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An introduction to ISO 15926-3Geometry and topology
David LealCAESAR Systems Limited
Objectives of of ISO 15926-3
• Information repository that can integrate CAD geometry and GIS geometry– interface to either type of system – ISO 10303-203/214 or ISO 19107
• Management of geometric information from different sources– different coordinate systems– different units of measure– separate audit trail for each data item– missing and conflicting data
• Support of property distributions defined over meshes– FE analysis input and results– sub-surface exploration results
• Integration of geometry and topology with other ISO 15926 information
Subject areas in ISO 15926-3
geometry and topologyontology derived from
ISO 10303-42
spatial and temporal variation of propertiesontology for meshes and functions over meshes
link toISO 15926-2
ontology
link to individuals
geodesyontology
link to geodesy
some basic mathematical concepts
A solid sphere of material
:MyObjectAt2008-05-08T12:39 rdl:occupiesSpace [ a part3:SolidSphere ; part3:centre [ rdl:wgs84 (1.234556 2.345678 3.4565678) ] ; part3:radius [ part4:metre 10.5 ] ] .
centre at (1.234556, 2.345678, 3.4565678)WGS84 (GPS) coordinate system
10.5 m
MyObject at 2008-05-08T12:39
volume of space is not usually identified – but can be
A solid sphere of material
:MyObjectAt2008-05-08T12:39 rdl:occupiesSpace [ a part3:SolidSphere ; part3:centre [ rdl:wgs84 (1.234556 2.345678 3.4565678) ] ; part3:radius [ part4:metre 10.5 ] ] .
centre at (1.234556, 2.345678, 3.4565678)WGS84 (GPS) coordinate system
10.5 m
MyObject at 2008-05-08T12:39
not in the part 2 ontology
A solid sphere of material
:MyObjectAt2008-05-08T12:39 rdl:occupiesSpace [ a part3:SolidSphere ; part3:centre [ rdl:wgs84 (1.234556 2.345678 3.4565678) ] ; part3:radius [ part4:metre 10.5 ] ] .
centre at (1.234556, 2.345678, 3.4565678)WGS84 (GPS) coordinate system
10.5 m
MyObject at 2008-05-08T12:39
temporal parts need not be identified
A solid sphere of material
[ part2:temporalPartOf :MyObject] part2:atInstant [ t:inXSDDateTime 2008-05-08T12:39 ] rdl:occupiesSpace [ a part3:SolidSphere ; part3:centre [ rdl:wgs84 (1.234556 2.345678 3.4565678) ] ; part3:radius [ part4:metre 10.5 ] ] .
centre at (1.234556, 2.345678, 3.4565678)WGS84 (GPS) coordinate system
10.5 m
MyObject at 2008-05-08T12:39
a useful vocabulary for time inhttp://www.w3.org/TR/owl-time/
A solid sphere of material
[ part2:temporalPartOf :MyObject] part2:atInstant [ t:inXSDDateTime 2008-05-08T12:39 ] rdl:occupiesSpace [ a part3:SolidSphere ; part3:centre [ rdl:wgs84 (1.234556 2.345678 3.4565678) ] ; part3:radius [ part4:metre 10.5 ] ] .
classification of a volume of space according to its geometry
ISO 15926-3 has a small set of classes – other vocabularies can add to it
A solid sphere of material
[ part2:temporalPartOf :MyObject] part2:atInstant [ t:inXSDDateTime 2008-05-08T12:39 ] rdl:occupiesSpace [ a part3:SolidSphere ; part3:centre [ rdl:wgs84 (1.234556 2.345678 3.4565678) ] ; part3:radius [ part4:metre 10.5 ] ] .
a property (iso159262:ClassOfRelationship) valid for a SolidSphere
A solid sphere of material
[ part2:temporalPartOf :MyObject] part2:atInstant [ t:inXSDDateTime 2008-05-08T12:39 ] rdl:occupiesSpace [ a part3:SolidSphere ; part3:centre [ rdl:wgs84 (1.234556 2.345678 3.4565678) ] ; part3:radius [ part4:metre 10.5 ] ] .
