ISO 10303-108:2005

INTERNATIONAL ISO
STANDARD 10303-108
First edition
2005-02-01
Industrial automation systems and
integration — Product data
representation and exchange —
Part 108:
Integrated application resource:
Parameterization and constraints for
explicit geometric product models
Systèmes d'automatisation industrielle et intégration — Représentation
et échange de données de produits —
Partie 108: Ressources d'application intégrées: Paramétrage et
contraintes pour les modèles de produits géométriques explicites

Reference number
©
ISO 2005
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ii © ISO 2005 – All rights reserved

Contents Page
1 Scope . . . . . . . . . 1
1.1 Parameterizationschema . . . . . . . 2
1.2 Explicitconstraintschema . . . . . . 3
1.3 Variational representation schema . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Explicit geometric constraint schema . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Sketchschema . . . . . . . . 4
2 Normativereferences . . . . . . . . 4
3 Terms, definitions and abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.1 TermsdefinedinISO10303-1 . . . . . . 5
3.2 TermsdefinedinISO10303-11 . . . . . . 6
3.3 TermsdefinedinISO10303-42 . . . . . . 6
3.4 TermsdefinedinISO10303-43 . . . . . . 6
3.5 TermsdefinedinISO10303-50 . . . . . . 7
3.6 TermsdefinedinISO13584-20 . . . . . . 7
3.7 Othertermsanddefinitions . . . . . . 7
3.8 Abbreviations . . . . . . . . 14
4 Parameterization . . . . . . . . 15
4.1 Introduction . . . . . . . . 15
4.2 Fundamental concepts and assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2.1 Modelparameters . . . . . . . 16
4.2.2 Parameter binding to an instance attribute . . . . . . . . . . . . . . . . . . . . . 17
4.3 Parameterization type definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.3.1 attributeidentifier . . . . . . . 18
4.4 Parameterization entity definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.4.1 modelparameter . . . . . . . 19
4.4.2 bound modelparameter . . . . . . 20
4.4.3 unbound modelparameter . . . . . . 22
4.4.4 bound parameterenvironment . . . . . . 23
4.4.5 unbound parameterenvironment . . . . . 23
4.4.6 instance attributereference . . . . . . 24
4.4.7 unbound model parametersemantics . . . . . 25
4.4.8 fixed instance attributeset . . . . . . 25
4.4.9 generated finite numericspace . . . . . 26
4.5 Parameterization function definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.5.1 make numericset . . . . . . . 27
4.5.2 validate attributeid . . . . . . 28
5 Explicitconstraint . . . . . . . . 30
5.1 Introduction . . . . . . . . 30
5.2 Fundamental concepts and assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.2.1 Free-form and defined constraints . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.2.2 Simultaneous groups of constraints . . . . . . . . . . . . . . . . . . . . . . . . 32
5.2.3 Use of the current result in the resolution of ambiguities . . . . . . . . . . . . . 32
5.2.4 Directed and undirected constraints . . . . . . . . . . . . . . . . . . . . . . . . 33
5.2.5 Roles of model parameters in free-form constraints . . . . . . . . . . . . . . . . 33
5.2.6 Accuracy of constraint satisfaction . . . . . . . . . . . . . . . . . . . . . . . . . 34
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5.3 Explicit constraint type definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.3.1 constraint group member . . . . . . 34
5.4 Explicit constraint entity definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.4.1 explicit constraint . . . . . . . 34
5.4.2 definedconstraint . . . . . . . 35
5.4.3 equal parameterconstraint. . . . . . 36
5.4.4 free formconstraint . . . . . . 37
5.4.5 free formassignment . . . . . . 38
5.4.6 free formrelation . . . . . . . 39
5.4.7 simultaneous constraintgroup . . . . . . 40
6 Variationalrepresentation . . . . . . . 43
6.1 Introduction . . . . . . . . 43
6.2 Fundamental concepts and assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 43
6.3 Variational representation entity definitions . . . . . . . . . . . . . . . . . . . . . . . 45
