ISO 10303-42:1994
(Main)Industrial automation systems and integration — Product data representation and exchange — Part 42: Integrated generic resources: Geometric and topological representation
Industrial automation systems and integration — Product data representation and exchange — Part 42: Integrated generic resources: Geometric and topological representation
La présente partie de l'ISO 10303 spécifie les ressources élémentaires relatives à la représentation géométrique et topologique explicite de la forme d'un produit. Le domaine d'application est déterminé par les exigences relatives à la représentation explicite d'un modèle de produit idéal ; les tolérances et les formes implicites de représentation, en termes de caractéristiques, ne font pas partie du domaine d'application. La géométrie décrite à l'article 4 et la topologie décrite à l'article 5 peuvent être utilisées indépendamment, tout comme elles sont utilisées largement par les différentes formes de modèle géométrique, décrites à l'article 6. En outre, la présente partie de l'ISO 10303 précise les spécialisations des concepts de représentation, où les éléments de représentation sont géométriques.
Systèmes d'automatisation industrielle et intégration — Représentation et échange de données de produits — Partie 42: Ressources génériques intégrées: Représentation géométrique et topologique
General Information
Relations
Standards Content (Sample)
INTERNATIONAL
IS0
STANDARD
10303-42
First edition
1994-l 2-l 5
Industrial automation systems and
integration - Product data representation
and exchange -
Part 42:
Integrated generic resources: Geometric and
topological representation
Sys t&mes d ‘automa tisa tion indus trielle et in t6gra tion - Rep&en ta tion
et Gchange de don&es de produits -
Partie 42: Ressources gbnbriques in t&g&es: Rep&en tation geom&rique
et topologique
Reference number
IS0 10303-42: 1994(E)
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IS0 10303-42:1994(E)
Page
Contents
1
1 Scope . . .e.O.~.~.‘O~O
1
11 . Geometry . e . . . . . . . . . . . . . . . . o o . . o o . . . O . . . ., . o . s . . e
i
‘
2
12 . Topology . e . . . . . . . . . . . 0 . . . . . . . . . 0 . . . . . . . . . . e D . . .
2
13 . Geometric Shape Models O . . . . . e . . . . . . . . . . . . . s . . . . . . . . .
3
2 Normative references . . . . . . . . . . . o . . . . . . . . . . . . . . . . . . . . . . . . .
3
3 Definitions, symbols and abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
31 . Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a . . . . . . .
3
arcwise connected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . O
3.1.1
. . . . . . . . . . . . . 3
. . . . . . . . . .
3.1.2 axi-symmetric . . . . . . . . . .
:. . 4
.....................
3.1.3 bounds
....................................
4
3.1.4 boundary
.................
4
3.1.5 boundary representation solid model (Brep)
..................................
4
3.16 closed curve.
.................................
4
3.1.7 closed surface.
......................
4
3.1.8 completion of a topological entity
....................................
4
connected
3.1.9
.............................
4
3.1.10 connected component
......................
4
3.1.11 constructive solid geometry (CSG)
................................
4
3.1.12 coordinate space
...................................... 4
3.1.13 curve
4
3.1.14 cycle .
...........................
5
3.1.15 d-manifold with boundary
.................................
5
3.1.16 dimensionality
5
3.1.17 domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.................................
5
3.1.18 euler equations
:ej
3.1.19 extent-. .
.......................................
5
3.1.20 finite
................................
5
3.1.21 genus of a graph
...............................
5
3.1.22 genus of a surface
.............................
5
3.1.23 geometrically founded
..............................
5
3.1.24 geometrically related
0 IS0 1994
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or
utilized in any form or by any means, electronic or mechanical, including photocopying and
microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case Postale 56 l W-121 1 Genkve 20 l Switzerland
Printed in Switzerland
ii
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......................... 5
3.1.25 geometric coordinate system
5
......................................
3.1.26 graph
6
3.1.27 handle .
