1、Adopted by INCITS (InterNational Committee for Information Technology Standards) as an American National Standard.Date of ANSI Approval: 12/24/2003Published by American National Standards Institute,25 West 43rd Street, New York, New York 10036Copyright 2003 by Information Technology Industry Council
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4、 19107:2003(E)ISO 2003INTERNATIONAL STANDARD ISO19107First edition2003-05-01Geographic information Spatial schema Information gographique Schma spatial ISO 19107:2003(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobes licensing policy, this file may be printed
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9、copyrightiso.org Web www.iso.org Published in Switzerland ii ISO 2003 All rights reservedISO 19107:2003(E) ISO 2003 All rights reserved iiiContents 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 defin
10、itions. 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 Organiza
11、tion 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
12、. 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.
13、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) iv ISO 2003 All rights r
14、eserved6.4.9 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_ArcStringByBulge62 6.4.18 GM_ArcByBulge 63 6.4.19 GM_Conic.64 6.4.20 GM_Placement.66 6.4.21 GM_Aff
15、inePlacement 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_SplineCurve71 6.4.27 GM_PolynomialSpline.71 6.4.28 GM_CubicSpline72 6.4.29 GM_SplineCurveForm.73 6.4.30 GM_BSplineCurve .73 6.4.31 GM_Bezier 74 6.4.32 GM_SurfaceInterpolation75 6.4.33 GM_
16、GenericSurface 75 6.4.34 GM_SurfacePatch77 6.4.35 GM_PolyhedralSurface .78 6.4.36 GM_Polygon.78 6.4.37 GM_TriangulatedSurface80 6.4.38 GM_Triangle.80 6.4.39 GM_Tin .81 6.4.40 GM_ParametricCurveSurface.82 6.4.41 GM_GriddedSurface85 6.4.42 GM_Cone86 6.4.43 GM_Cylinder 86 6.4.44 GM_Sphere.86 6.4.45 GM_
17、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_MultiSo
18、lid91 6.6 Geometric complex package92 6.6.7 Semantics.92 6.6.8 GM_Complex93 6.6.9 GM_Composite 94 6.6.10 GM_CompositePoint .95 6.6.11 GM_CompositeCurve96 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 ISO 19107:2003(E)
19、 ISO 2003 All rights reserved v7.5.1 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 T
20、P_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
21、.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. 1
22、25 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 Ge
23、ometric 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 Collecti
24、ons 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) vi ISO 2003 Al
25、l rights reservedAnnex D (informative) Examples for application schemata .154 D.1 Introduction154 D.2 Simple Topology154 D.3 Feature Topology 158 D.4 MiniTopo.159 Bibliography165 Figures Figure 1 UML example association .16 Figure 2 UML example package dependency .20 Figure 3 Normative clause as UML
26、 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 1
27、1 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 Arcs59 Figure 18 Conics and placements .65 Figure 19 Spline and specialty curves.69 Figure 20 Surface patches.76
28、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_Composite95 Figure 27 GM_CompositePoint .96 Figure 28 GM_CompositeCurve 96 Figure 29 GM_CompositeSurface .97 Figure 30 G
29、M_CompositeSolid98 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_Object102 Figure 35 Boundary and coboundary operation represented as associations 103 Figure 36 Import
30、ant classes in topology104 Figure 37 Boundary relation data types.106 Figure 38 TP_Primitive 108 Figure 39 TP_DirectedTopo subclasses110 Figure 40 TP_DirectedTopo 110 ISO 19107:2003(E) ISO 2003 All rights reserved viiFigure 41 TP_Node . 113 Figure 42 TP_Edge . 114 Figure 43 TP_Face 116 Figure 44 TP_
31、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 an
32、d 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 Clas
33、sic 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 Ta
34、ble 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 i
35、ntersection pattern matrix . 126 Table D.1 Correspondence between original MiniTopo pointers and the current model 164 ISO 19107:2003(E) viii ISO 2003 All rights reservedForeword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO memb
36、er 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, government
37、al 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 Direct
38、ives, 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 bodie
39、s 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/Ge
40、omatics. ISO 19107:2003(E) ISO 2003 All rights reserved ixIntroduction 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 sta
41、ndards. 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 charact
42、eristics 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 deals only with vector data. In the model defined in this Internati
43、onal Standard, spatial characteristics are described by one or more spatial attributes whose value is given by a geometric object (GM_Object) or a topological object (TP_Object). Geometry provides the means for the quantitative description, by means of coordinates and mathematical functions, of the
44、spatial characteristics of features, including dimension, position, size, shape, and orientation. The mathematical functions used for describing the geometry of an object depend on the type of coordinate reference system used to define the spatial position. Geometry is the only aspect of geographic
45、information that changes when the information is transformed from one geodetic reference system or coordinate system to another. Topology deals with the characteristics of geometric figures that remain invariant if the space is deformed elastically and continuously for example, when geographic data
46、is transformed from one coordinate system to another. Within the context of geographic information, topology is commonly used to describe the connectivity of an n-dimensional graph, a property that is invariant under continuous transformation of the graph. Computational topology provides information
47、 about the connectivity of geometric primitives that can be derived from the underlying geometry. Spatial operators are functions and procedures that use, query, create, modify, or delete spatial objects. This International Standard defines the taxonomy of these operators in order to create a standa
48、rd for their definition and implementation. The goals are to: a) Define spatial operators unambiguously, so that diverse implementations can be assured to yield comparable results within known limitations of accuracy and resolution. b) Use these definitions to define a set of standard operations tha
49、t will form the basis of compliant systems, and, thus act as a test-bed for implementers and a benchmark set for validation of compliance. c) Define an operator algebra that will allow combinations of the base operators to be used predictably in the query and manipulation of geographic data. Standardized conceptual schemas for spatial characteristics will increase the ability to share geographic information amo
