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

Point Curve Surface

Geometric object In a 2-dimensinal coordinate reference system

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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

Point p ( 5, 5 )

p1 ( 3, 3 ) p2 ( 3, 8 )

P1 → P2

P2 → P1

Curve C1 = (P1 → P2)Curve C2 = (P2 → P1)

C1 = - C2

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Surface in 2 - D

P3

P1 P2

P4

C1

C3

C2C4 S

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?

Surface Consists of a number of curves connected in a cycle. The boundary is curves.

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Surface in 2 - D

P3

P1 P2

P4

C1

C3

C2C4 S

Point P1, P2, P3, P4Curve C1, C2, C3, C4

if Orientation AC1 = (P1 → P2) C2 = (P2 → P3) C3 = (P3 → P4)C4 = (P4 → P1)then Surface S

S = {C1, C2, C3, C4 }

In general geometry model Interior is the left side of curves orientation. (Counterclockwise)

AB

if Orientation BC1 = (P2 → P1) C2 = (P3 → P2) C3 = (P4 → P3)C4 = (P1 → P4)

S = {-C1, -C2, -C3, -C4 }

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C1

C3

C2C4

C5

C7

C6

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

Point Curve Surface

Geometric object In a 3-dimensinal coordinate reference system

Solid

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Solid

S1

S2

S3

S4 S5

S6

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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P1

P2P3

P4

P5

P6P7

P8

Solid

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Use of Orientation in Surface

Solid Inside , Outward Reduce duplication of data

S2

SO1 = {S1, S2, S3, S4, S5,S6 }SO2 = {S5, C6, C7, -S2, S8, S9 }

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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

Exterior boundary

Interior boundary

GM_Surface s1

Interior boundary

Exterior boundary

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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 -

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Orientation

Figure – GM_OrientablePrimitive -

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GM_Curve

GM_Curve constructor Using GM_CurveSegment

Figure – GM_Curve -

C1=GM_Curve < segment =< CP1, CP2, CP3> >

CP1CP2

CP3

How can you express this curve that is not linear? This is answer for question!

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GM_CurveSegment

Figure – GM_CurveSegment -

Default

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Example

GM_LineSegment

GM_Arc

GM_ArcString

GM_LineString

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

SP1 SP2

SP3

S1 = GM_Surface < patch =< SP1, SP2, SP3> >

Figure – GM_Surface -

You want to represent more complex surface, aren't you? This is answer!

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GM_SurfacePatch

Figure – GM_SurfacePatch -

Default

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Example

GM_ParametericCurveSurface GM_Cone GM_PolyhedralSurfaec

GM_SphereGM_Cylinder

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GM_Solid

Figure – GM_Solid -

GM_Solid constructor Using GM_SolidBoundary

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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~!