« geometrijo in topologijo. Opredeljuje standardne prostorske operacije za dostop, poizvedbe, upravljanje, obdelavo in izmenjavo podatkov geografskih informacij za prostorske (geometrijske in topološke) objekte. Zaradi narave geografskih informacij bodo ti geometrijski koordinatni prostori običajno imeli največ tri prostorske dimenzije, časovno dimenzijo in poljubno število drugih prostorsko odvisnih parametrov, odvisno od potreb predvidene uporabe. Na splošno so topološke dimenzije prostorskih projekcij geometrijskih objektov največ tri.

General Information

• Status: Published
• Publication Date: 23-Jan-2020
• ICS: 07.040 - Astronomy. Geodesy. Geography
• ICS: 35.240.70 - IT applications in science
• Technical Committee: GIG - Geographic information
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 06-Jan-2020
• Due Date: 12-Mar-2020
• Completion Date: 24-Jan-2020
• Ref Project: EN ISO 19107:2019 - Geographic information - Spatial schema (ISO 19107:2019)

Relations

• Replaces: SIST EN ISO 19107:2005 - Geographic information - Spatial schema (ISO 19107:2003)
• Effective Date: 01-Mar-2020

Overview

SIST EN ISO 19107:2020 (ISO 19107:2019) - Geographic information - Spatial schema - defines a conceptual spatial schema for describing the geometric and topological characteristics of geographic entities. The standard addresses vector geometry and topology, specifying standard spatial operations and data structures to support access, query, management, processing and data exchange of spatial objects. It is part of the ISO 19100 series for geographic information and supersedes the 2005 edition.

Key topics and technical requirements

• Conceptual schemas for geometry and topology: formal models for geometric primitives and topological relationships used in GIS and geodata systems.
• Coordinate systems and reference surfaces: support for geometric coordinate spaces (typically up to 3 spatial dimensions and one temporal dimension), including compound and homogeneous coordinate systems.
• Data types and interfaces: definitions such as DirectPosition, RSID, Envelope, GeometryData, and interfaces for Point, Curve, Surface, and higher-order constructs.
• Primitive and complex geometry: definitions and encodings for primitives (Point, Curve, Surface) and composite geometries, with interpolation and boundary semantics.
• Spatial operations and queries: standardized operations for 2D and 3D querying (e.g., spatial predicates, topological relations) and encoding/query interfaces (Query2D, Query3D).
• Conformance and profiles: conformance classes, requirement classes, and codelists to express vendor or application capabilities and geometry metrics (geodesy), interpolation schemes, and dimensionality limits.
• Modeling and documentation: use of UML notation, naming conventions and metadata roles to describe and exchange spatial schema definitions.

Practical applications and users

ISO 19107 is aimed at enabling interoperable spatial data models and services. Typical applications:

• GIS software design and data modeling (desktop, web, and mobile GIS)
• Spatial databases and spatial indexing implementations
• Web and enterprise geospatial services (WFS, WMS, APIs that serve vector data)
• Geospatial data exchange and cataloguing (data producers/consumers)
• Mapping, cadastral systems, utilities, transportation planning, environmental monitoring, urban planning, and remote sensing data integration

Primary users:

• GIS developers and architects
• Spatial data modelers and integrators
• National mapping agencies and cadastral authorities
• Software vendors and system implementers
• Standards bodies and metadata specialists

Related standards

• Part of the ISO 19100 series managed by ISO/TC 211 (geographic information/geomatics).
• This edition updates and replaces EN ISO 19107:2005; implementers should consider companion ISO 191xx standards for coordinate reference systems, metadata and encoding when designing interoperable geospatial solutions.

Keywords: ISO 19107, spatial schema, geographic information, vector geometry, topology, coordinate systems, GIS standards, spatial operations, spatial data exchange.

