Standard
Track updates
AS/NZS ISO 19107:2020
[Current]Geographic information — Spatial schema
This Standard adopts ISO 19107:2019 which 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.
Published: 17/04/2020
Pages: 224
Table of contents
Cited references
Content history
Table of contents
Header
About this publication
Preface
Foreword
Introduction
1 Scope
2 Normative references
3 Terms and definitions
4 Symbols, notation and abbreviated terms
4.1 Presentation and notation
4.1.1 Unified Modeling Language (UML)
4.1.2 Naming conventions
4.2 Organization
4.3 Abbreviated terms and symbols
5 Conformance
5.1 Requirements class conformance targets
5.1.1 Conformance targets
5.1.2 Geometry metrics (geodesy)
5.1.3 Topological dimensionality
5.1.4 Interpolation schemes
5.1.5 Structural complexity
5.1.6 Functional complexity
5.2 Conformance classes
5.3 Requirements classes
6 Coordinates and core geometry
6.1 Semantics
6.2 Requirements Class Coordinate
6.2.1 Codelists to specify capabilities
6.2.2 Coordinate systems for Geometry — Semantics
6.2.2.1 Coordinates, points and locations
6.2.2.2 Coordinate systems
6.2.2.3 Metrics and distance measures
6.2.2.4 Underlying geometric space
6.2.3 GeometricReferenceSurface
6.2.3.1 Interface GeometricReferenceSurface
6.2.3.2 CodeList: GeometricSurfaceType
6.2.3.3 Interface PlaneMap
6.2.3.4 Interface Sphere
6.2.3.5 Interface Ellipsoid
6.2.3.6 Interface GeoSurface
6.2.3.7 Interface Geoid
6.2.4 Interface ReferenceSystem
6.2.4.1 Semantics
6.2.4.2 Attribute id
6.2.4.3 Attribute rsid
6.2.4.4 ttribute dimension
6.2.4.5 Attribute axis
6.2.4.6 Attribute datum
6.2.4.7 Role parameter
6.2.5 Codelist ReferenceSystemTypes
6.2.6 Interface CompoundReferenceSystem
6.2.6.1 Semantics
6.2.6.2 Role projection
6.2.6.3 Attribute rsid
6.2.7 Interface HomogeneousCoordinateSystem
6.2.8 Interface GeometricCoordinateSystem
6.2.8.1 Semantics
6.2.8.2 Attribute name
6.2.8.3 Attribute spatialDimension
6.2.8.4 Attribute temporalDimension
6.2.8.5 Attribute parmetricDimension
6.2.8.6 Attribute permutation
6.2.8.7 Attribute spatialProjection
6.2.8.8 Attribute temporalProjection
6.2.8.9 Operation: csDistance
6.2.8.10 Operation: distance
6.2.8.11 Operation: pointAtDistance
6.2.8.12 Operation: geoLocate
6.2.8.13 Operation: bearing
6.2.8.14 Operation: csInnerProduct
6.2.9 Datatype DirectPosition
6.2.9.1 Semantics
6.2.9.2 Attribute rsid
6.2.9.3 Attribute dimension
6.2.9.4 Attribute coordinate
6.2.9.5 Derived Role referenceSystem
6.2.9.6 Operation: spatialProjection
6.2.9.7 Operation: pointProjection
6.2.9.8 Operations derivable from Point by type coercion
6.2.9.8.1 Semantics
6.2.9.8.2 Operation: vectorToPoint (toPoint: DirectPosition): Vector
6.2.9.8.3 Operation: pointAtDistance (bearing: Vector): DirectPosition
6.2.10 Union Datatype RSID
6.2.11 Codelist Axis
6.2.12 Role metadata: AxisDescription
6.2.13 Datatype Axis Description
6.2.14 Codelist SpatialAxis
6.2.15 Codelist SphericalAxis
6.2.16 Codelist TemporalAxis
6.2.17 Codelist ParametricAxis
6.2.18 Codelist Datum
6.2.19 Datatype Parameter
6.2.19.1 Semantics
6.2.19.2 Attribute name
6.2.19.3 Attribute value
