ISO 10303-508:2001
(Main)Industrial automation systems and integration — Product data representation and exchange — Part 508: Application interpreted construct: Non manifold surface
Industrial automation systems and integration — Product data representation and exchange — Part 508: Application interpreted construct: Non manifold surface
This part of ISO 10303 specifies the interpretation of the integrated resources to satisfy requirements for the description of geometric shapes by means of non-manifold surface models. The following are within the scope of this part of ISO 10303: — 3D points; — points defined in the parameter space of curves or surfaces; — 3D curves; — curves defined in the parameter space of surfaces; NOTE - Such curves are also known as pcurves or cons, which are acronyms for parametrised curve and curve on surface. — the elementary curve types line, circle, ellipse, parabola, and hyperbola; — intersection curves; — polylines that consist of at least three points; — the elementary surface types plane, cylinder, cone, torus, and sphere; — swept surfaces created by rotation or linear extrusion of a curve; — sculptured curves and surfaces; — trimming of curves and surfaces using topological entities; — composition of curves and surfaces using topological entities; — replication of curves, surfaces, and surface models; — 3D offsets of curves and surfaces; — non-manifolds. The following are outside the scope of this part of ISO 10303: — unbounded geometry; — self-intersecting geometry; — geometry in a 2D cartesian coordinate space; — replication of points; — topology without an association to a corresponding geometric domain.
Systèmes d'automation industrielle et intégration — Représentation et échange de données de produits — Partie 508: Établissement interprété d'application: Surface non manifold
General Information
Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 10303-508
First edition
2001-04-15
Industrial automation systems and
integration — Product data representation
and exchange —
Part 508:
Application interpreted construct:
Non-manifold surface
Systèmes d'automation industrielle et intégration — Représentation
et échange de données de produits —
Partie 508: Établissement interprété d'application: Surface non manifold
Reference number
©
ISO 2001
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ii © ISO 2001 – All rights reserved
Contents Page
1 Scope . . . . . . . . . 1
2 Normativereferences . . . . . . . . 2
3 Terms,definitions,andabbreviations . . . . . . 3
3.1 Terms defined in ISO 10303–1 . . . . . . 3
3.2 Terms defined in ISO 10303–42 . . . . . . . . 4
3.3 Terms defined in ISO 10303–202 . . . . . . . 4
3.4 Terms defined in ISO 10303–511 . . . . . . . 4
3.5 Othertermsanddefinitions . . . . . . 5
3.6 Abbreviations . . . . . . . . 5
4 EXPRESSshortlisting . . . . . . . . 5
4.1 Fundamental concepts and assumptions . . . . . 7
4.2 aic_non_manifold_surface schema entity definition: non_manifold_surface_shape_re-
presentation . . . . . . . . . . 7
4.3 aic_non_manifold_surface function definitions . . . . 14
4.3.1 nmsf_curve_check . . . . . . . 14
4.3.2 nmsf_surface_check . . . . . . 19
Annex A (normative) Short names of entities. . . . . 23
AnnexB(normative) Informationobjectregistration . . . . 24
B.1 Documentidentification . . . . . . . 24
B.2 Schemaidentification . . . . . . . 24
Annex C (informative) EXPRESS-G diagrams . . . . . 25
AnnexD(informative) Computerinterpretablelistings . . . . 49
Index . . . . . . . . . . 50
Figures
Figure C.1 EXPRESS-G diagram 1 of 22 . . . . . . . . 27
Figure C.2 EXPRESS-G diagram 2 of 22 . . . . . . . . 28
Figure C.3 EXPRESS-G diagram 3 of 22 . . . . . . . . 29
Figure C.4 EXPRESS-G diagram 4 of 22 . . . . . . . . 30
Figure C.5 EXPRESS-G diagram 5 of 22 . . . . . . . . 31
Figure C.6 EXPRESS-G diagram 6 of 22 . . . . . . . . 32
Figure C.7 EXPRESS-G diagram 7 of 22 . . . . . . . . 33
Figure C.8 EXPRESS-G diagram 8 of 22 . . . . . . . . 34
Figure C.9 EXPRESS-G diagram 9 of 22 . . . . . . . . 35
Figure C.10 EXPRESS-G diagram 10 of 22 . . . . . . . 36
Figure C.11 EXPRESS-G diagram 11 of 22 . . . . . . . 37
Figure C.12 EXPRESS-G diagram 12 of 22 . . . . . . . 38
Figure C.13 EXPRESS-G diagram 13 of 22 . . . . . . . 39
Figure C.14 EXPRESS-G diagram 14 of 22 . . . . . . . 40
Figure C.15 EXPRESS-G diagram 15 of 22 . . . . . . . 41
Figure C.16 EXPRESS-G diagram 16 of 22 . . . . . . . 42
Figure C.17 EXPRESS-G diagram 17 of 22 . . . . . . . 43
Figure C.18 EXPRESS-G diagram 18 of 22 . . . . . . . 44
Figure C.19 EXPRESS-G diagram 19 of 22 . . . . . . . 45
Figure C.20 EXPRESS-G diagram 20 of 22 . . . . . . . 46
Figure C.21 EXPRESS-G diagram 21 of 22 . . . . . . . 47
Figure C.22 EXPRESS-G diagram 22 of 22 . . . . . . . 48
Tables
Table A.1 Short names of entities . . . . . . 23
iv © ISO 2001 – All rights reserved
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 committee 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 standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3.