Standards Content (Sample)

SLOVENSKI STANDARD
01-marec-2020
Nadomešča:
SIST EN ISO 19107:2005
Geografske informacije - Prostorska shema (ISO 19107:2019)
Geographic information - Spatial schema (ISO 19107:2019)
Geoinformation - Raumbezugsschema (ISO 19107:2019)
Information géographique - Schéma spatial (ISO 19107:2019)
Ta slovenski standard je istoveten z: EN ISO 19107:2019
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.

EN ISO 19107
EUROPEAN STANDARD
NORME EUROPÉENNE
December 2019
EUROPÄISCHE NORM
ICS 35.240.70 Supersedes EN ISO 19107:2005
English Version
Geographic information - Spatial schema (ISO
19107:2019)
Information géographique - Schéma spatial (ISO Geoinformation - Raumbezugsschema (ISO
19107:2019) 19107:2019)
This European Standard was approved by CEN on 11 May 2019.

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 CEN-CENELEC Management Centre 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 CEN-CENELEC Management
Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2019 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 19107:2019 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 19107:2019) has been prepared by Technical Committee ISO/TC 211
"Geographic information/Geomatics" in collaboration with Technical Committee CEN/TC 287
“Geographic Information” the secretariat of which is held by BSI.
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 June 2020, and conflicting national standards shall be
withdrawn at the latest by June 2020.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 19107:2005.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the
United Kingdom.
Endorsement notice
The text of ISO 19107:2019 has been approved by CEN as EN ISO 19107:2019 without any modification.

INTERNATIONAL ISO
STANDARD 19107
Second edition
2019-12
Geographic information — Spatial
schema
Information géographique — Schéma spatial
Reference number
ISO 19107:2019(E)
©
ISO 2019
ISO 19107:2019(E)
© ISO 2019
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting
on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address
below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Fax: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii © ISO 2019 – All rights reserved