6.2.20 Datatype Permutation, Projection
6.2.20.1 Semantics
6.2.20.2 Attribute outOrder
6.2.20.3 Attribute axis
6.2.21 Interface ReferenceDirection
6.2.22 Datatype Bearing
6.2.22.1 Semantics
6.2.22.2 Attribute angle
6.2.22.3 Attribute direction
6.2.22.4 Attribute reference: ReferenceDirection
6.2.22.5 Attribute rotation: Rotation
6.2.22.6 Constructor: bearing
6.2.23 Codelist Rotation
6.2.24 Codelist RelativeDirection
6.2.25 Codelist FixedDirection
6.2.26 Codelist CurveRelativeDirection
6.2.27 Datatype Vector
6.2.27.1 Semantics
6.2.27.2 Attribute origin
6.2.27.3 Attribute offset
6.2.27.4 Attribute dimension
6.2.27.5 Attribute coordinateSystem
6.2.27.6 Operations: CrossProduct, DotProduct
6.2.28 Interface Envelope
6.2.28.1 Semantics
6.2.28.2 Attribute upperCorner
6.2.28.3 Attribute lowerCorner
6.2.29 Engineering coordinate systems, Tangent spaces and local interpolations
6.3 Requirements Class Coordinate Data
6.4 Requirements Class Geometry
6.4.1 Semantics
6.4.2 Interface TransfiniteSetOfDirectPositions
6.4.3 CodeList: BoundaryType
6.4.4 Interface Geometry
6.4.4.1 Semantics
6.4.4.2 Attribute isEmpty
6.4.4.3 Attribute asBinary
6.4.4.4 Attribute asGML: XML
6.4.4.5 Attribute asText: CharacterString
6.4.4.6 Attribute asData: GeometryData
6.4.4.7 Attribute boundary: Geometry
6.4.4.8 Attribute centroid
6.4.4.9 Attribute closure
6.4.4.10 Attribute convexHull
6.4.4.11 Attribute coordinateDimension
6.4.4.12 Attribute envelope
6.4.4.13 Attribute is3D: Boolean
6.4.4.14 Attribute isCycle
6.4.4.15 Attribute isSimple
6.4.4.16 Attribute isValid
6.4.4.17 Attribute maximalComplex
6.4.4.18 Attribute metadata: URI[0..*]
6.4.4.19 Attribute representativePoint: DirectPosition
6.4.4.20 Attribute rsid: RSID [1..*]
6.4.4.21 Attribute spatialDimension: Integer
6.4.4.22 Attribute topologicalDimension: Integer
6.4.4.23 Attribute type: GeometryType [1..*]
6.4.4.24 Operation buffer (radius: Distance): Geometry
6.4.4.25 Operation: dimension (point: DirectPosition = NULL): Integer
6.4.4.26 Operation: distance
6.4.4.27 Operation equal
6.4.4.28 Operation transform
6.4.4.29 Constructors Geometry
6.4.4.30 Operations from TransfiniteSet realization
6.4.5 Datatype GeometryData
6.4.6 CodeList: GeometryType
6.4.7 Interface Encoding
6.4.8 Interface Query2D
6.4.8.1 Semantics
6.4.8.2 Operation: distance
6.4.8.3 Operation: buffer (distance: Distance): Geometry
6.4.8.4 Set operation: intersection
6.4.8.5 Set operation: difference
6.4.8.6 Set operation: symDifference
6.4.8.7 Set operation: union
6.4.8.8 Map query operations
6.4.9 Interface Query3D
6.4.10 Interface Empty
6.4.11 Interface Primitive
6.4.11.1 Semantics
6.4.11.2 Association: Role segment
6.4.12 Datatype PrimitiveData
6.4.13 Interface Point
6.4.13.1 Semantics
6.4.13.2 Attribute position: DirectPosition
6.4.13.3 Attribute boundary: Geometry = Empty
6.4.13.4 Operation: vectorToPoint (toPoint: DirectPosition): Vector
6.4.13.5 Operation: Bearing (toPoint: DirectPosition): Bearing
6.4.13.6 Operation: pointAtDistance (bearing: Vector): DirectPosition
6.4.13.7 Constructor: Point (pt: DirectPosition): PointConstructor: Point (data: PointData): Point
