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

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
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Point

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The boundary is null.
Curve

The boundary is Start Point and End Point.
 Orientation
p1 ( 3, 3 )
Point p ( 5, 5 )
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

Surface

Consists of a number of curves connected in a cycle.
 The boundary is curves.
P4
C3
P3
Point P1, P2, P3, P4
Curve C1, C2, C3, C4
C4
S
C2
C1 = (P1 → P2)
C2 = (P2 → P3)
C3 = (P3 → P4)
C4 = (P4 → P1)
or
or
or
or
C1 = (P2 → P1)
C2 = (P3 → P4)
C3 = (P4 → P3)
C4 = (P1 → P4)
Surface S
S = {C1, C2, C3, C4 } or {C1, C4, C3, C2 } ?
P1
C1
P2
How can you know interior?
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Surface in 2 - D
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In general geometry model

Interior is the left side of curves orientation. (Counterclockwise)
P4
C3
P3
Point P1, P2, P3, P4
Curve C1, C2, C3, C4
C4
S
B
A
C2
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)
then Surface S
S = {C1, C2, C3, C4 } S = {-C1, -C2, -C3, -C4 }
P1
C1
P2
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Use of Orientation in Curve
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Constraint of order of curves in the boundary of surface.

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The end point of each curve is the start point of the next curve
Surface Interior , exterior
Reduce duplication of data
C3
C4
S1
C1
S = {C1, C2, C3, C4 }
C7
C2
S2
C6
C5
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
S1
S3
S6
S5
S4
S2
Solid So = { S1, S2, S3, S4, S5, S6 }
How can you know interior of solid?
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Surface in 3-D
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Surface

Orientation
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The conceptual “up” and “down” direction of surface
The upNormal
+ : The front side (outward)
- : The back side (inside)
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Solid
P1
P2
P4
P3
P5
P6
P8
P7
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Use of Orientation in Surface
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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
Interior
boundary
GM_Surface s1
Interior
boundary
Exterior
boundary
Exterior
boundary
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GM_Point
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The DirectPosition depend on coordinate Reference system
GM_Point constructor

Using DirectPosition


p1 = GM_Point < position = < 2, 3 > >
Using GM_PointRef
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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
C1=GM_Curve < segment =< CP1, CP2, CP3> >
CP1
CP2
CP3
How can you express this curve that is not linear?
This is answer for question!
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
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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
You want to represent more complex surface, aren't you?
This is answer!
Figure – GM_Surface -
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GM_SurfacePatch
Default
Figure – GM_SurfacePatch -
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Example
GM_ParametericCurveSurface
GM_Cylinder
GM_Cone
GM_PolyhedralSurfaec
GM_Sphere
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GM_Solid
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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
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3D Geometric Data

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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~!