Draft International Standards 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 International Standard may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
International Standard ISO 10303-508 was prepared by Technical Committee ISO/TC 184 Industrial automation
systems and integration, Subcommittee SC 4, Industrial data.
This International Standard is organized as a series of parts, each published separately. The structure of this
International Standard is described in ISO 10303-1.
Each part of this International Standard is a member of one of the following series: description methods,
implementation 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 application interpreted construct series.
A complete list of parts of ISO 10303 is available from the Internet:
Annexes A and B form a normative part of this part of ISO 10303. Annexes C and D are for information only.
Introduction
ISO 10303 is an International Standard for the computer-interpretable representation and exchange 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 de-
scription 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
ISO 10303 fall into one of the following series: description methods, integrated resources, application
interpreted constructs, application protocols, abstract test suites, implementation methods, and confor-
mance testing. The series are described in ISO 10303–1. This part of ISO 10303 is a member of the
application interpreted constructs series.
An application interpreted construct (AIC) provides a logical grouping of interpreted constructs that
supports a specific functionality for the usage of product data across multiple application contexts. An
interpreted construct is a common interpretation of the integrated resources that supports shared infor-
mation requirements among application protocols.
This document specifies the application interpreted construct for the description of geometric shapes by
means of non-manifold surface models. It includes the geometric and topological resources to define
non-manifolds that may consist of elementary and sculptured curves and surfaces.
vi © ISO 2001 – All rights reserved
INTERNATIONAL STANDARD ISO 10303-508:2001(E)
Industrial automation systems and integration —
Product data representation and exchange —
Part 508:
Application interpreted construct:
Non-manifold surface
1Scope
This part of ISO 10303 specifies the interpretation of the integrated resources to satisfy requirements for
the description of geometric shapes by means of non-manifold surface models.
The following are within the scope of this part of ISO 10303:
— 3D points;
— points defined in the parameter space of curves or surfaces;
— 3D curves;
— curves defined in the parameter space of surfaces;
NOTE - Such curves are also known as pcurves or cons, which are acronyms for parametrised curve
and curve on surface.
— the elementary curve types line, circle, ellipse, parabola, and hyperbola;
— intersection curves;
— polylines that consist of at least three points;
— the elementary surface types plane, cylinder, cone, torus, and sphere;
— swept surfaces created by rotation or linear extrusion of a curve;
— sculptured curves and surfaces;
— trimming of curves and surfaces using topological entities;
— composition of curves and surfaces using topological entities;
— replication of curves, surfaces, and surface models;
— 3D offsets of curves and surfaces;
c
� ISO 2001 – All rights reserved 1
— non-manifolds.
The following are outside the scope of this part of ISO 10303:
— unbounded geometry;
— self-intersecting geometry;
— geometry in a 2D cartesian coordinate space;
— replication of points;
— topology without an association to a corresponding geometric domain.
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute
provisions of this part of ISO 10303. For dated references, subsequent amendments to, or revisions of,
any of these publications do not apply. However, parties to agreements based on this part of ISO 10303
are encouraged to investigate the possibility of applying the most recent editions of the normative docu-
ments indicated below. For undated references, the latest edition of the normative document referred to
applies. Members of ISO and IEC maintain registers of currently valid International Standards.
