An introduction to ISO 15926-3Geometry and topology

David LealCAESAR 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

• 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