................................. 6
3.1.28 homeomorphic
6
inside .
3.1.29
6
interior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.30
.
6
. . . . . .* . . . . . . . . . . . . l .* . . . . . . . . . . . . . . . .
3.1.31 11st
6
model space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.32
................................... 6
3.1.33 open curve
.................................. 6
open surface
3.1.34
....................................
6
orientable
3.1.35
6
3.1.36 overlap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
................................ 6
parameter range
3.1.37
................................ 6
3.1.38 parameter space
......................... 6
3.1.39 placement coordinate system
.................................. 7
3.1.40 self-intersect
..................................... 7
3.1.41 self-loop
7
set .
3.1.42
..............................
7
3.1.43 space dimensionality
..................................... 7
3.1.44 surface
................................ 7
3.1.45 topological sense
7
32 . Symbols.
7
3.2.1 Geometry and mathematical symbology . . . . . . . . . . . . . . . . . . .
7
3.2.2 Topology symbols . e . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
33 . Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
........................................... 11
4 Geometry
..................................... 12
41 . Introduction
...................... 12
Fundamental concepts and assumptions
42 .
.............................. 12
4.2.1 Space dimensionality
............................ 12
4.2.2 Geometric relationships
............... 13
4.2.3 Parametrisation of analytic curves and surfaces
13
4.2.4 Curves .
13
Surfaces .
4.2.5
................................. 14
4.2.6 Preferred form
.......................... 14
43 . geometry-schema type definitions
................................ 14
4.3.; dimension-count
................................. 14
4.3.2 transition-code
.................... 15
4.3.3 preferred-surface-curverepresent ation
.............................. 15
4.3.4 bspline-curve-form
..............................
16
4.3.5 bspline-surface-form
.................................... 17
knot-type
4.3.6
.............................. 18
4.3.7 extent-enumeration
.............................. 18
4.3.8 trimming-preference
................................ 19
4.3.9 axis2-placement
................................ 19
4.3.10 curve-on-surface
. . .
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4.3.11 pcurve-or-surface
20
.................................
trimming-select
4.3.12
20
...............................
4.3.13 vector-or-direction
20
.........................
44 . geometryschema entity definitions
....................... 20
4.4.1 geometricrepresentation-context
21
.........................
4.4.2 geometricrepresentationitem
22
4.4.3 point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
................................. 23
4.4.4 Cartesian-point
23
.................................
4.4.5 point -on-curve
................................ 24
4.4.6 point -on-surface
24
4.4.7 point -replica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
...............................
4.4.8 degenerate-pcurve
......................... 26
4.4.9 evaluated-degenerate-pcurve
26
....................................
direction
4.4.10
27
4.4.11 vector. .
.................................... 27
4.4.12 placement
................................ 28
4.4.13 axis 1 -placement
28
...............................
4.4.14 axis2-placement -2d
............................... 29
4.4.15 axis2-placement -3d
31
......................
4.4.16 Cartesian-transformation-operator
.................... 33
4.4.17 Cartesian-transformation-operator-3d
.................... 36
4.4.18 Cartesian-transformation-operator_2d
37
4.4.19 curve .
37
4.4.20 line .
38
4.4.21 conic . . . . . . .
38
.................................
4.4.22 circle . . . . .
39
4.4.23 ellipse . . . . . .
41
.................................
4.4.24 hyperbola . . .
43
4.4.25 parabola . . . .
44
.................................
4.4.26 bounded-curve
45
polyline . . . . .
4.4.27
r
43
4.4.28 bspline-curve . .
48
4.4.29 bspline-curve-with-knots . . . . . . . . . . . . . . . . . . . . . . . . . . .
.................................. 50
uniform-curve
4.4.30
.............................. 50
4.4.31 quasi-uniform-curve
51
...................................
4.4.32 bezier-curve
52
rational-b-spline-curve .