6.4.14 Datatype PointData
6.4.15 Interface Orientable
6.4.15.1 Semantics
6.4.15.2 Attribute orientation: sign
6.4.15.3 Association Roles: proxy and primitive operation reverse (): Orientable
6.4.16 Datatype OrientableData
6.4.17 Datatype Knot
6.4.17.1 Semantics
6.4.17.2 Attribute value: Real
6.4.17.3 Attribute multiplicity: Integer
6.4.18 Interface Curve
6.4.18.1 Semantics
6.4.18.2 Attribute controlPoint
6.4.18.3 Attribute dataPoint
6.4.18.4 Attribute knot
6.4.18.5 Attribute interpolation
6.4.18.6 Attribute startPoint
6.4.18.7 Attribute endPoint
6.4.18.8 Attribute isRing
6.4.18.9 Attribute length
6.4.18.10 Attribute numDerivativesInterior
6.4.18.11 Attribute numDerivativesStart
6.4.18.12 Attribute numDerivativesEnd
6.4.18.13 Attribute startParam, endParam
6.4.18.14 Attribute reverse
6.4.18.15 Attribute startConstrParam, endConstrParam
6.4.18.16 Attribute boundary
6.4.18.17 Operation asLine
6.4.18.18 Operation constrParam
6.4.18.19 Operations length
6.4.18.20 Operation param
6.4.18.21 Operation paramForPoint
6.4.18.22 Operation tangent
6.4.19 DataType CurveData
6.4.20 Interface OffsetCurve
6.4.20.1 Semantics
6.4.20.2 Attribute distance: Length
6.4.20.3 Attribute refDirection
6.4.20.4 Association role: baseCurve: Curve
6.4.21 Datatype OffsetCurveData
6.4.22 Interface ProductCurve
6.4.22.1 Semantics
6.4.22.2 Attribute parameterRange: Interval
6.4.22.3 Attribute projection: Projection [1..*]
6.4.22.4 Aggregation role: element
6.4.22.5 Constructor: ProductCurve(data: ProductCurveData)
6.4.23 ProductCurveData
6.4.24 CodeList: CurveInterpolation
6.4.25 Interface Surface
6.4.25.1 Semantics
6.4.25.2 Attribute boundary: Curve [1..*]
6.4.25.3 Attribute interpolation
6.4.25.4 Attribute numDerivativesBoundary: Integer [0..1]
6.4.25.5 Attribute numDerivativeInterior: Integer [0.., 1]
6.4.25.6 Attribute perimeter: Length
6.4.25.7 Attribute area: Area
6.4.25.8 Attribute dataPoint: DirectPosition [0..*]
6.4.25.9 Attribute controlPoint: DirectPosition [0..*]
6.4.25.10 Attribute knot: Knot[0..1]
6.4.25.11 Operation: upNormal (point: DirectPosition): Vector
6.4.25.12 Operation: Surface (constructors)
6.4.26 Datatype SurfaceData
6.4.27 CodeList: SurfaceInterpolation
6.4.28 Interface Solid
6.4.28.1 Semantics
6.4.28.2 Attribute boundary: Surface [1..*]
6.4.28.3 Attribute area: Area
6.4.28.4 Attribute volume: Volume
6.4.28.5 Attribute dataPoint: DirectPosition [0..*]
6.4.28.6 Attribute controlPoint: DirectPosition [0..*]
6.4.28.7 Attribute interpolation: SolidInterpolation [0..1]
6.4.28.8 Attribute knot: Knot[0..3]
6.4.28.9 Operation: Solid (constructor)
6.4.29 Datatype SolidData
6.4.29.1 Attribute boundary: CurveData*[1..*]
6.4.29.2 Attribute segment: SolidData*[0..*]
6.4.30 CodeList: SolidInterpolation
6.4.31 Interface Collection
6.4.31.1 Semantics
6.4.31.2 Attribute elementType: GeometryType [0..*]
6.4.31.3 Attribute numElement: Integer
6.4.32 Role element: Geometry
6.4.32.1 The role element is an alternate access point to the elements in the Geometric object. The two logical arrays Attribute element and role: element are identical.