6.3.1 variational representationitem . . . . . 45
6.3.2 auxiliary geometric representationitem. . . . . 46
6.3.3 variationalrepresentation . . . . . . 46
6.3.4 variational current representationrelationship . . . . 48
6.4 Variational representation function definitions . . . . . . . . . . . . . . . . . . . . . . 49
6.4.1 invalidate vrepitem . . . . . . 49
7 Explicitgeometricconstraint . . . . . . . 52
7.1 Introduction . . . . . . . . 52
7.2 Fundamental concepts and assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 52
7.2.1 Dimensional constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
7.2.2 Semantics of dimensional constraints . . . . . . . . . . . . . . . . . . . . . . . 55
7.2.3 Constraints on procedurally defined model elements . . . . . . . . . . . . . . . 56
7.3 Explicit geometric constraint type definitions . . . . . . . . . . . . . . . . . . . . . . 56
7.3.1 geometric constraintelement . . . . . . 56
7.3.2 point curve or surface constraintelement. . . . 57
7.3.3 curve or surface constraintelement . . . . . 57
7.3.4 linear geometry constraintelement . . . . . 57
7.3.5 radial geometry constraintelement . . . . . 57
7.3.6 axial geometry constraintelement . . . . . 58
7.3.7 swept surface orsolid . . . . . . 59
7.3.8 tangent contacttype . . . . . . 59
7.3.9 parallel offsettype . . . . . . . 59
7.3.10 non negative lengthmeasure . . . . . . 60
7.4 Explicit geometric constraint entity definitions . . . . . . . . . . . . . . . . . . . . . 60
7.4.1 explicit geometricconstraint. . . . . . 60
7.4.2 fixed element geometricconstraint . . . . . 61
7.4.3 parallel geometricconstraint . . . . . . 62
7.4.4 pgc withdimension . . . . . . 63
7.4.5 point distance geometricconstraint . . . . . 64
7.4.6 pdgc withdimension. . . . . . 65
7.4.7 skew line distance geometricconstraint . . . . 65
7.4.8 near pointrelationship . . . . . . 66
7.4.9 curve distance geometricconstraint . . . . . 67
7.4.10 cdgc withdimension . . . . . . 69
7.4.11 surface distance geometricconstraint . . . . . 69
7.4.12 sdgc withdimension . . . . . . 71
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7.4.13 radius geometricconstraint . . . . . . 72
7.4.14 rgc with dimension . . . . . . 72
7.4.15 curve length geometricconstraint . . . . . 73
7.4.16 clgc with dimension . . . . . . 74
7.4.17 parallel offset geometricconstraint . . . . . 74
7.4.18 pogc withdimension. . . . . . 76
7.4.19 angle geometricconstraint. . . . . . 77
7.4.20 agc withdimension . . . . . . 78
7.4.21 perpendicular geometricconstraint . . . . . 79
7.4.22 incidence geometricconstraint . . . . . 80
7.4.23 coaxial geometricconstraint . . . . . . 82
7.4.24 tangent geometricconstraint. . . . . . 82
7.4.25 symmetry geometricconstraint . . . . . 84
7.4.26 swept point curve geometricconstraint . . . . . 86
7.4.27 swept curve surface geometricconstraint . . . . 87
7.4.28 curve segmentset . . . . . . . 88
7.4.29 curve smoothness geometricconstraint . . . . . 89
7.4.30 surface patchset . . . . . . . 90
7.4.31 surface smoothness geometricconstraint . . . . 90
8 Sketch . . . . . . . . . 92
8.1 Introduction . . . . . . . . 92
8.2 Fundamental concepts and assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 92
8.3 Sketchtypedefinitions . . . . . . . 93
8.3.1 surface or solidmodel . . . . . . 93
8.3.2 planar curveselect . . . . . . . 94
8.3.3 sketch elementselect . . . . . . 95
8.3.4 sketch basisselect . . . . . . . 95
8.3.5 sketch typeselect . . . . . . . 95
8.3.6 curves orarea . . . . . . . 96
8.4 Sketchentitydefinitions . . . . . . . 96
8.4.1 implicit point onplane . . . . . . 96
8.4.2 implicit planar intersectionpoint . . . . . 98
8.4.3 implicit planar projectionpoint . . . . . 98
8.4.4 implicit planarcurve . . . . . . 99
8.4.5 implicit intersectioncurve . . . . . . 100
8.4.6 implicit projectedcurve . . . . . . 100
8.4.7 implicit model intersectioncurve . . . . . 101
8.4.8 implicit silhouettecurve. . . . . . 101
8.4.9 neutral sketchrepresentation . . . . . . 102
8.4.10 positionedsketch. . . . . . . 103
8.4.11 repositioned neutralsketch . . . . . . 105
8.4.12 implicit explicit positioned sketchrelationship . . . . 106