4.4.33
54
.................................
4.4.34 trimmed-curve
56
................................
4.4.35 composite-curve
........................... 57
4.4.36 composite-curve-segment
59
..................
4.4.37 reparametrised-composite-curve-segment
59
4.4.38 pcurve .
60
................................
4.4.39 bounded-pcurve
61
..................................
4.4.40 surface-curve
62
4.4.41 intersection-curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
4.4.42 seam-curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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.............................
bounded-surface-curve
4.4.43
64
..........................
composite-curve-on-surface
4.4.44
65
.................................
offset-curve-2d
4.4.45
66
.................................
offset-curve-3d
4.4.46
67
..................................
4.4.47 curve-replica
68
.....................................
4.4.48 surface
69
...............................
4.4.49 elementarysurface
69
plane .
4.4.50
70
...............................
cylindrical-surface
4.4.51
71
.................................
4.4.52 conical-surface
spherical-surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4.53
74
.................................
4.4.54 toroidalsurface
75
..........................
degenerate-toroidal-surface
4.4.55
76
..................................
4.4.56 swept-surface
76
..........................
4.4.57 surface-oflinear-extrusion
77
..............................
surface-of-revolution
4.4.58
78
................................
bounded-surface
4.4.59
78
bspline-surface .
4.4.60
bspline-surface-with-knots . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.4.61
83
.................................
4.4.62 uniform-surface
83
.............................
4.4.63 quasi-uniform-surface
84
..................................
bezier-surface
4.4.64
85
............................
4.4.65 rational-b-spline-surface
86
rectangular-trimmed-surface .
4.4.66
87
..............................
4.4.67 curve-bounded-surface
boundary-curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.4.68
89
.............................
outer-boundary-curve
4.4.69
90
........................
4.4.70 rectangular-composite-surface
91
surface-patch .
4.4.71
92
..................................
4.4.72 offsetsurface
93
.................................
4.4.73 surfaceseplica
94
..........................
geometryschema rule definitions
45 .
94
.............................
4.5.1 compatible-dimension
95
........................
46 . geometryschema function definitions
95
dimension-of .
4.6.1
96
..............................
4.6.2 acyclic-curve-replica
97
..............................
4.6.3 acyclic-point-replica
97
.............................
4.6.4 acyclic-surface-replica
98
...............................
4.6.5 associated-surface
99
base-axis .
4.6.6
100
...................................
4.6.7 build-2axes
100
...................................
4.6.8 build-axes.
101
............................
orthogonal-complement
4.6.9
102
..................................
4.6.10 first-projaxis
103
................................
second-proj-axis
4.6.11
103
..................................
4.6.12 cross-product
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dot-product .
4.6.13
105
normalise .
4.6.14
107
...............................
4.6.15 scalar-times-vector
108
...................................
4.6.16 vectorsum
109
vector-difference .
4.6.17
110
...........................
4.6.18 default-bspline-knotmult
111
default-bspline-knots .
4.6.19
112
........................
default-bspline-curve-weights
4.6.20
113
.......................
4.6.21 default -bspline-surface-weights
114
..........................
constraints-param-b-spline
4.6.22
115
.............................
4.6.23 curve-weights-positive
116
...................
4.6.24 constraints-composite-curve-on-surface
116
4.6.25 get-basis-surface .
117
............................
4.6.26 surface-weights-positive
118
..................
4.6.27 constraints-rectangular-composite-surface
119
4.6.28 list-to-array .
120
..............................
4.6.29 make-array-of-array
122
...........................................
5 Topology
122
. Introduction .
51
122
......................
52 . Fundamental concepts and assumptions
123
5.2.1 Geometric associations .
124
................
5.2.2 Associations with parameter space geometry
126,
.........................
5.2.3 Graphs, cycles, and traversals
127
..........................
53 . topology-schema type definitions
f & . 127
...........................
5.3.1 shell
128
W . L .