6.4.32.2 Operation: add (geo: Geometry): Boolean
6.4.32.3 Operation: remove (geo: Geometry): Boolean
6.4.32.4 Constructor: Collection (data: CollectionData): Collection
6.4.32.5 Association: element: Geometry
6.4.33 DataType CollectionData
6.4.34 Interface Complex
6.4.35 Role Complex: generator: Primitive
6.4.36 Role Complex: superComplex and subComplex
6.4.36.1 Cellular complexes (informative example for use in topology)
6.4.36.2 Operation: Complex: isMaximal
6.4.36.3 Contains association
6.4.36.4 Association role element
6.5 Requirements Class Geometry Data
7 Interpolations for Curves
7.1 Requirements Class Line Curve
7.1.1 Semantics
7.1.2 Interface Line
7.1.2.1 Semantics
7.1.2.2 Attribute interpolation: CurveInterpolation=linear
7.1.2.3 Operation: Line (constructor)
7.1.3 DataType LineData
7.2 Requirements Class Line Data
7.3 Requirements Class Geodesic Curve
7.3.1 Semantics
7.3.2 Interface Geodesic
7.3.2.1 Semantics
7.3.2.2 Attribute interpolation
7.3.2.3 Operation: Geodesic (constructor)
7.3.3 DataType GeodesicData
7.4 Requirements Class Geodesic Curve Data
7.5 Requirements Class Rhumb
7.5.1 Interface Rhumb
7.5.1.1 Semantics
7.5.1.2 Attribute interpolation
7.5.1.3 Rhumb (constructor)
7.5.2 DataType RhumbData
7.6 Requirements Class Rhumb Curve Data
7.7 Requirements Class Polynomial Curves
7.7.1 Semantics
7.7.2 Interface RealFunction
7.7.2.1 Semantics
7.7.2.2 Attribute name
7.7.2.3 Attribute domain
7.7.2.4 Attribute metadata
7.7.2.5 Operation: value
7.7.3 Interface FunctionArc
7.7.3.1 Semantics
7.7.3.2 Attribute domain
7.7.4 Association Role function
7.7.5 Interface FunctionCurve
7.7.5.1 Semantics
7.7.5.2 Attribute FunctionCurve: numArc: Integer
7.7.5.3 Attribute FunctionCurve: metadata: URL
7.7.5.4 Association Role segment: FunctionArc
7.7.6 Interface RealPolynomial
7.7.6.1 Semantics
7.7.6.2 Attribute name, domain, metadata
7.7.6.3 Attribute degree
7.7.6.4 Attribute c: Real
7.7.6.5 Operation: value
7.7.7 Interface PolynomialArc
7.7.7.1 Attribute degree: Integer
7.7.7.2 Constructor: PolynomialArc
7.7.7.3 Association Role function (coordinateOffset: Integer): RealPolynomial
7.7.8 Datatype PolynomialArcData
7.7.8.1 Semantics
7.7.8.2 Attribute CoordinateOffset
7.7.9 Interface PolynomialCurve
7.7.9.1 Semantics
7.7.9.2 Attribute degree
7.7.10 DataType PolynomialCurveData
7.8 Requirements Class Polynomial Curve Data
7.9 Requirements Class Conic Curves
7.9.1 Semantics
7.9.2 Interface Arc
7.9.2.1 Semantics
7.9.2.2 Attribute numArc
7.9.2.3 Attribute controlPoints
7.9.2.4 Attribute dataPoints
7.9.2.5 Attribute radius
7.9.2.6 Constructor Arc (data:ArcData): ArcString
7.9.3 Datatype ArcData
7.9.4 Interface Circle
7.9.4.1 Semantics
7.9.4.2 Constructor Circle
7.9.5 Interface Conic
7.9.5.1 Semantics
7.9.5.2 Attribute dataPoint and controlPoints
7.9.6 Interface EllipticArc, Datatype EllipticArcData
7.10 Requirements Class Conic Curve Data
7.11 Requirements Class Spiral Curve
7.11.1 Semantics, Mathematical background: curves and curvature
7.11.1.1 Fundamental Theorem of Plane Curves (in E2):
