An introduction to ISO 15926 3 Geometry and

Objectives of of ISO 15926 -3 • Information repository that can integrate CAD geometry

Subject areas in ISO 15926 -3 link to ISO 15926 -2 ontology some basic

A solid sphere of material My. Object at 2008 -05 -08 T 12: 39

A solid sphere of material [ part 2: temporal. Part. Of : My. Object]

Topology Not everything has a simple shape 1 volume 1 boundary

Topology Not everything has a simple shape 1 volume 1 1 boundary – 4

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

Topology Vertex 2 My. Axis 1 Placement Edge 1 My. Circle Vertex 1 :

Curve ontology Manifold 1 d Manifold. Projection Sub. Metric. Space Parameterised. Set Curve Non.

Surface ontology Manifold 2 d Manifold. Projection Sub. Metric. Space Parameterised. Set Surface Non.

Still some loose ends • Key relationships between a physical object and space –

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

A solid sphere of material My. Object at 2008 -05 -08 T 12: 39 centre at (1. 234556, 2. 345678, 3. 4565678) WGS 84 (GPS) coordinate system 10. 5 m volume of space is not usually identified – but can be : My. Object. At 2008 -05 -08 T 12: 39 rdl: occupies. Space [ a part 3: Solid. Sphere ; part 3: centre [ rdl: wgs 84 (1. 234556 2. 345678 3. 4565678) ] ; part 3: radius [ part 4: metre 10. 5 ].

A solid sphere of material My. Object at 2008 -05 -08 T 12: 39 centre at (1. 234556, 2. 345678, 3. 4565678) WGS 84 (GPS) coordinate system 10. 5 m not in the part 2 ontology : My. Object. At 2008 -05 -08 T 12: 39 rdl: occupies. Space [ a part 3: Solid. Sphere ; part 3: centre [ rdl: wgs 84 (1. 234556 2. 345678 3. 4565678) ] ; part 3: radius [ part 4: metre 10. 5 ].

A solid sphere of material My. Object at 2008 -05 -08 T 12: 39 centre at (1. 234556, 2. 345678, 3. 4565678) WGS 84 (GPS) coordinate system 10. 5 m temporal parts need not be identified : My. Object. At 2008 -05 -08 T 12: 39 rdl: occupies. Space [ a part 3: Solid. Sphere ; part 3: centre [ rdl: wgs 84 (1. 234556 2. 345678 3. 4565678) ] ; part 3: radius [ part 4: metre 10. 5 ].

A solid sphere of material My. Object at 2008 -05 -08 T 12: 39 centre at (1. 234556, 2. 345678, 3. 4565678) WGS 84 (GPS) coordinate system a useful vocabulary for time in http: //www. w 3. org/TR/owl-time/ 10. 5 m [ part 2: temporal. Part. Of : My. Object] part 2: at. Instant [ t: in. XSDDate. Time 2008 -05 -08 T 12: 39 ] rdl: occupies. Space [ a part 3: Solid. Sphere ; part 3: centre [ rdl: wgs 84 (1. 234556 2. 345678 3. 4565678) ] ; part 3: radius [ part 4: metre 10. 5 ].

A solid sphere of material [ part 2: temporal. Part. Of : My. Object] part 2: at. Instant [ t: in. XSDDate. Time 2008 -05 -08 T 12: 39 ] rdl: occupies. Space [ a part 3: Solid. Sphere ; part 3: centre [ rdl: wgs 84 (1. 234556 2. 345678 3. 4565678) ] ; part 3: radius [ part 4: 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 [ part 2: temporal. Part. Of : My. Object] part 2: at. Instant [ t: in. XSDDate. Time 2008 -05 -08 T 12: 39 ] rdl: occupies. Space [ a part 3: Solid. Sphere ; part 3: centre [ rdl: wgs 84 (1. 234556 2. 345678 3. 4565678) ] ; part 3: radius [ part 4: metre 10. 5 ]. a property (iso 159262: Class. Of. Relationship) valid for a Solid. Sphere