5.3.2 reversible-topologyitem .
128
.........................
5.3.3 list-of-reversible-to,poEogyitem
128
set-ofseversible-topologyitem .
5.3.4
128
...............................
5.3.5 reversible-topology
129
.........................
54 . topology-schema entity definitions
129
5.4.1 topological-representationitem .
129
5.4.2 vertex .
130
vertex-point
5.4.3 .
130
edge. .
5.4.4
132
5.4.5 edge-curve .
133
oriented-edge
5.4.6 .
133
5.4.7 path .
5.4.8 oriented-path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
135
open-path. .
5.4.9
136
5.4.10 loop .
5.4.11 vertexloop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.4.12 edgeloop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
138
5.4.13 polyloop .
139
5.4.14 face-bound .
5.4.15 face-outer-bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
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face .
5.4.16 140
5.4.17 face-surface
................................... 142
5.4.18 oriented-face
.................................. 143
5.4.19 subface
143
.....................................
5.4.20 connected-face-set
............................... 144
5.4.21 vertex-shell 144
...................................
5.4.22 wire-shell
145
....................................
5.4.23 open-shell 146
....................................
5.4.24 oriented-open-shell
149
...............................
5.4.25 closed-shell
................................... 150
5.4.26 oriented-closed-shell
.............................. 151
5.4.27 connected-edge-set
............................... 152
55 . topology-schema function definitions
........................ 153
conditional-reverse
5.5.1 153
...............................
topology-reversed
5.5.2 153
...............................
edge-reversed
5.5.3
.................................. 154
path-reversed
5.5.4 155
..................................
5.5.5 face-bound-reversed
155
..............................
faceseversed
5.5.6 156
..................................
shell-reversed
5.5.7 156
..................................
5.5.8 set-of-topology-reversed
............................ 157
list-of-topology_reversed
5.5.9
............................ 158
5.5.10 boolean-choose
................................. 158
5.5.11 path-head-to-tail
................................ 159
5.5.12 list-faceloops
159
..................................
5.5.13 listloop-edges
................................. 160
5.5.14 list-shell-edges
..... ‘. 160
...........................
5.5.15 list-shell-faces
161
..................................
5.5.16 list-shell-loops
................................. 161
5.5.17 mixedloop-typeset
162
..............................
5.5.18 list-to-set
163
....................................
edge-curve-pcurves
5.5.19 163
...............................
5.5.20 vertex-point-pcurves
164
..............................
6 Geometric models
...................................... 166
61 . Introduction
166
.....................................
62 . Fundamental concepts and assumptions
166
......................
.
63 geometric-model-schema type definitions
...................... 167
boolean-operand
6.3.1 167
................................
6.3.2 boolean-operator
............................... 167
csg-primitive
6.3.3 168
..................................
6.3.4 csgselect
168
....................................
6.3.5 geometricsetselect
.............................. 169
6.3.6 surface-model.
169
.................................
6.3.7 wireframemodel
................................ 169
geometricmodel-schema entity definitions
64 .
..................... 170
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................................... 170
6.4.1 solid-model
170
..............................
manifold-solid-brep
6.4.2
173
.................................
brep-with-voids
6.4.3
173
..................................
6.4.4 faceted-brep
174
.....................................
csgsolid
6.4.5
175
.................................
boolean-result
6.4.6
175
......................................
6.4.7 sphere
176
...............................
6.4.8 right-circular-cone
177
.............................
6.4.9 right -circular-cylinder
177
......................................
torus.
6.4.10
178
......................................
block
6.4.11
179
..............................
right -angular-wedge
6.4.12
180
.................................
sweptfacesolid
6.4.13
181
...............................
6.4.14 extruded_facesolid
............................... 181
6.4.15 revolvedface,solid
183
................................
6.4.16 swept-area-solid
183
...............................
6.4.17 extruded-areasolid
184
...............................