7.11.1.2 Fundamental Theorem of Space Curves (in E3):
7.11.1.3 Using the theorems
7.11.1.4 Creating a spiral from a curvature function
7.11.2 Interface Spiral Curves
7.11.2.1 Semantics
7.11.2.2 Attribute curvature
7.11.2.3 Attribute torsion: RealFunction
7.11.2.4 Attribute startFrame
7.11.2.5 Constructor Spiral
7.11.3 Interface Clothoid Curve
7.11.4 Datatype SpiralData
7.12 Requirements Class Spiral Curve Data
7.13 Requirements Class Spline Curve
7.13.1 Semantics
7.13.2 CodeList: KnotType
7.13.3 CodeList: SplineCurveForm
7.13.4 Interface SplineCurve
7.13.4.1 Semantics
7.13.4.2 Attribute curveForm
7.13.4.3 Attribute knot
7.13.4.4 Attribute degree
7.13.4.5 Attribute knotSpec
7.13.4.6 Attribute isRational
7.13.5 Interface PolynomialSpline
7.13.5.1 Semantics
7.13.5.2 Attribute derivativeAtStart
7.13.6 Interface CubicSpline
7.13.7 Interface Bezier
7.13.8 Interface BSplineCurve (and NURBS)
7.13.8.1 Semantics
7.13.8.2 Operation: BSplineCurve
7.13.9 DataType BsplineData
7.14 Requirements Class Spline Curve Data
8 Interpolations for Surfaces
8.1 Requirements Class Polygon Surface
8.1.1 Semantics
8.1.2 Interface Polygon
8.1.2.1 Semantics
8.1.2.2 Attribute Polygon: boundary: Curve [1..*]
8.1.2.3 Association role: spanningSurface: GriddedSurface [0..1]
8.1.2.4 Operation: Polygon (constructor)
8.1.3 Datatype PolygonData
8.1.4 Interface PolyhedralSurface
8.1.4.1 Semantics
8.1.4.2 Operation: PolyhedralSurface (constructor)
8.1.4.3 Association role: segment: Polygon [1..*]
8.1.5 Datatype PolyhedralSurfaceData
8.1.6 Interface Triangle
8.1.7 Datatype TriangleData
8.1.8 Interface TriangulatedSurface
8.1.9 Datatype TriangulatedSurfaceData
8.2 Requirements Class Polygon Surface Data
8.3 Requirements Class Parametric Curve Surface
8.3.1 Semantics
8.3.2 Interface ParametricCurveSurface
8.3.2.1 Semantics
8.3.2.2 Attribute horizontalCurveType, verticalCurveType
8.3.2.3 Attribute rows
8.3.2.4 Attribute columns
8.3.2.5 Attribute dataPoints
8.3.2.6 Attribute controlPoints
8.3.2.7 Attribute horizontalCurveType
8.3.2.8 Attribute verticalCurveType
8.3.2.9 Operation: horizontalCurve: Curve
8.3.2.10 Operation: verticalCurve: Curve
8.3.2.11 Operation: surface: DirectPosition
8.3.3 Datatype ParametricCurveSurfaceData
8.3.4 Interface BilinearGrid
8.3.5 Extensions of ParametricCurveSurface
8.4 Requirements Class Parametric Curve Surface Data
8.5 Requirements Class Conic Surface
8.5.1 Semantics
8.5.2 Interface Sphere
8.5.3 Interface Cone
8.5.4 Interface Cylinder
8.6 Requirements Class Conic Surface Data
8.7 Requirements Class Spline Surface
8.7.1 Semantics
8.7.2 Interface BSplineSurface (and NURBS)
8.7.2.1 Semantics
8.7.2.2 Attribute degree: Integer
8.7.2.3 Attribute knot: Knot[2]
8.7.2.4 Attribute surfaceForm: BSPlineSurfaceForm
8.7.2.5 Attribute knotSpec: KnotType
8.7.2.6 Attribute isPolynomial: Boolean
8.7.2.7 BSplineSurfaceData (default constructor datatype)
8.7.3 Codelist BSplineSurfaceForm
8.8 Requirements Class Spline Surface Data
9 Interpolations for Solids
9.1 Requirements Class Boundary Representation Solid