8.4.13 subsketch . . . . . . . . 107
8.4.14 rigidsubsketch . . . . . . . 108
8.5 Sketchfunctiondefinitions . . . . . . 108
8.5.1 get relative direction2points . . . . . . 108
8.5.2 check curveplanarity . . . . . . 109
8.5.3 get plane of implicitgeometry . . . . . 110
Annex A (normative) Short names of entities . . . . . . . . . . . . . . . . . . . . . . . . . . 113
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Annex B (normative) Information object registration . . . . . . . . . . . . . . . . . . . . . 115
B.1 Documentidentification . . . . . . . 115
B.2 Schemaidentification . . . . . . . 115
B.2.1 parameterization schemaidentification . . . . . 115
B.2.2 explicit constraint schema identification . . . . . . . . . . . . . . . . . . . . . 115
B.2.3 variational representation schema identification . . . . . . . . . . . . . . . . . 115
B.2.4 explicit geometric constraint schema identification . . . . . . . . . . . . . . . . 116
B.2.5 sketchschemaidentification . . . . . . 116
Annex C (informative) Computer interpretable listings . . . . . . . . . . . . . . . . . . . . . 117
Annex D (informative) EXPRESS-G diagrams . . . . . . . . . . . . . . . . . . . . . . . . . 118
Annex E (informative) Technical discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 137
E.1 Role of parameterization and constraints in procedural and hybrid representations . . . 137
E.2 Justification of representational choices made in this part of ISO 10303 . . . . . . . . 139
E.2.1 Non-binary constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
E.2.2 The modelling of variational representations . . . . . . . . . . . . . . . . . . . 140
E.3 Application-related sketches with specific geometric forms . . . . . . . . . . . . . . . 141
AnnexF(informative) Examples. . . . . . . 142
F.1 Examples of the intended usage of the ISO 10303-108 mechanism for linking param-
eters with attributes of entity instances . . . . . . . . . . . . . . . . . . . . . . . . . . 142
F.1.1 Example1 . . . . . . . 142
F.1.2 Example2 . . . . . . . 144
F.1.3 Relationship between ISO 10303-108 and ISO 13584-20 . . . . . . . . . . . . . 145
F.2 Example of a two-dimensional sketch . . . . . . . . . . . . . . . . . . . . . . . . . . 147
F.3 Usage of ISO 10303-108 for the representation of incompletely defined models . . . . 148
Bibliography . . . . . . . . . 151
Index . . . . . . . . . . 152
Figures
Figure 1 Schema level diagram of relationships between ISO 10303-108 schemas (inside the
box)andotherresourceschemas . . . . . . xi
Figure 2 Schema level diagram of relationships among ISO 10303-108 schemas . . . . . . . xii
Figure 3 Embedding of a current result representation in a variational representation. 45
Figure D.1 EXPRESS-G diagram of the parameterization schema (1 of 2) . . . . . . . . . . . 119
Figure D.2 EXPRESS-G diagram of the parameterization schema (2 of 2) . . . . . . . . . . . 120
Figure D.3 EXPRESS-G diagram of the explicit constraint schema (1 of 1) . . . . . . . . . . . 121
Figure D.4 EXPRESS-G diagram of the variational representation schema (1 of 1) . . . . . . . 122
Figure D.5 EXPRESS-G diagram of the explicit geometric constraint schema (1 of 10) . . . . 123
Figure D.6 EXPRESS-G diagram of the explicit geometric constraint schema (2 of 10) . . . . 124
Figure D.7 EXPRESS-G diagram of the explicit geometric constraint schema (3 of 10) . . . . 125
Figure D.8 EXPRESS-G diagram of the explicit geometric constraint schema (4 of 10) . . . . 126
Figure D.9 EXPRESS-G diagram of the explicit geometric constraint schema (5 of 10) . . . . 127
Figure D.10 EXPRESS-G diagram of the explicit geometric constraint schema (6 of 10) . . . . 128
Figure D.11 EXPRESS-G diagram of the explicit geometric constraint schema (7 of 10) . . . . 129
Figure D.12 EXPRESS-G diagram of the explicit geometric constraint schema (8 of 10) . . . . 130
Figure D.13 EXPRESS-G diagram of the explicit geometric constraint schema (9 of 10) . . . . 131
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Figure D.14 EXPRESS-G diagram of the explicit geometric constraint schema (10 of 10) . . . 132