A solid sphere of material [ part 2: temporal. Part. Of : My. Object] part 2: at. Instant [ t: in. XSDDate. Time 2008 -05 -08 T 12: 39 ] rdl: occupies. Space [ a part 3: Solid. Sphere ; part 3: centre [ rdl: wgs 84 (1. 234556 2. 345678 3. 4565678) ] ; part 3: radius [ part 4: metre 10. 5 ]. a point in space – anonymous, but defined by its coordinates with respect to WGS 84

A solid sphere of material [ part 2: temporal. Part. Of : My. Object] part 2: at. Instant [ t: in. XSDDate. Time 2008 -05 -08 T 12: 39 ] rdl: occupies. Space [ a part 3: Solid. Sphere ; part 3: centre [ rdl: wgs 84 (1. 234556 2. 345678 3. 4565678) ] ; part 3: radius [ part 4: metre 10. 5 ]. a length – anonymous, but defined by its representation with respect to metre

Topology Not everything has a simple shape 1 volume 1 boundary

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

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

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

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

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

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

Topology Vertex 2 My. Axis 1 Placement Edge 1 My. Circle Vertex 1 : Vertex 1 a a rdf: wgs 84 part 3: Vertex ; part 2: Point. In. Space ; ( 1. 234556 2. 345678 3. 4565678 ).

Topology Vertex 2 My. Axis 1 Placement Edge 1 My. Circle Vertex 1 : Edge 1 a part 3: end 1 part 3: end 2 a part 3: has. Containing. Curve part 3: Directed. Edge; : Vertex 1 ; : Vertex 2 ; part 2: Directed. Curve ; : My. Curve.

Topology Vertex 2 My. Axis 1 Placement Edge 1 My. Circle Vertex 1 : My. Circle a part 2: Directed. Curve ; a part 2: Circle ; part 3: axial. Reference. Placement : My. Axis 1 Placement; part 3: radius [ part 4: metre 10. 5 ].

Curve ontology Manifold 1 d Manifold. Projection Sub. Metric. Space Parameterised. Set Curve Non. Self. Intersecting. Curve Unlbounded. Curve Finite. Curve Infinite. Curve Directed. Curve Parameterised. Curve Bounded. Finite. Curve Un. Bounded. Finite. Curve Polyline Conic Line Clothoid Circular. Involute Ellipse Hyperbola Parabola Circle Canonically. Parameterised. Hyperbola Canonically. Parameterised. Line Canonically. Parameterised. Ellipse Canonically. Parameterised. Circle BSpline. Curve Canonically. Parameterised. Parabola Canonically. Parameterised. Clothoid Canonically. Parameterised. Circular. Involute

Surface ontology Manifold 2 d Manifold. Projection Sub. Metric. Space Parameterised. Set Surface Non. Self. Intersecting. Surface Bounded. Finite. Surface Oriented. Surface Finite. Surface Unbounded. Surface Infinite. Surface Unbounded. Finite. Surface Ellipsoidal. Surface Toroidal. Surface Conical. Surface Cylindrical. Surface Plane Inner. Degerenate. Toroidal. Surface Spherical. Surface Outer. Degerenate. Toroidal. Surface (Faceted. Plane. Surface. Primitive) Swept. Surface Parameterised. Surface Triangular. Surface Plane. Convex. Quadrilateral. Surface VBounded. Surface VUnbounded. Surface. Curve. Swept. Surface. Of. Linear. Extrusion Surface. Of. Revolution Fixed. Reference. Swept. Surface UBounded. Surface UUnbounded. Surface Cannonically. Parameterised. Fixed. Reference. Swept. Surface BSpline. Surface

Still some loose ends • Key relationships between a physical object and space – occupies. Space c. f. during – has. Centre. Of. Mass – has. Centre. Line • Reference data for GIS systems – WGS 84 – OSGB • Geometry and topology as ISO 10303 -42 + GIS coordinate systems + extensible using ontologies + links to measurements