9.2 Requirements Class Boundary Representation Solid Data
9.3 Requirements Class Parametric Curve Solid
9.3.1 Interface ParametricCurveSolid
9.3.1.1 Semantics
9.3.1.2 Attribute: horizontalCurveType, verticalCurveType, depthCurveType
9.3.1.3 Attribute: dataPoint, controlPoint
9.3.2 Interface BSolidSpline
9.3.3 Other interpolations
9.4 Requirements Class Parametric Curve Solid Data
10 Topology
10.1 Requirements Class Topology root
10.1.1 Semantics
10.1.2 Interface Topology
10.1.2.1 Semantics
10.1.2.2 Attribute isEmpty
10.1.2.3 Attribute dimension
10.1.2.4 Attribute boundary
10.1.2.5 Attribute coBoundary
10.1.2.6 Attribute interior
10.1.2.7 Attribute exterior
10.1.2.8 Attribute closure
10.1.2.9 Attribute maximalComplex
10.1.3 Interface Primitive
10.1.3.1 Semantics
10.1.3.2 Association: Realization
10.1.3.3 Association: Complex
10.1.3.4 Association: Isolated In
10.1.4 Interface DirectedTopo
10.1.4.1 Semantics
10.1.4.2 Attribute orientation
10.1.4.3 Attribute negate
10.1.4.4 Attribute expression
10.1.4.5 Association: Centre
10.1.4.6 Constraints
10.1.5 Datatype TopologyData
10.1.5.1 Semantics
10.1.5.2 Attribute id: GenericName
10.1.5.3 Attribute boundaryData
10.1.5.4 Attribute geometryData
10.1.6 DataType PrimitiveData
10.1.7 DataType ComplexData
10.1.7.1 Semantics
10.1.7.2 Attribute primitive
10.1.8 Datatype Expression
10.1.8.1 Semantics
10.1.8.2 Attribute negate
10.1.8.3 Attribute boundary
10.1.8.4 Attribute coBoundary
10.1.8.5 Attribute support
10.1.8.6 Attribute asSet
10.1.8.7 Operation: plus(expression)
10.1.8.8 Operation: minus
10.1.8.9 Operation: equals
10.1.9 Datatype ExpressionTerm
10.2 Requirements Class Topology Root Data
10.3 Requirements Class Node
10.3.1 Semantics
10.3.2 Interface Node
10.3.2.1 Semantics
10.3.2.2 Association: Centre
10.3.2.3 Attribute boundary
10.3.2.4 Constraints
10.3.3 Interface DirectedNode
10.4 Requirements Class Edge
10.4.1 Interface Edge
10.4.1.1 Semantics
10.4.1.2 Attribute coBoundary
10.4.1.3 Attribute boundary
10.4.1.4 Association: Centre
10.4.1.5 Constraints
10.4.2 Interface DirectedEdge
10.5 Requirements Class Face
10.5.1 Semantics
10.5.2 Interface Face
10.5.2.1 Attribute boundary
10.5.2.2 Attribute coBoundary
10.5.2.3 Association Centre roles
10.5.2.4 Constraints
10.5.3 Interface DirectedFace
10.6 Requirements Class Topology Solid
10.6.1 Interface Solid
10.6.1.1 Semantics
10.6.1.2 Attribute boundary
10.6.1.3 Attribute coBoundary
10.6.1.4 Association role: Centre
10.6.2 Interface DirectedSolid
10.7 Requirements Class Topological Complex
10.7.1 Semantics
10.7.2 Interface Complex
10.7.2.1 Semantics
10.7.2.2 Complex: constructor of a topological complex
10.7.2.3 Association role: maximalComplex
10.7.2.4 Attribute isMaximal
10.7.2.5 Attribute isConnected
10.7.2.6 Association: Contains
10.7.2.7 Association: Complex
10.7.2.8 Association: Realization
10.8 Requirements Class Derived Topological Relations
10.8.1 Introduction
10.8.2 Canonical form for Geometry
10.8.3 Boundary operators for aggregate objects
10.8.3.1 Common semantics