Figure D.15 EXPRESS-G diagram of the sketch schema(1of4) . . . . 133
Figure D.16 EXPRESS-G diagram of the sketchschema(2of4) . . . . 134
Figure D.17 EXPRESS-G diagram of the sketch schema(3of4) . . . . 135
Figure D.18 EXPRESS-G diagram of the sketchschema(4of4) . . . . 136
Figure F.1 Key relationships between ISO 10303-108 parameterization schema and ISO
13548 generic expressions schema . . . . . . 146
Figure F.2 A simple sketch composed of line segments and circular arcs . . . . . . . . . . . . 147
Tables
A.1 Shortnamesofentities . . . . . . . 113
c ISO 2005 — All rights reserved vii

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical com-
mittee has been established has the right to be represented on that committee. International organizations,
governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates
closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical stan-
dardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Stan-
dards adopted by the technical committees are circulated to the member bodies for voting. Publication
as an International Standard requires approval by at least 75% of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this part of ISO 10303 may be the
subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 10303–108 was prepared by Technical Committee ISO/TC184, Industrial automation systems
and integration, Subcommittee SC4, Industrial data.
ISO 10303 consists of a series of parts, under the general title Industrial automation systems and inte-
gration — Product data representation and exchange. The structure of ISO 10303 is described in ISO
10303-1.
Each part of ISO 10303 is a member of one of the following series: description methods, implementa-
tion methods, conformance testing methodology and framework, integrated generic resources, integrated
application resources, application protocols, abstract test suites, application interpreted constructs, and
application modules. This part is a member of the integrated application resources series. The inte-
grated generic resources and the integrated application resources specify a single conceptual product
data model.
A complete list of parts of ISO 10303 is available from the Internet:

viiic ISO 2005 — All rights reserved

Introduction
ISO 10303 is an International Standard for the computer-interpretable representation of product infor-
mation and for the exchange of product data. The objective is to provide a neutral mechanism capable of
describing products throughout their life cycle. This mechanism is suitable not only for neutral file ex-
change, but also as a basis for implementing and sharing product databases, and as a basis for archiving.
This part of ISO 10303 is a member of the integrated resources series. Major subdivisions of this part of
ISO 10303 are:
— Parameterization schema;
— Explicit constraint schema;
— Variational representation schema;
— Explicit geometric constraint schema;
— Sketch schema.
This part of ISO 10303 provides representations of parameters and constraint relationships for use in
models exchanged using ISO 10303, and specifies mechanisms for the association of such elements with
other elements of the models in which they apply. Parameters and constraints are used in CAD systems
to indicate, respectively, variant and invariant characteristics of a model under editing operations. This
part of ISO 10303 also specifies representations forsketches, two-dimensional geometric configurations,
possibly including parameters and constraints, that are often used by CAD systems as basic elements in
constructional operations.
Models with explicitly represented parameterization and constraints are described asvariational. The
schemas provided are intended in the first instance to supplement the ISO 10303 integrated generic
resources to allow the representation of product shape models enhanced with variational information.
However, the basic mechanisms provided in the first three schemas can be used for representing parame-
terization and constraints in the context of any ISO 10303 model, whether of a product, a plan, a process
or an organization.
