The concept of 3D Geometry Model based on ISO19107

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

• Chan-Hyun Kang

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What is the geometry model?

• Data Model
• Geometry Data Model
• ISO 19107
• International standard of geometry data model

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About 2-D

• Geometric object In a 2-dimensinal coordinate
  reference system

Point
Curve
Surface
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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
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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?
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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
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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
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About 3-D

• Geometric object In a 3-dimensinal coordinate
  reference system

Point
Curve
Surface
Solid
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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?
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Surface in 3-D

• Surface
• Orientation
• The conceptual up and down direction of
  surface
• The upNormal

The front side (outward)
- The back side (inside)
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Solid
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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
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Geometry basic classes in ISO 19107
Figure - Geometry basic classes with
specialization relations in ISO 19107 -
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Boundary
Figure GM_Boundary -
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Boundary
Interior boundary
GM_Surface s1
Interior boundary
Exterior boundary
Exterior boundary
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GM_Point

• The DirectPosition depend on coordinate Reference
  system
• GM_Point constructor
• Using DirectPosition
• p1 GM_Point lt position lt 2, 3 gt gt
• Using GM_PointRef
• p2 GM_Point lt position p1 gt

Figure GM_Point -
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Orientation
Figure GM_OrientablePrimitive -
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GM_Curve

• GM_Curve constructor
• Using GM_CurveSegment

C1GM_Curve lt segment lt CP1, CP2, CP3gt gt
CP3
CP2
CP1
This is answer for question!
How can you express this curve that is not linear?
Figure GM_Curve -
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GM_CurveSegment
Default
Figure GM_CurveSegment -
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Example
GM_LineString
GM_ArcString
GM_LineSegment
GM_Arc
GM_BSplineCurve
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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 lt patch lt SP1, SP2, SP3gt gt
SP1
SP2
SP3
This is answer!
You want to represent more complex surface,
aren't you?
Figure GM_Surface -
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GM_SurfacePatch
Default
Figure GM_SurfacePatch -
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Example
GM_ParametericCurveSurface
GM_Cone
GM_PolyhedralSurfaec
GM_Sphere
GM_Cylinder
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GM_Solid

• GM_Solid constructor
• Using GM_SolidBoundary

Figure GM_Solid -
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The rule of ISO19107
Figure Overview of data interchange between two
systems -
ISO 19107 is Application schema for geometry
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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!