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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
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~!