Other resource parts of ISO 10303 provide capabilities for the representation and exchange of models
having no associated variational information. That information, if present in the originating system,
affects the behaviour of a model under editing operations there; it forms an important part of what is
sometimes referred to as design intent. The use of this part of ISO 10303 for its capture and transfer
potentially allows the reconstruction of key elements of design intent in a receiving system. The trans-
ferred variational information asserts relationships that already exist in the exchanged model; its purpose
is to initiate processes in the receiving system that will ensure that those relationships are maintained if
the model is modified there. This will assist in the efficient modification of the exchanged model in the
receiving system, through the use of the original designer’s scheme of parameterization and constraints.
Such modification of models transferred using ISO 10303 has proved to be difficult or impossible in the
absence of design intent information.
EXAMPLE It may be desired to optimize the model in the receiving system for structural integrity, or to modify
it to make it cheaper to manufacture.
This part of ISO 10303 is intended to interoperate with other closely related parts, notably ISO 10303-55,
which defines procedural and hybrid representations, specified in terms of the constructional operations
c ISO 2005 — All rights reserved ix

used in building a model. The primary forms of shape representation used by many modern CAD systems
are of these types. ISO 10303-108 (this document) and ISO 10303-55 between them provide for the
capture of the two major aspects of design intent. Procedural representations are outside the normative
scope of the present document, but annex F provides some discussion of the role of parameterization
and constraints in procedural and hybrid representations, and of the interplay between the explicit and
procedural approaches to shape modelling.
A further aspect of modern CAD systems is their provision of feature-based design methods. This
part of ISO 10303 does not address the topic of features, though it provides essential resources for the
positioning and orientation of features in CAD models.
Three books providing further background on the topics covered by this part of ISO 10303 are given in
the Bibliography [3,4,6].
The contents of the schemas making up this part of ISO 10303 are as follows:
parameterization schema: Mechanisms for associating parameters with variable quantities in an
instantiated EXPRESS model;
explicit constraint schema: Definitions of generic constraint relationships between elements of
an instantiated EXPRESS model;
variational representation schema: Specification of the relationship between parameter and con-
straint information and the non-variational model with which it is associated;
explicit geometric constraint schema: Specialization of the explicit constraint schema for the
representation of commonly used geometric constraints (such as parallelism or tangency) between
explicitly represented elements of geometric models;
sketch schema: Means for the representation of two-dimensional sketches, which may contain
variational elements, for use as basic elements in shape modelling operations.
The relationships of the schemas in this part of ISO 10303 to other schemas that define the integrated
resources of ISO 10303 are illustrated in Figure 1 using the EXPRESS-G notation. EXPRESS-G is
defined in annex D of ISO 10303-11. The internal relationships among ISO 10303-108 schemas are
shown in Figure 2. The schemas occurring in Figure 1 are (with two exceptions that form part of ISO
13584) components of ISO 10303 integrated resources, and they are specified in the following resource
parts:
measure schema ISO 10303-41
product property representation schema ISO 10303-41
support resource schema ISO 10303-41
geometric model schema ISO 10303-42
geometry schema ISO 10303-42
topology schema ISO 10303-42
representation schema ISO 10303-43
mathematical functions schema ISO 10303-50
ISO13584 generic expressions schema ISO 13584-20
ISO13584 expressions schema ISO 13584-20
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mathematical_
functions_schema
parameterization_
schema
ISO13584_generic_
expressions_schema
explicit_constraint_
ISO13584_
schema
expressions_schema
support_resource_
schema
explicit_geometric_
constraint_schema
representation_
schema
variational_represen-
tation_schema
measure_schema
geometry_schema
sketch_schema
product_property_ geometric_model_
topology_schema
representation_schema schema
Figure 1 – Schema level diagram of relationships between ISO 10303-108
schemas (inside the box) and other resource schemas
c ISO 2005 — All rights reserved xi

parameterization_ explicit_constraint_
schema schema
variational_represen-
tation_schema
explicit_geometric_
sketch_schema
constraint_schema
Figure 2 – Schema level diagram of relationships among ISO 10303-108
schemas
xiic ISO 2005 — All rights reserved

INTERNATIONAL STANDARD ISO 10303-108:2005(E)
Industrial automation systems and integration —
Product data representation and exchange —
Part 108:
Integrated application resource: Parameterization and
constraints for explicit geometric product models
1 Scope
This part of ISO 10303 specifies the resource constructs for the representation of model parameters
and constraints, together with the mechanisms necessary for associating them with geometric or other
elements of transferred models. The use of these capabilities potentially allows certain aspects of the
behaviour of a model in its originating system to be conveyed together with the basic model itself. The
intention in transferring this additional information is to provide the receiving system with data that will
enable it to reconstruct corresponding behavioural characteristics in the model following the transfer.