ISO/IEC 8824–1:1998, Information technology – Abstract Syntax Notation Onw (ASN.1): Specification
of basic notation.
ISO 10303–1:1994, Industrial automation systems and integration – Product data representation and
exchange – Part 1 : Overview and fundamental principles.
ISO 10303–11:1994, Industrial automation systems and integration – Product data representation and
exchange – Part 11 : Description methods: The EXPRESS language reference manual.
ISO 10303–41:1994, Industrial automation systems and integration – Product data representation and
exchange – Part 41 : Integrated generic resources: Fundamentals of product description and support.
ISO 10303–42:1994, Industrial automation systems and integration – Product data representation and
exchange – Part 42 : Integrated generic resources: Geometric and topological representation.
ISO 10303–43:1994, Industrial automation systems and integration – Product data representation and
exchange – Part 43 : Integrated generic resources: Representation structures.
ISO 10303–202:1996, Industrial automation systems and integration – Product data representation and
exchange: – Part 202: Application protocol: Associative draughting.
NOTE - ISO 10303-202 is referenced normatively solely for the definition of the term AIC.
ISO 10303–511:2001, Industrial automation systems and integration – Product data representation and
exchange – Part 511 : Application interpreted construct: Topologically bounded surface.
2 �c ISO 2001 – All rights reserved
3 Terms, definitions, and abbreviations
3.1 Terms defined in ISO 10303–1
For the purposes of this part of ISO 10303, the following terms defined in ISO 10303-1 apply:
— abstract test suite (ATS);
— application;
— application context;
— application protocol (AP);
— data;
— data exchange;
— generic resource;
— implementation method;
— information;
— integrated resource;
— interpretation;
— model;
— product;
— product data;
— structure.
�c ISO 2001 – All rights reserved 3
3.2 Terms defined in ISO 10303–42
For the purposes of this part of ISO 10303, the following terms defined in ISO 10303-42 apply:
— boundary;
— boundary representation solid model;
— connected;
— coordinate space;
— curve;
— dimensionality;
— domain;
— parameter space;
— self-intersect;
— surface.
3.3 Terms defined in ISO 10303–202
For the purposes of this part of ISO 10303, the following terms defined in ISO 10303-202 apply:
3.3.1
application interpreted construct (AIC)
a logical grouping of interpreted constructs that supports a specific function for the usage of product data
across multiple application contexts.
3.4 Terms defined in ISO 10303–511
For the purposes of this part of ISO 10303, the following terms defined in ISO 10303-511 apply:
— advanced face;
— sculptured surface;
— swept surface.
4 �c ISO 2001 – All rights reserved
3.5 Other terms and definitions
For the purposes of this part of ISO 10303, the following terms and definitions apply:
3.5.1
2-manifold
a shape where on any point of its boundary one may create a sufficiently small sphere so that the interior
of the sphere is divided into exactly two regions by this boundary. The boundary may typically consist
of edges and faces.
NOTE - This definition eliminates self-intersection of surfaces, surface intersections that are not along
edges, and edges joining three or more faces.
3.5.2
non-manifold
a surface model that uses topological constructs to define its boundaries and connectivity and that in-
cludes either at least two connected_face_sets sharing one face or more than two faces sharing one
edge.
3.6 Abbreviations
For the purposes of this part of ISO 10303, the following abbreviations apply.
AIC application interpreted construct
AP application protocol
ATS abstract test suite
4 EXPRESS short listing
This clause specifies the EXPRESS schema that uses elements from the integrated resources and con-
tains the types, entity specializations, and functions that are specific to this part of ISO 10303.
NOTE 1 - There may be subtypes and items of select lists that appear in the integrated resources that are
not imported into the AIC. Constructs are eliminated from the subtype tree or select list through the use of
the implicit interface rules of ISO 10303-11. References to eliminated constructs are outside the scope of the
AIC. In some cases, all items of the select list are eliminated. Because AICs are intended to be implemented
in the context of an application protocol, the items of the select list will be defined by the scope of the
application protocol.
This application interpreted construct provides a consistent set of geometric and topological entities for
the definition of non-manifold surface representations that consist of elementary or sculptured curves
and surfaces. The highest level entity of this part of ISO 10303 is non_manifold_surface_shape_-
representation.A non_manifold_surface_shape_representation is bounded. The bounding of the
geometry is achieved by topological entities, such as vertex, edge,and face.