10.8.3.2 "Mod 2" boundaries
10.8.3.3 "At least 2" boundaries
10.8.4 Boolean or set operators
10.8.4.1 Form of the Boolean operators (originally Egenhofer 4 matrix)
10.8.4.2 Relate Reference Operation
10.8.4.3 Relation to set operations
10.8.5 Egenhofer operators
10.8.5.1 Form of the Egenhofer operators (originally Egenhofer 9 matrix)
10.8.5.2 Egenhofer relate
10.8.5.3 Relation to set operations
10.8.6 Full topological operators
10.8.6.1 Form of the full topological operators
10.8.6.2 Full topological relate
10.8.6.3 Named Operators
10.8.6.3.1 Equals
10.8.6.3.2 Contains
10.8.6.3.3 Disjoint
10.8.6.3.4 Intersects
10.8.6.3.5 Touches
10.8.6.3.6 Crosses
10.8.6.3.7 Within
10.8.6.3.8 Overlaps
10.8.7 Combinations
11 Special Requirements Classes
11.1 Requirements Class Simplicial geometry
11.1.1 Semantics
11.1.2 Datatype Simplex
11.1.2.1 Semantics
11.1.2.2 Attribute dimension
11.1.2.3 Attribute numVertex
11.1.2.4 Attribute vertex
11.1.2.5 Operation BoundarySimplex
11.1.2.6 Operation Boundary
11.1.3 DataType SimplicialTerm
11.1.4 DataType::SimplicialPolynomial
11.1.5 DataType::SimplicialComplex
11.2 Requirements Class Point Clouds
11.2.1 Semantics
11.2.2 Interface PointCloud
11.2.2.1 1Semantics
11.2.2.2 Attribute range: Range
11.2.2.3 Attribute point
11.2.2.4 Operation: SubCloud
11.2.2.5 Operation: SimplicialComplex
Annex A
A.1 Conformance Class for Behaviour and for Data
A.2 Conformance Class Coordinate
A.3 Conformance Class Coordinate Data
A.4 Conformance Class Geometry
A.4.1 Dependency: Coordinate
A.4.2 Test Geometry
A.5 Conformance Class Geometry Data
A.5.1 Dependency: Coordinate Data
A.5.2 Test Geometry Data
A.6 Conformance Class Line Curve
A.6.1 Dependency: Conformance Class Geometry
A.6.2 Test Line Curve
A.7 Conformance Class Line Curve Data
A.7.1 Dependency: Geometry Data
A.7.2 Test Lines Curve Data
A.8 Conformance Class Geodesic Curve
A.8.1 Dependency: Line Curve
A.8.2 Test Geodesics
A.9 Conformance Class Geodesic Curve Data
A.9.1 Dependency: : Line Data
A.9.2 Test Geodesic Data
A.10 Conformance Class Rhumb Curve
A.10.1 Dependency: Line Curve
A.10.2 Test Rhumb
A.11 Conformance Class Rhumb Curve Data
A.11.1 Dependency: : Line Curve Data
A.11.2 Test Rhumb Data
A.12 Conformance Class Polynomial Curve
A.12.1 Dependency: : Line Curve
A.12.2 Test Polynomial Curve
A.13 Conformance Class Polynomial Curve Data
A.13.1 Dependency: : Line Curve Data
A.13.2 Test Polynomial Curve Data
A.14 Conformance Class Conic Curves
A.14.1 Dependency: : Polynomial Curves
A.14.2 Test Conic Curves
A.15 Conformance Class Conic Curve Data
A.15.1 Dependency: : Polynomial Curve Data
A.15.2 Test Conic Curve Data
A.16 Conformance Class Spiral Curves
A.16.1 Dependency: : Conics
A.16.2 Test Spiral Curves
A.17 Conformance Class Spiral Curve Data
A.17.1 Dependency: : Conic Curve Data
A.17.2 Test Spiral Curve Data
A.18 Conformance Class Spline Curves
A.18.1 Dependency: : Polynomial Curves
A.18.2 Test Spline Curves
A.19 Conformance Class Spline Curve Data
A.19.1 Dependency: : Polynomial Curve Data
A.19.2 Test Spline Data