ISO 19107:2019(E)
Contents Page
Foreword .viii
Introduction .ix
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols, notation and abbreviated terms .17
4.1 Presentation and notation .17
4.1.1 Unified Modeling Language (UML) .17
4.1.2 Naming conventions .17
4.2 Organization .18
4.3 Abbreviated terms and symbols .18
5 Conformance .19
5.1 Requirements class conformance targets .19
5.1.1 Conformance targets .19
5.1.2 Geometry metrics (geodesy) .22
5.1.3 Topological dimensionality .22
5.1.4 Interpolation schemes .22
5.1.5 Structural complexity .23
5.1.6 Functional complexity .24
5.2 Conformance classes .24
5.3 Requirements classes .25
6 Coordinates and core geometry .26
6.1 Semantics .26
6.2 Requirements Class Coordinate .27
6.2.1 Codelists to specify capabilities .27
6.2.2 Coordinate systems for Geometry — Semantics .27
6.2.3 GeometricReferenceSurface .31
6.2.4 Interface ReferenceSystem .35
6.2.5 Codelist ReferenceSystemTypes .36
6.2.6 Interface CompoundReferenceSystem .36
6.2.7 Interface HomogeneousCoordinateSystem .37
6.2.8 Interface GeometricCoordinateSystem .37
6.2.9 Datatype DirectPosition.42
6.2.10 Union Datatype RSID .44
6.2.11 Codelist Axis .45
6.2.12 Role metadata: AxisDescription .45
6.2.13 Datatype Axis Description .45
6.2.14 Codelist SpatialAxis .45
6.2.15 Codelist SphericalAxis .45
6.2.16 Codelist TemporalAxis .45
6.2.17 Codelist ParametricAxis .46
6.2.18 Codelist Datum .46
6.2.19 Datatype Parameter .47
6.2.20 Datatype Permutation, Projection .47
6.2.21 Interface ReferenceDirection .48
6.2.22 Datatype Bearing .48
6.2.23 Codelist Rotation .50
6.2.24 Codelist RelativeDirection .50
6.2.25 Codelist FixedDirection .50
6.2.26 Codelist CurveRelativeDirection .50
6.2.27 Datatype Vector.51
6.2.28 Interface Envelope .52
ISO 19107:2019(E)
6.2.29 Engineering coordinate systems, Tangent spaces and local interpolations .53
6.3 Requirements Class Coordinate Data .53
6.4 Requirements Class Geometry .54
6.4.1 Semantics .54
6.4.2 Interface TransfiniteSetOfDirectPositions .55
6.4.3 CodeList: BoundaryType .55
6.4.4 Interface Geometry .56
6.4.5 Datatype GeometryData .70
6.4.6 CodeList: GeometryType .70
6.4.7 Interface Encoding .70
6.4.8 Interface Query2D .71
6.4.9 Interface Query3D .74
6.4.10 Interface Empty .75
6.4.11 Interface Primitive .76
6.4.12 Datatype PrimitiveData .77
6.4.13 Interface Point .78
6.4.14 Datatype PointData . .80
6.4.15 Interface Orientable .80
6.4.16 Datatype OrientableData .81
6.4.17 Datatype Knot .82
6.4.18 Interface Curve .83
6.4.19 DataType CurveData .93
6.4.20 Interface OffsetCurve .93
6.4.21 Datatype OffsetCurveData .94
6.4.22 Interface ProductCurve .94
6.4.23 ProductCurveData .96
6.4.24 CodeList: CurveInterpolation.96
6.4.25 Interface Surface .97
6.4.26 Datatype SurfaceData .101
6.4.27 CodeList: SurfaceInterpolation .101
6.4.28 Interface Solid .101
6.4.29 Datatype SolidData .104
6.4.30 CodeList: SolidInterpolation .104
6.4.31 Interface Collection .105
6.4.32 Role element: Geometry .106
6.4.33 DataType CollectionData .107
6.4.34 Interface Complex .107
6.4.35 Role Complex: generator: Primitive .110
6.4.36 Role Complex: superComplex and subComplex.110
6.5 Requirements Class Geometry Data .111
7 Interpolations for Curves .111
7.1 Requirements Class Line Curve .111
7.1.1 Semantics .111
7.1.2 Interface Line .111
7.1.3 DataType LineData . .113
7.2 Requirements Class Line Data .114
7.3 Requirements Class Geodesic Curve .114
7.3.1 Semantics .114
7.3.2 Interface Geodesic .115
7.3.3 DataType GeodesicData .115
7.4 Requirements Class Geodesic Curve Data .115
7.5 Requirements Class Rhumb .116
7.5.1 Interface Rhumb .116
7.5.2 DataType RhumbData .116
7.6 Requirements Class Rhumb Curve Data.117
7.7 Requirements Class Polynomial Curves .117
7.7.1 Semantics .117
7.7.2 Interface RealFunction . .118
iv © ISO 2019 – All rights reserved

