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An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited

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Presentation on theme: "An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited"— Presentation transcript:

1 An introduction to ISO 15926-3 Geometry 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 geometry and topology ontology derived from ISO 10303-42 spatial and temporal variation of properties ontology for meshes and functions over meshes link to ISO 15926-2 ontology link to individuals geodesy ontology link to geodesy some basic mathematical concepts

4 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

5 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

6 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

7 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 in http://www.w3.org/TR/owl-time/

8 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

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

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

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

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

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

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

26 A circle radius r plane centre O geometric properties radius r plane centre O reference axis z parameter  parameterisation properties circle O r O canonically parameterised circle z axis1_placement axis2_placement 

27 Omission flagged by BSI review 2½D Geodesy reference surface height model offset surfaces defined by distance along normal

28 Parameterised surface p physical =  (u, v)  : R 2  physical space Parameterisation function for surface X(p physical ) = (u, v) X: physical space  R 2 Coordinate system for surface z x y inverse function: X =  -1

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