A.20 Conformance Class Polygon Surfaces
A.20.1 Dependency: : Geometry
A.20.2 Test Polygon Surfaces
A.21 Conformance Class Polygon Surface Data
A.21.1 Dependency: : Geometry Data
A.21.2 Test Polygon Surface Data
A.22 Conformance Class Parametric Curve Surfaces
A.22.1 Dependency: : Conformance Class Geometry
A.22.2 Test Parametric Curve Surfaces
A.23 Conformance Class Parametric Curve Surface Data
A.23.1 Dependency: : Geometry Data
A.23.2 Test Parametric Curve Surface Data
A.24 Conformance Class Conic Surface
A.24.1 Dependency: : Parametric Curve Surfaces
A.24.2 Test Conic Surface
A.25 Conformance Class Conic Surface Data
A.25.1 Dependency: : Geometry Data
A.25.2 Test Conic Surface Data
A.26 Conformance Class Spline Surface
A.26.1 Dependency: : Parametric Curve Surfaces
A.26.2 Test Spline Surface
A.27 Conformance Class Spline Surface Data
A.27.1 Dependency: : Geometry Data
A.27.2 Test Spline Surface Data
A.28 Conformance Class Boundary Representation Solid
A.28.1 Dependency: : Geometry
A.28.2 Test Boundary Representation
A.29 Conformance Class Boundary Representation Solid Data
A.29.1 Dependency: : Geometry Data
A.29.2 Test Boundary Representation Solid Data
A.30 Conformance Class Parametric Curve Solid
A.30.1 Dependency: : Geometry
A.30.2 Test Parametric Curve Solid
A.31 Conformance Class Parametric Curve Solid Data
A.31.1 Dependency: : Geometry Data
A.31.2 Test Parametric Curve Solid Data
A.32 Conformance Class Topology root
A.32.1 Dependency: : Geometry
A.32.2 Test Topological Root
A.33 Conformance Class Topology Data
A.34 Conformance Class Node
A.34.1 Dependency: : Topology root
A.34.2 Test Node
A.35 Conformance Class Edge
A.35.1 Dependency: : Node
A.35.2 Test Edge
A.36 Conformance Class Face
A.36.1 Dependency: : Edge
A.36.2 Test Face
A.37 Conformance Class Topology Solid
A.37.1 Dependency: : Face
A.37.2 Test Solid
A.38 Conformance Class Topological complex
A.38.1 Dependency: : Topology root
A.38.2 Test Topological complex
A.39 Conformance Class Derived Topological Relations
A.39.1 Dependency: Topology Complex
A.39.2 Test Derived Topological Relations
A.40 Conformance Class Simplicial Geometry
A.40.1 Dependency: Geometry
A.40.2 Test Simplicial Geometry
A.41 Conformance Class Point Clouds
A.41.1 Dependency: Geometry
A.41.2 Test Point Clouds
Annex B
B.1 Introduction
B.2 Packages for Simple topology
B.2.1 Semantics
B.2.2 Root
B.2.3 Node
B.2.4 Edge
B.2.5 DirectedEdge
B.2.6 Face
B.2.7 Theme
B.2.8 Feature
B.2.9 PointComponent
B.2.10 CurveComponent
B.2.11 SurfaceComponent
B.3 Feature Topology
B.3.1 Semantics
B.4 Classes for feature topology at the theme level
B.4.1 Feature: Complex
B.4.2 Feature: Primitive
B.4.3 Feature: Node
B.4.4 Feature: Edge
B.4.5 Feature: Face
Annex C
Annex D
Bibliography
Cited references in this standard
[Current]
Information technology — Object Management Group Unified Modeling Language (OMG UML) — Part 2: Superstructure
Content history
[Current]
[Superseded]
AS/NZS ISO 19107:2005 Rec:2016
DR AS/NZS ISO 19107:2020
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