The concept of 3D Geometry Model based on ISO-19107

1. The concept of 3D Geometry Model based on ISO-19107 Chan-Hyun Kang

2. What is the geometry model? • Data Model • Geometry Data Model • ISO 19107 • International standard of geometry data model

3. About 2-D • Geometric object In a 2-dimensinal coordinate reference system Point Curve Surface

4. Point and Curve in 2 - D • Point • The boundary is null. • Curve • The boundary is Start Point and End Point. • Orientation p2 ( 3, 8 ) p1 ( 3, 3 ) Point p ( 5, 5 ) P1→ P2 P2→ P1 Curve C1 = (P1 → P2) Curve C2 = (P2 → P1) C1 = - C2

5. Surface in 2 - D • Surface • Consists of a number of curves connected in a cycle. • The boundary is curves. Point P1, P2, P3, P4 Curve C1, C2, C3, C4 C1 = (P1 → P2) or C1 = (P2 → P1) C2 = (P2 → P3) or C2 = (P3 → P4) C3 = (P3 → P4) or C3 = (P4 → P3) C4 = (P4 → P1) or C4 = (P1 → P4) Surface S S = {C1, C2, C3, C4 } or {C1, C4, C3, C2 } ? How can you know interior?

6. Surface in 2 - D • In general geometry model • Interior is the left side of curves orientation. (Counterclockwise) Point P1, P2, P3, P4 Curve C1, C2, C3, C4 if Orientation A C1 = (P1 → P2) C2 = (P2 → P3) C3 = (P3 → P4) C4 = (P4 → P1) if Orientation B C1 = (P2 → P1) C2 = (P3 → P2) C3 = (P4 → P3) C4 = (P1 → P4) B A then Surface S S = {-C1, -C2, -C3, -C4 } S = {C1, C2, C3, C4 }

7. Use of Orientation in Curve • Constraint of order of curves in the boundary of surface. • The end point of each curve is the start point of the next curve • Surface Interior , exterior • Reduce duplication of data S1 S2 S = {C1, C2, C3, C4 } S2 = {C5, C6, C7, -C2 }

8. About 3-D • Geometric object In a 3-dimensinal coordinate reference system Point Curve Surface Solid

9. Solid • Solid • Consists of a number of surface connected in a cycle. • The boundary is surfaces Solid So = { S1, S2, S3, S4, S5, S6 } How can you know interior of solid?

10. Surface in 3-D • Surface • Orientation • The conceptual “up” and “down” direction of surface • The upNormal + : The front side (outward) - : The back side (inside)

11. Solid

12. Use of Orientation in Surface • Solid Inside , Outward • Reduce duplication of data S2 SO2 = {S5, C6, C7, -S2, S8, S9 } SO1 = {S1, S2, S3, S4, S5,S6 }

13. Geometry basic classes in ISO 19107 Figure - Geometry basic classes with specialization relations in ISO 19107 -

14. Boundary Figure – GM_Boundary -

15. Boundary Interior boundary GM_Surface s1 Interior boundary Exterior boundary Exterior boundary

16. GM_Point • The DirectPosition depend on coordinate Reference system • GM_Point constructor • Using DirectPosition • p1 = GM_Point < position = < 2, 3 > > • Using GM_PointRef • p2 = GM_Point < position = p1 > Figure – GM_Point -

17. Orientation Figure – GM_OrientablePrimitive -

18. GM_Curve • GM_Curve constructor • Using GM_CurveSegment C1=GM_Curve < segment =< CP1, CP2, CP3> > CP3 CP2 CP1 This is answer for question! How can you express this curve that is not linear? Figure – GM_Curve -

19. GM_CurveSegment Default Figure – GM_CurveSegment -

20. Example GM_LineString GM_ArcString GM_LineSegment GM_Arc GM_BSplineCurve

21. GM_Surface • GM_Surface constructor • Using GM_SurfacePatch • Using GM_SurfaceBoundary • 2 coordinate space • GM_Surface is plane in 3 coordinate space S1 = GM_Surface < patch =< SP1, SP2, SP3> > SP1 SP2 SP3 This is answer! You want to represent more complex surface, aren't you? Figure – GM_Surface -

22. GM_SurfacePatch Default Figure – GM_SurfacePatch -

23. Example GM_ParametericCurveSurface GM_Cone GM_PolyhedralSurfaec GM_Cylinder GM_Sphere

24. GM_Solid • GM_Solid constructor • Using GM_SolidBoundary Figure – GM_Solid -

25. The rule of ISO19107 Figure – Overview of data interchange between two systems - ISO 19107 is Application schema for geometry

26. Consideration 3D Model • 3D Geometric Data • The quantity of data is huge. • LOD (Level of Detail) • For the various application • The quantity of data transmission as well as visualization. Thank you for the listening~!