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An introduction to ISO 15926-3 Geometry and topology

An introduction to ISO 15926-3 Geometry and topology. David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk. 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

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An introduction to ISO 15926-3 Geometry and topology

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  1. An introduction to ISO 15926-3Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk

  2. 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

  3. Subject areas in ISO 15926-3 link to ISO 15926-2 ontology some basic mathematical concepts geometry and topology ontology derived from ISO 10303-42 geodesy ontology link to individuals link to geodesy spatial and temporal variation of properties ontology for meshes and functions over meshes

  4. volume of space is not usually identified – but can be A solid sphere of material MyObject at 2008-05-08T12:39 centre at (1.234556, 2.345678, 3.4565678) WGS84 (GPS) coordinate system 10.5 m :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 ] .

  5. A solid sphere of material MyObject at 2008-05-08T12:39 centre at (1.234556, 2.345678, 3.4565678) WGS84 (GPS) coordinate system 10.5 m not in the part 2 ontology :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 ] .

  6. A solid sphere of material MyObject at 2008-05-08T12:39 centre at (1.234556, 2.345678, 3.4565678) WGS84 (GPS) coordinate system temporal parts need not be identified 10.5 m :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 ] .

  7. a useful vocabulary for time in http://www.w3.org/TR/owl-time/ A solid sphere of material MyObject at 2008-05-08T12:39 centre at (1.234556, 2.345678, 3.4565678) WGS84 (GPS) coordinate system 10.5 m [ 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 ] .

  8. 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 ] .

  9. 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

  10. 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

  11. 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

  12. 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

  13. Topology Not everything has a simple shape 1 volume 1 boundary

  14. Topology Not everything has a simple shape 1 volume 1 boundary – 4 part faces 1

  15. Topology Not everything has a simple shape 1 volume 1 boundary – 4 part faces 2

  16. Topology Not everything has a simple shape 1 volume 1 boundary – 4 part faces 3

  17. Topology Not everything has a simple shape 1 volume 1 boundary – 4 part faces 4

  18. Topology Not everything has a simple shape 1 volume 1 boundary – 4 part faces 6 edges

  19. Topology Not everything has a simple shape 1 volume 1 boundary – 4 part faces 6 edges 4 vertices

  20. MyAxis1Placement MyCircle :Vertex1 a part3:Vertex ; a part2:PointInSpace ; rdf:wgs84 ( 1.234556 2.345678 3.4565678 ) . Topology Vertex2 Edge1 Vertex1

  21. MyAxis1Placement MyCircle Topology Vertex2 Edge1 Vertex1 :Edge1 a part3:DirectedEdge; part3:end1 :Vertex1 ; part3:end2 :Vertex2 ; a part2:DirectedCurve ; part3:hasContainingCurve :MyCurve .

  22. MyAxis1Placement MyCircle Topology Vertex2 Edge1 Vertex1 :MyCircle a part2:DirectedCurve ; a part2:Circle ; part3:axialReferencePlacement :MyAxis1Placement; part3:radius [ part4:metre 10.5 ] .

  23. Curve ontology SubMetricSpace ParameterisedSet Manifold1d ManifoldProjection Curve DirectedCurve NonSelfIntersectingCurve SelfIntersectingCurve FiniteCurve InfiniteCurve ParameterisedCurve BoundedCurve UnlboundedCurve BoundedFiniteCurve UnBoundedFiniteCurve Conic Polyline Line Clothoid CircularInvolute Parabola Ellipse Hyperbola Circle CanonicallyParameterisedHyperbola BSplineCurve CanonicallyParameterisedLine CanonicallyParameterisedParabola CanonicallyParameterisedEllipse CanonicallyParameterisedClothoid CanonicallyParameterisedCircularInvolute CanonicallyParameterisedCircle

  24. Surface ontology SubMetricSpace ParameterisedSet Manifold2d ManifoldProjection Surface NonSelfIntersectingSurface SelfIntersectingSurface OrientedSurface FiniteSurface BoundedSurface UnboundedSurface InfiniteSurface BoundedFiniteSurface UnboundedFiniteSurface EllipsoidalSurface ToroidalSurface CylindricalSurface ConicalSurface Plane InnerDegerenateToroidalSurface SweptSurface SphericalSurface OuterDegerenateToroidalSurface (FacetedPlaneSurfacePrimitive) ParameterisedSurface TriangularSurface PlaneConvexQuadrilateralSurface VBoundedSurface VUnboundedSurface SurfaceCurveSweptSurface SurfaceOfLinearExtrusion SurfaceOfRevolution FixedReferenceSweptSurface UBoundedSurface UUnboundedSurface BSplineSurface CannonicallyParameterisedFixedReferenceSweptSurface

  25. 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

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