Ideally, this will enable the model to be edited in the receiving system just as as though it had been
created there. That would not be possible without the exchange of what is known as design intent
information. This part of ISO 10303 enables the capture and transfer of an important aspect of design
intent.
Clause 4 defines a means for the association of model parameters with individual quantities in the model,
to provide for the editing of dimensional values and other variable attributes. Clause 5 provides for the
modelling of constraint relationships in terms of mathematical relationships among model parameters.
Such constraints are not restricted to the modelling of product shape; they are designed to be applicable
in any situation where it may be useful to capture and transfer mathematically specified relationships.
Clause 5 also defines a class of descriptive (non-mathematical) constraints. Clause 6 defines avariational
representation, containing a model together with all the associated parameters and constraints that poten-
tially facilitate its effective editing following a transfer. Clause 7 defines specialized representations for a
set of explicit geometric constraints applicable specifically to elements of shape models of the boundary
representation and closely related types. These are subtypes of the descriptive constraints specified in
clause 5. Finally, clause 8 provides representations for two-dimensional sketches, which form the basis
of many shape construction methods in CAD modelling. Sketches are an important application area for
the parameterization and constraint information defined in earlier clauses. The capabilities provided in
this schema may also be used as a basis for the representation of parameterized drawings.
The following are within the scope of this part of ISO 10303:
— Parameterization of models through the association of variables with quantities occurring in them;
— Constraints defining mathematical relationships between parameters;
— Constraints on models expressed as relationships between their constituent elements or attributes of
those elements;
— Association of parameters and constraints with models at therepresentation level, to create varia-
tional models of products, plans, processes or organizations;
c ISO 2005 — All rights reserved 1

— Specific representations for the geometric constraints commonly used in product shape modelling;
— Applications of parameterization and constraints to two- and three-dimensional shape models, in
particular two-dimensional geometric sketches;
— Representation of models that are incompletely defined in the sense that certain values in the model
may be regarded as not fully constrained.
NOTE 1 The scopes of the individual schemas comprising this part of ISO 10303 are specified in more detail in
clauses 1.1 – 1.5.
The following are outside the scope of this part of ISO 10303:
— Procedural or history-based model representations, expressed in terms of sequences of construc-
tional operations;
NOTE 2 Procedural or history-based representations are the subject of ISO 10303-55.
— Implicit or procedurally defined constraints;
— Solution methods for systems of constraint equations;
— Form features of shape models;
— Behaviour of a system in which a variational model is edited following a transfer;
NOTE 3 The information transmitted by the use of this part of ISO 10303 is intended to allow implementers to
provide ‘reasonable’ or ‘intuitive’ behaviour by their systems in the circumstances mentioned, but this document
does not prescribe the detailed nature of such behaviour or of its presentation to the system user.
— Considerations of accuracy in constraint satisfaction.
NOTE 4 Such considerations are essentially the same in this context as those arising in the geometric modelling
of product shape. Limited general means are provided elsewhere in ISO 10303 for addressing accuracy issues.
Clauses 4, 5 and 6 of this part of ISO 10303 are applicable to any representation specified using the
EXPRESS language defined in ISO 10303-11. The capabilities provided in those three schemas allow the
association of parameters with attributes of entity data type instances and the specification of constraint
relationships between such attributes in instantiated EXPRESS representations in general. These may
include models of products, plans, processes or organizations, for example. Clauses 7 and 8 of this
part of ISO 10303 are applicable more specifically to shape representations associated with discrete
products. They provide additional specialization for the association of parameterization and constraints
with geometric elements. The scopes of the individual clauses are given in more detail below.
