an introduction to iso 15926-3 geometry and topology

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An introduction to ISO 15926-3 Geometry and topology David Leal CAESAR Systems Limited [email protected]

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An introduction to ISO 15926-3 Geometry and topology. David Leal CAESAR Systems Limited [email protected]. 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 - PowerPoint PPT Presentation

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Page 1: An introduction to ISO 15926-3 Geometry and topology

An introduction to ISO 15926-3Geometry and topology

David LealCAESAR Systems Limited

[email protected]

Page 2: An introduction to ISO 15926-3 Geometry and topology

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

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

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

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

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

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

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

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

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

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

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

TopologyNot everything has a simple shape

1 volume

1 boundary

Page 14: An introduction to ISO 15926-3 Geometry and topology

TopologyNot everything has a simple shape

1 volume

1 boundary – 4 part faces1

Page 15: An introduction to ISO 15926-3 Geometry and topology

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

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

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

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

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

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

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

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

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

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

Page 25: An introduction to ISO 15926-3 Geometry and topology

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