a point in space – anonymous, but defined by its coordinates with respect to WGS84
A solid sphere of material
[ part2:temporalPartOf :MyObject] part2:atInstant [ t:inXSDDateTime 2008-05-08T12:39 ] rdl:occupiesSpace [ a part3:SolidSphere ; part3:centre [ rdl:wgs84 (1.234556 2.345678 3.4565678) ] ; part3:radius [ part4:metre 10.5 ] ] .
a property valid for a SolidSphere
A solid sphere of material
[ part2:temporalPartOf :MyObject] part2:atInstant [ t:inXSDDateTime 2008-05-08T12:39 ] rdl:occupiesSpace [ a part3:SolidSphere ; part3:centre [ rdl:wgs84 (1.234556 2.345678 3.4565678) ] ; part3:radius [ part4:metre 10.5 ] ] .
a length – anonymous, but defined by its representation with respect to metre
TopologyNot everything has a simple shape
1 volume
1 boundary
TopologyNot everything has a simple shape
1 volume
1 boundary – 4 part faces1
TopologyNot everything has a simple shape
1 volume
1 boundary – 4 part faces
2
TopologyNot everything has a simple shape
1 volume
1 boundary – 4 part faces
3
TopologyNot everything has a simple shape
1 volume
1 boundary – 4 part faces
4
TopologyNot everything has a simple shape
1 volume
1 boundary – 4 part faces
6 edges
TopologyNot everything has a simple shape
1 volume
1 boundary – 4 part faces
6 edges
4 vertices
Topology
Edge1
Vertex2
MyCircle
MyAxis1Placement
Vertex1
:Vertex1 a part3:Vertex ; a part2:PointInSpace ; rdf:wgs84 ( 1.234556 2.345678 3.4565678 ) .
Topology
Edge1
Vertex2
MyCircle
MyAxis1Placement
Vertex1
:Edge1 a part3:DirectedEdge; part3:end1 :Vertex1 ; part3:end2 :Vertex2 ; a part2:DirectedCurve ; part3:hasContainingCurve :MyCurve .
Topology
Edge1
Vertex2
MyCircle
MyAxis1Placement
Vertex1
:MyCircle a part2:DirectedCurve ; a part2:Circle ; part3:axialReferencePlacement :MyAxis1Placement; part3:radius [ part4:metre 10.5 ] .
Curve ontology
Line
Conic
Hyperbola ParabolaEllipse
Circle
Clothoid CircularInvolutePolyline
InfiniteCurve
CanonicallyParameterisedLine
CanonicallyParameterisedEllipse
CanonicallyParameterisedCircle
CanonicallyParameterisedHyperbola
CanonicallyParameterisedParabola
CanonicallyParameterisedClothoid
CanonicallyParameterisedCircularInvolute
BSplineCurve
ManifoldProjection
Curve
SelfIntersectingCurve
ParameterisedCurveBoundedCurveUnlboundedCurve
DirectedCurve
ParameterisedSet
FiniteCurve
SubMetricSpace
NonSelfIntersectingCurve
Manifold1d
BoundedFiniteCurve
UnBoundedFiniteCurve
Surface ontology
PlaneEllipsoidalSurface
SphericalSurface
ToroidalSurface ConicalSurface
(FacetedPlaneSurfacePrimitive)
FiniteSurface
BSplineSurface
ManifoldProjection
Surface
SelfIntersectingSurface
ParameterisedSurface
BoundedSurface UnboundedSurface
OrientedSurface
ParameterisedSet
InfiniteSurface
SubMetricSpace
NonSelfIntersectingSurface
Manifold2d
CylindricalSurface
OuterDegerenateToroidalSurface
InnerDegerenateToroidalSurfaceSweptSurface
SurfaceOfLinearExtrusionSurfaceOfRevolution
SurfaceCurveSweptSurfaceFixedReferenceSweptSurface
PlaneConvexQuadrilateralSurfaceTriangularSurface
UBoundedSurface UUnboundedSurface
VBoundedSurface VUnboundedSurface
CannonicallyParameterisedFixedReferenceSweptSurface
BoundedFiniteSurface UnboundedFiniteSurface
Still some loose ends
• Key relationships between a physical object and space– occupiesSpace c.f. during– hasCentreOfMass– hasCentreLine
• Reference data for GIS systems– WGS84– OSGB
• Geometry and topology as ISO 10303-42+ GIS coordinate systems+ extensible using ontologies+ links to measurements