1.1 Parameterization schema
The following are within the scope of the parameterization schema:
— The representation of variable parameters in an ISO 10303 model;
— The association of such variable parameters with quantities in an ISO 10303 model expressed as
values of attributes of entity data type instances in a populated schema;
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— The specification of allowable domains for model parameters;
— The specification of entity data type instance attribute values that are required to be fixed, i.e., whose
allowable domains are each restricted to a single value. The intention is that these values should not
be modified in a receiving system following a transfer.
NOTE 1 The last provision allows, in particular, for dimensional values to be fixed in appropriate cases.
NOTE 2 The presence of parameters in a model, and of specified relationships between parameters, indicate
possibilities for changes that are permissible after a model transfer. This preserves part of the intention of the
model’s creator, as expressed by the parameterization imposed on the model in the originating system.
1.2 Explicit constraint schema
The following are within the scope of the explicit constraint schema:
— Specification of constraint relationships between constituent elements in a model, expressing the
intention that these relationships should be preserved on modification of the model following an
ISO 10303 transfer;
— Constraint relationships of the following specific types:
a) Free-form constraints enabling the capture and transmission of explicitly defined mathematical
relationships between quantities in a model;
b) Defined constraints, for the representation of relationships defined descriptively, with implied
mathematical semantics;
NOTE A constraint imposed in an originating system typically encapsulates requirements for the preservation
of specific aspects of the functionality or validity of the modelled object. The transmission of such constraint
information in a model exchange is intended to enable these requirements to be maintained during any subsequent
modification of the model in the receiving system.
— Specification of sets of constraints that are required to hold simultaneously in the model.
The following are outside the scope of the explicit constraint schema:
— The actual representation of mathematical expressions, functions or procedures (such representa-
tions are provided elsewhere in ISO 10303);
— Solution methods for systems of constraint equations;
— Sequential application of constraints;
— Implicit or procedurally defined constraints.
1.3 Variational representation schema
The following are within the scope of the variational representation schema:
— Characterization of parameterization and constraint information asvariational;
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— Specification of the relationship between variational information and the explicit model with which
it is associated;
— Specification of auxiliary geometric elements for use in defining variational relationships.
1.4 Explicit geometric constraint schema
The following are within the scope of the explicit geometric constraint schema:
— Explicit geometric constraints as descriptive relationships between points, curves and surfaces in a
product shape model, both in two and in three dimensions.
NOTE CAD systems provide two-dimensional constraints for use in defining planar profiles that are extruded or
rotated to generate volumes. Such volumes are often used to provide the basic forms for protrusions or depressions
in a shape model. Three-dimensional constraints play an important role in the definition of inter-feature geometric
relationships in part models and inter-part geometric relationships in assembly models.
1.5 Sketch schema
The following are within the scope of the sketch schema:
— Sketches as planar geometric constructs for use in the generation of surfaces and solids by means
of sweep operations and other operations of related types;
— Neutral sketches, defined in general two-dimensional coordinate systems;
— Positioned sketches, defined in three-dimensional model space;
— Relationships between neutral sketches and positioned sketches defined by mappings;
— The use of parameters and constraints to define variational sketches;
— Subsketches as partial sketches subject to special treatment;
— Geometric elements imported into the plane of a sketch but defined in terms of other model elements
lying outside that plane, used for constraining sketch elements with respect to external geometry.
EXAMPLE An example of an imported curve is a curve defined by projecting an external curve onto the plane
of a sketch. Sketch elements may be constrained with respect to imported elements lying in the same plane.
NOTE The entities defined in this schema are also suitable for the representation of parametric drawings. The
generation of such drawings (for example, by projection from a three-dimensional CAD model) will require spe-
cialized system capabilities to handle the graphical aspects, the relationships between component models and as-
sembly models, etc. However, the actual representational requirements of a sketch and of a parameterized drawing
are very similar.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
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ISO/IEC 8824-1, Information technology — Abstract Syntax Notation One (ASN.1): Specification of
basic notation.
ISO10303-1, Industrial automation systems and integration — Product data representation and exchange
— Part 1: Overview and fundamental principles.
ISO10303-11, Industrial automation systems and integration — Product data representation and ex-
change — Part 11: Description methods: The EXPRESS language reference manual.
ISO 10303-21, Industrial automation systems and integration — Product data representation and ex-
change — Part 21: Implementation methods: Clear text encoding of the exchange structure.
