An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited...
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Transcript of An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited...
![Page 1: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/1.jpg)
An introduction to ISO 15926-3Geometry and topology
David LealCAESAR Systems Limited
![Page 2: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/2.jpg)
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
![Page 3: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/3.jpg)
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
![Page 4: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/4.jpg)
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
![Page 5: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/5.jpg)
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
![Page 6: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/6.jpg)
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
![Page 7: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/7.jpg)
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/
![Page 8: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/8.jpg)
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
![Page 9: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/9.jpg)
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
![Page 10: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/10.jpg)
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
![Page 11: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/11.jpg)
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
![Page 12: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/12.jpg)
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
![Page 13: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/13.jpg)
TopologyNot everything has a simple shape
1 volume
1 boundary
![Page 14: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/14.jpg)
TopologyNot everything has a simple shape
1 volume
1 boundary – 4 part faces1
![Page 15: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/15.jpg)
TopologyNot everything has a simple shape
1 volume
1 boundary – 4 part faces
2
![Page 16: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/16.jpg)
TopologyNot everything has a simple shape
1 volume
1 boundary – 4 part faces
3
![Page 17: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/17.jpg)
TopologyNot everything has a simple shape
1 volume
1 boundary – 4 part faces
4
![Page 18: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/18.jpg)
TopologyNot everything has a simple shape
1 volume
1 boundary – 4 part faces
6 edges
![Page 19: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/19.jpg)
TopologyNot everything has a simple shape
1 volume
1 boundary – 4 part faces
6 edges
4 vertices
![Page 20: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/20.jpg)
Topology
Edge1
Vertex2
MyCircle
MyAxis1Placement
Vertex1
:Vertex1 a part3:Vertex ; a part2:PointInSpace ; rdf:wgs84 ( 1.234556 2.345678 3.4565678 ) .
![Page 21: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/21.jpg)
Topology
Edge1
Vertex2
MyCircle
MyAxis1Placement
Vertex1
:Edge1 a part3:DirectedEdge; part3:end1 :Vertex1 ; part3:end2 :Vertex2 ; a part2:DirectedCurve ; part3:hasContainingCurve :MyCurve .
![Page 22: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/22.jpg)
Topology
Edge1
Vertex2
MyCircle
MyAxis1Placement
Vertex1
:MyCircle a part2:DirectedCurve ; a part2:Circle ; part3:axialReferencePlacement :MyAxis1Placement; part3:radius [ part4:metre 10.5 ] .
![Page 23: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/23.jpg)
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
![Page 24: An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited david.leal@caesarsystems.co.uk.](https://reader035.fdocuments.net/reader035/viewer/2022070401/56649f1f5503460f94c38231/html5/thumbnails/24.jpg)
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
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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