6.4.18 revolved-area-solid
185
.................................
6.4.19 half-spacesolid
................................ 185
6.4.20 boxed-half-space
186
...................................
6.4.21 box-domain
186
...................................
6.4.22 solid-replica
187
...........................
6.4.23 shell-basedsurface-model
........................... 188
6.4.24 face,based-surfacemodel
188
.........................
shell-based-wireframe-model
6.4.25
189
.........................
6.4.26 edge-based-wireframe-model
190
..................................
6.4.27 geometric-set
190
..............................
geometric-curve-set
6.4.28
190
..............................
6.4.29 geometricsetseplica
191
...................
65 . geometricmodel-schema function definitions
19 1
..............................
6.5.1 acyclic-solid-replica
192
...............................
6.5.2 acyclic-set-replica
192
..............
6.5.3 constraints-geometry-shell-based-surfacemodel
............. 193
6.5.4 constraints-geometryshell-based-wireframemodel
194
.............................
6.5.5 build-transformed-set
Annexes
Short names of entities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
A
B Information object registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
Computer-interpretable listings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
C
D EXPRESS-G diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
E Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
. . .
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Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Figures
31
1 Axis2 placement 3D .
33
2 (a) Cartesian transformation operator 3D .
34
2 (b) Cartesian transformation operator 3D .
.......................... 35
2 (c) Cartesian transformation operator
39
Circle .
3
40
4 Ellipse. .
42
Hyperbola .
5
44
Parabola .
6
47
B-spline curve. .
7
58
Composite curve .
8
72
Conical surface .
9
Curve bounded surface . 88
10
131
11 Edgecurve .
........................... 179
12 Right angular wedge and its attributes
Revolved face solid . 182
13
D.l geometryschema EXPRESS-G diagram 1 of 12 - Subtypes of geometric representa-
........................................... 205
tionitem
geometryschema EXPRESS-G diagram 2 of 12 - Placement and transformation sub-
D.2
............................................. 206
types
.......... 207
D.3 geometryschema EXPRESS-G diagram 3 of 12- Subtypes of point
......... 208
D.4 geometryschema EXPRESS-G diagram 4 of 12 - Subtypes of curve
. . 209
D5 geometryschema EXPRESS-G diagram 5 of 12 - Subtypes of surface
.......... 210
D6 . geometry-schema EXPRESS-G diagram 6 of 12 - Subtypes of conic
............ 211
D.7 geometry-schema EXPRESS-G diagram 7 of 12 - Surface curve
........... 212
D.8 geometry-schema EXPRESS-G diagram 8 of 12 - Bounded curves
........... 213
D9 . geometry-schema EXPRESS-G diagram 9 of 12 - B-spline-curve
214
D.10 geometryschema EXPRESS-G diagram 10 of 12 - Elementary surface . . . . . . . .
215
D.ll geometryschema EXPRESS-G diagram 11 of 12 - Subtypes of bounded surface . . .
216
D.12 geometry-schema EXPRESS-G diagram 12 of 12 - Bspline-surface . . . . . . . . . .
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D.13 topology-schema EXPRESS-G diagram 1 of 3 - Subtypes of topological representation
item . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
D.14 topology-schema EXPRESS-G diagram 2 of 3 . . . . . . . . . . . . . . . . . . . . . . 218
D.15 topology-schema EXPRESS-G diagram 3 of 3 . . . . . . . . . . . . . . . . . . . . . . 219
D.16 geometricmodelschema EXPRESS-G diagram 1 of 3 - Subtypes of solid model . . . 220
D.17 geometricmodel-schema EXPRESS-G diagram 2 of 3 - CSG solid . . . . . . . . . . 221
D.18 geometricmodelschema EXPRESS-G diagram 3 of 3 - Models of external shape . . 222
Tables
1 Geometry mathematical symbology .
8
2 Topology Symbol Definitions . 9
A.1 Short names of entities . 196
X
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Foreword
is a worldwide federation of national
The International Organization for Standardization (ISO)
standards bodies (IS0 member bodies). The work of preparing International Standards is nor-
mally carried out through IS0 technical committees. Ealch member body interested in a subject
for which a technical committee has been established has the right to be represented on that
International organizations, government al and non-government al, in liaison with
committee.