ISO 19107:2019(E)
7.7.3 Interface FunctionArc .118
7.7.4 Association Role function .118
7.7.5 Interface FunctionCurve .119
7.7.6 Interface RealPolynomial.119
7.7.7 Interface PolynomialArc .120
7.7.8 Datatype PolynomialArcData .121
7.7.9 Interface PolynomialCurve .121
7.7.10 DataType PolynomialCurveData .121
7.8 Requirements Class Polynomial Curve Data .121
7.9 Requirements Class Conic Curves .122
7.9.1 Semantics .122
7.9.2 Interface Arc .123
7.9.3 Datatype ArcData .124
7.9.4 Interface Circle . .125
7.9.5 Interface Conic .125
7.9.6 Interface EllipticArc, Datatype EllipticArcData .128
7.10 Requirements Class Conic Curve Data .128
7.11 Requirements Class Spiral Curve .128
7.11.1 Semantics, Mathematical background: curves and curvature .128
7.11.2 Interface Spiral Curves . .134
7.11.3 Interface Clothoid Curve .136
7.11.4 Datatype SpiralData .136
7.12 Requirements Class Spiral Curve Data .136
7.13 Requirements Class Spline Curve .136
7.13.1 Semantics .136
7.13.2 CodeList: KnotType .137
7.13.3 CodeList: SplineCurveForm .138
7.13.4 Interface SplineCurve .138
7.13.5 Interface PolynomialSpline .141
7.13.6 Interface CubicSpline .142
7.13.7 Interface Bezier .143
7.13.8 Interface BSplineCurve (and NURBS) .144
7.13.9 DataType BsplineData .145
7.14 Requirements Class Spline Curve Data .145
8 Interpolations for Surfaces .145
8.1 Requirements Class Polygon Surface .145
8.1.1 Semantics .145
8.1.2 Interface Polygon .145
8.1.3 Datatype PolygonData .147
8.1.4 Interface PolyhedralSurface .147
8.1.5 Datatype PolyhedralSurfaceData .147
8.1.6 Interface Triangle .147
8.1.7 Datatype TriangleData .148
8.1.8 Interface TriangulatedSurface .148
8.1.9 Datatype TriangulatedSurfaceData . .148
8.2 Requirements Class Polygon Surface Data .148
8.3 Requirements Class Parametric Curve Surface .148
8.3.1 Semantics .148
8.3.2 Interface ParametricCurveSurface .149
8.3.3 Datatype ParametricCurveSurfaceData .152
8.3.4 Interface BilinearGrid .152
8.3.5 Extensions of ParametricCurveSurface .153
8.4 Requirements Class Parametric Curve Surface Data .153
8.5 Requirements Class Conic Surface .154
8.5.1 Semantics .154
8.5.2 Interface Sphere .154
8.5.3 Interface Cone .155
8.5.4 Interface Cylinder .155
ISO 19107:2019(E)
8.6 Requirements Class Conic Surface Data .155
8.7 Requirements Class Spline Surface .156
8.7.1 Semantics .156
8.7.2 Interface BSplineSurface (and NURBS) .156
8.7.3 Codelist BSplineSurfaceForm .158
8.8 Requirements Class Spline Surface Data .158
9 Interpolations for Solids .158
9.1 Requirements Class Boundary Representation Solid .158
9.2 Requirements Class Boundary Representation Solid Data .159
9.3 Requirements Class Parametric Curve Solid .159
9.3.1 Interface ParametricCurveSolid .159
9.3.2 Interface BSolidSpline .160
9.3.3 Other interpolations .161
9.4 Requirements Class Parametric Curve Solid Data .161
10 Topology .161
10.1 Requirements Class Topology root .161
10.1.1 Semantics .161
10.1.2 Interface Topology .162
10.1.3 Interface Primitive .166
10.1.4 Interface DirectedTopo .168
10.1.5 Datatype TopologyData .170
10.1.6 DataType PrimitiveData .171
10.1.7 DataType ComplexData .171
10.1.8 Datatype Expression .171
10.1.9 Datatype ExpressionTerm .174
10.2 Requirements Class Topology Root Data.174
10.3 Requirements Class Node .174
10.3.1 Semantics .174
10.3.2 Interface Node .174
10.3.3 Interface DirectedNode .175
10.4 Requirements Class Edge .175
10.4.1 Interface Edge.175
10.4.2 Interface DirectedEdge .176
10.5 Requirements Class Face .177
10.5.1 Semantics .177
10.5.2 Interface Face .177
10.5.3 Interface DirectedFace .178
10.6 Requirements Class Topology Solid .178
10.6.1 Interface Solid .178
10.6.2 Interface DirectedSolid .179
10.7 Requirements Class Topological Complex .179
10.7.1 Semantics .179
10.7.2 Interface Complex .179
10.8 Requirements Class Derived Topological Relations .182
10.8.1 Introduction .182
10.8.2 Canonical form for Geometry .183
10.8.3 Boundary operators for aggregate objects .183
10.8.4 Boolean or set operators .185
10.8.5 Egenhofer operators .186
10.8.6 Full topological operators .187
10.8.7 Combinations .190
11 Special Requirements Classes .190
11.1 Requirements Class Simplicial geometry .190
11.1.1 Semantics .190
11.1.2 Datatype Simplex .191
11.1.3 DataType SimplicialTerm .193
11.1.4 DataType::SimplicialPolynomial .193
vi © ISO 2019 – All rights reserved
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