ISO 10303-41, Industrial automation systems and integration — Product data representation and ex-
change — Part 41: Integrated generic resource: Fundamentals of product description and support.
ISO 10303-42, Industrial automation systems and integration — Product data representation and ex-
change — Part 42: Integrated generic resource: Geometric and topological representation.
ISO 10303-43, Industrial automation systems and integration — Product data representation and ex-
change — Part 43: Integrated generic resource: Representation structures.
ISO 10303-50, Industrial automation systems and integration — Product data representation and ex-
change — Part 50: Integrated generic resource: Mathematical constructs.
1)
ISO 10303-55:— , Industrial automation systems and integration — Product data representation and
exchange — Part 55: Integrated generic resource: Procedural and hybrid representation.
ISO 13584-20, Industrial automation systems and integration — Parts library — Part 20: Logical re-
source: Logical model of expressions.
3 Terms, definitions and abbreviations
3.1 Terms defined in ISO 10303-1
For the purposes of this document, the following terms defined in ISO 10303-1 apply.
— application;
— application context;
— application protocol (AP);
— assembly;
— component;
— data exchange;
— exchange structure;
1)
To be published
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— implementation method;
— integrated resource (IR);
— product;
— product data;
— structure.
3.2 Terms defined in ISO 10303-11
For the purposes of this document, the following terms defined in ISO 10303-11 apply.
— entity;
— entity data type;
— entity (data type) instance;
— instance;
— value.
3.3 Terms defined in ISO 10303-42
For the purposes of this document, the following terms defined in ISO 10303-42 apply.
— boundary representation solid model (B-rep);
— constructive solid geometry (CSG);
— coordinate space;
— curve;
— dimensionality;
— geometrically founded;
— model space;
— surface.
3.4 Terms defined in ISO 10303-43
For the purposes of this document, the following terms defined in ISO 10303-43 apply.
— context of representation;
— element of representation;
— representation.
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3.5 Terms defined in ISO 10303-50
For the purposes of this document, the following terms defined in ISO 10303-50 apply.
— expression;
— function;
— function domain;
— variable.
3.6 Terms defined in ISO 13584-20
For the purposes of this document, the following terms defined in ISO 13584-20 apply. In all
cases the context is that of a mathematical variable.
— environment;
— semantics;
— syntactic representation.
3.7 Other terms and definitions
For the purposes of this document, the following definitions apply. Where synonyms are given the first
term listed is the one preferred for use in the remainder of the document.
3.7.1
auxiliary geometry
geometric elements such as centre-lines and centre-planes used for locational or tolerancing purposes,
but excluding geometry used in the actual representation of a product shape
3.7.2
constrained elements
model elements that are controlled by a constraint if the model is edited following transfer into another
system
3.7.3
constraint
relationship between two or more elements in a model, which should be maintained in any modifications
made subsequent to a model transfer
3.7.4
constraint solution
solution of a system of one or more constraint relationships expressed as mathematical equations or
inequalities
NOTE Geometric constraint systems are often nonlinear, possessing multiple constraint solutions. The user may
have to choose one of them to obtain a unique design.
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3.7.5
constraint solver
software system for solving sets of equations that are mathematical representations of constraint rela-
tionships
NOTE 1 Methods used by constraint solvers for determining solutions are outside the scope of this part of ISO
10303.
NOTE 2 In straightforward cases a constraint set will have the same number of unknowns as equations. Ideally,
however, a constraint solver should also handle underconstrained and overconstrained constraint sets having, re-
spectively, more unknowns and less unknowns than the number of equations. The specification of system response
in such cases is also outside the scope of this part of ISO 10303, but it could include the generation of diagnostic
information or of partial solutions as appropriate.
3.7.6
construction geometry
geometry used as an aid in the construction of a shape that is not an element of the shape itself
EXAMPLE This concept may be illustrated by the case of a ‘spine’ curve used in the generation of certain types
of swept surfaces. A planar generating curve is defined, together with a reference point lying in its plane. The
reference point is then swept along the spine curve, the plane of the generating curve being maintained normal to
it. The generating curve sweeps out the desired surface. If the reference point does not lie on the generating curve
the spine curve
...