ISO, also take part in the work. IS0 collaborates closely with the International Electrotechnical
on all matters of electrotechnical standardization.
Commission (IEC)
Draft International Standards adopted by technical committees are circulated to the member
Publication as an International Standard requires approval by at least 7’5%
bodies for voting.
of the member bodies casting a vote.
International Standard IS0 10303-42 was prepared by Technical Committee ISO/TC 184, In-
dustrial automation systems and integration, Subcommittee SC4, Industrial data and global
manufacturing programming languages.
IS0 10303 consists of the following parts under the general title Industrial automation systems
and integration - Product data representation and exchange:
- Part 1, Overview and fundamental principles;
- Part 11, Description methods: The EXPRESS language reference manual;
- Part 21, Implementation methods: Clear text encoding of the exchange structure;
- Part 22, Implementation methods: Standard data access interface specification;
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Part 31, Conformance testing methodology and framework: General concepts;
- Part 32, Conformance testing methodology and framework: Requirements on testing
laboratories and clients;
- Part 41, Integrated generic resources: Fundamentals of product description and support;
Geometric and topological representation;
- Part 42, Integrated generic resources:
- Part 43, Integrated generic resources: Representation structures;
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Part 44, Integrated generic resources: Product structure configuration;
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Part 45, Integrated generic resources: Materials;
- Part 46, Integrated generi c resources: Visual presen tation;
- Part 47, Integrated generic resources: Shape variation tolerances;
Process structure and properties;
Part 49, Integrated generic resources:
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Part 101, Integrated application resources: Draughting;
- Part 104, Integrated application resources: Finite element analysis;
- Part 105, Integrated application resources: Kinematics;
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Part 201, Application protocol: Explicit draughting;
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Part 202, Application protocol: Associative draughting;
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Part 203, Application protocol: Configuration controlled design;
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Part 207, Application protocol: Sheet metal die planning and design;
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Part 210, Application protocol: Printed circuit assembly product design data;
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Part 213, Application protocol: Numerical control process plans for machined parts.
The structure of this International Standard is described in IS0 10303-l. The numbering of the
parts of this International Standard reflects its structure:
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Part 11 specifies the description methods;
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Parts 21 and 22 specify the implementation methods;
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Parts 31 and 32 specify the conformance testing methodology and framework;
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Parts 41 to 49 specify the integrated generic resources;
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Parts 101 to 105 specify the integrated application resources;
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Parts 201 to 213 specify the application protocols.
Should further parts be published, they will follow the same numbering pattern.
Annexes A and B form an integral part of this part of IS0 10303. Annexes C, D, E are for
information only.
Diskette
Users should note that this part of IS0 10303 comprises a diskette:
- the short names of entities given in annex A are also included on the diskette;
- the EXPRESS listings (annex C) are provided on the diskette only;
a method to enable users to report errors in the documentation is given. Full details are
provided in the file.
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Introduction
IS0 10303 is an International Standard for the computer-interpretable representation and ex-
change of product data. The objective is to provide a neutral mechanism capable of describing
product data throughout the life cycle of a product independent from any particular system.
The nature of this description makes it suitable not only for neutral file exchange, but also as a
basis for implementing and sharing product databases and archiving.
This International Standard is organized as a series of parts, each published separately. The
parts of IS0 10303 fall into one of the following series: description methods, integrated resources,
application protocols, abstract test suites, implementation methods, and conformance testing.
The series are described in IS0 10303-l. This part of IS0 10303 is a member of the integrated
resources series. Major subdivisions of this Int
...
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