ISO19107 Geographic information – Spatial schema Pusan National University Dept. of Computer Engineering Spatiotemporal Database Lab. Joon-Seok Kim

2 Outline Introduction Schema –Geometry Geometry root Geometry primitive Coordinate geometry Geometry aggregate Geometry complex –Topology Topology root Topology primitive Topology complex Summary

3 Introduction ISO19107 –Providing conceptual schemas for describing and manipulating the spatial characteristic –Formal language Unified Modeling Language (UML) ISO19103 –Vector geometry and topology up to 3-D –Spatial operations For use in access, query, management, processing, and data exchange of geographic information

4 Package Clients of ISO19107

5 Package Suppliers of ISO19107

6 Main Diagram of ISO19107 Spatial Schema

Geometry

8 Geometry Packages

9 Geometry basic classes

10 Basic Concept Geometry object  Infinite set of points Point Line Rectangle …  Point set theory

11 Concept of Interior, Exterior and Boundary U Boundary Interior Exterior Interior U Boundary = Closure

12 Boundary and Dimension Dim.BoundaryExample Point0Empty Curve1Point Surface2Curve Solid3Surface

13 Simple and Cycle se s e s e se (a)(b)(c)(d) simplecycle (a), (b), (d)(d)

14 GM_Object

15 convexHull() and buffer() convexHull()buffer (radius: d) d

16 Geometry Boundary Data Types

17 The Number of Exterior of GM_SurfaceBoundary x y x z y 2-Dimension plane  1 exterior 3-Dimension surface  0 exterior

18 GM_Primitive

Geometric Primitive

20 GM_Point

21 Concept of Orientation s e For curves, direction in which the curve is traversed When used as bounding curves, “left” of oriented curve For surfaces, Z-axis that would form a right-handed system When used as bounding surfaces, “below” the surface “+” “-” “+”

22 GM_OrientedPrimitive

23 GM_Curve

24 GM_Surface

25 GM_Solid

Coordinate Geometry

27 DirectPosition

28 Curve segment classes

29 Linear and Geodetic Interpolation

30 Arcs

31 Conics and placements

32 Spline and specialty curves

33 Surface patches

34 Polygonal surface

35 TIN construction

36 GM_ParmetricCurveSurface and its subtypes

Geometric Aggregate Geometric Complex

38 GM_Aggregate

39 GM_Complex

40 CM_Composite

Topology

42 Concept of Topology Topology –Deal with characteristics of geometric figures that remain invariant if the space is deformed elastically and continuously –E.g. connectivity of an n-dimensional graph

43 Topology packages

44 Topological class diagram

45 Relation between geometry and topology

46 TP_Object

47 Boundary and coboundary operation

48 Boundary relation data types

49 TP_Primitive

50 TP_DirectedTopo subclasses

51 TP_Node

52 TP_Edge

53 TP_Face

54 TP_Solid

55 TP_Expression

56 TP_Complex

Summary

58 Geometry and Topology Packages

59 Geometry basic classes

60 Geometry Boundary Data Types

61 Topological class diagram

62 Relation between geometry and topology

Spatial Examples from ISO19107

64 Geometric objects in a 2-D CRS

65 P1 = GM_Point > P2 = GM_Point > P3 = GM_Point > P4 = GM_Point > P5 = GM_Point > P6 = GM_Point > P7 = GM_Point >

66 CS1 = GM_CurveSegment, interpolation = “linear” > CS2 = GM_CurveSegment, interpolation = “linear” > CS3 = GM_CurveSegment, interpolation = “linear” > CS4 = GM_CurveSegment, interpolation = “linear” > CS5 = GM_CurveSegment interpolation = “arc”> CS6 = GM_CurveSegment, interpolation = “linear” > CS7 = GM_CurveSegment, interpolation =“linear”>

67 C1 = GM_Curve segments = C2 = GM_Curve segments = C3 = GM_Curve segments = C4 = GM_Curve segments = C5 = GM_Curve segments = C6 = GM_Curve segments =

68 S0 = GM_Surface patch = > > S1 = GM_Surface patch =, interior = > > S2 = GM_Surface patch =, interior = > > S3 = GM_Surface patch = >

69 Lake = AreaFeature featureType=“Hydrography::WaterBody”, extent = S3 RoadCenterline = LineFeature featureType = “Transportation::Road”, centerline = C2 RoadArea = RoadCenterLine.centerline.buffer RoadExtent = AreaFeature featureType = “LandCover::Road”, extent = RoadArea RoadInstance = ComplexFeature featureType = “LandUse::Road”, featureComponents = {RoadCenterline, RoadArea } Trail = LineFeature featureType = “CulturalFacilities::HikingTrail”, centerline = C5 School = PointFeature featureType = “CulturalFacilities::School”, Location = P4