�c ISO 2001 – All rights reserved 5
Topological entities shall not exist without an association to a corresponding geometric domain.
NOTE 2 - This part of ISO 10303 uses all the entities and types from ISO 10303-511, aic_topologically_-
bounded_surface.
EXPRESS specification:
*)
SCHEMA aic_non_manifold_surface;
USE FROM aic_topologically_bounded_surface; -- ISO 10303-511
USE FROM geometric_model_schema ( -- ISO 10303-42
face_based_surface_model);
USE FROM geometry_schema ( -- ISO 10303-42
b_spline_curve,
b_spline_surface,
bounded_pcurve,
bounded_surface_curve,
cartesian_transformation_operator_3d,
curve,
curve_replica,
degenerate_pcurve,
evaluated_degenerate_pcurve,
intersection_curve,
offset_curve_3d,
offset_surface,
point_on_curve,
point_on_surface,
seam_curve,
surface,
surface_replica);
USE FROM product_property_representation_schema ( -- ISO 10303-41
shape_representation);
USE FROM representation_schema ( -- ISO 10303-43
mapped_item,
representation,
representation_item,
representation_map);
USE FROM topology_schema ( -- ISO 10303-42
closed_shell,
connected_face_set,
face,
open_shell,
oriented_face);
6 �c ISO 2001 – All rights reserved
(*
NOTE 3 - The schemas referenced above can be found in the following parts of ISO 10303:
aic_topologically_bounded_surface ISO 10303-511
geometric_model_schema ISO 10303-42
geometry_schema ISO 10303-42
product_property_representation_schema ISO 10303-41
representation_schema ISO 10303-43
topology_schema ISO 10303-42
4.1 Fundamental concepts and assumptions
The following entities are intended to be independently instantiated in the application protocol schemas
that use this AIC:
– non_manifold_surface_shape_representation.
4.2 aic_non_manifold_surface schema entity definition:
non_manifold_surface_shape_representation
A non_manifold_surface_representation describes the shape or portions of the shape of a product
using non-manifolds with boundaries.
NOTE 1 - Non-manifolds are topologically less constrained than manifolds. For example, the restriction
that only a maximum of two faces may share the same edge does not apply. They are, therefore, not nec-
essarily suitable for building solid models. They are, however, often found in applications that support the
finite element analysis method.
NOTE 2 - A non_manifold_surface_representation may well hold a manifold surface model, but not vice
versa.
NOTE 3 - Entity product is not included in this part of ISO 10303.
A non_manifold_surface_shape_representation is a shape_representation as defined in ISO 10303-
41 that consists of one or many face_based_surface_models. Each face_based_surface_model is
built up of connected_face_sets, which in the context of this part of ISO 10303 may be instantiated
as connected_face_set or as one of its subtypes open_shell or closed_shell. Connected_face_sets con-
sist of faces which use edgesand vertexs; the latter three shall reference geometric entities, such as
points, curves, and surfaces. The link between topology and geometry may be established by either
using face_surface or advanced_face as defined in ISO 10303-511. The two options differ both in
the selection of valid point, curve,and surface subtypes and in constraints on references to underlying
geometry.
NOTE 4 - The representation of face_surfacesas advanced_faces is recommended for non-manifold sur-
face models that are intended to be used together with boundary representation solid models; the integration
of such a non-manifold surface model into for example an advanced boundary representation model, which
is defined in ISO 10303-514, will be easier.
�c ISO 2001 – All rights reserved 7
All geometric entities shall be of dimensionality three except for two-dimensional geometry that is used
for the purpose of defining pcurves. The use of one-dimensional cartesian_points is excluded.
All unbounded geometry shall be trimmed by using topological constructs.
The items of a non_manifold_surface_shape_representation may also be of type mapped_item,
which is defined in ISO 10303-43, or axis2_placement_3d. These are used to assemble one or sev-
eral non_manifold_surface_shape_representations into one other non_manifold_surface_shape_-
representation.
The WHERE-rules of this entity restrict the use of the entity data types that are imported from ISO 10303-
42 and ISO 10303-43 according to the statements above. Some of these validations of entity type and
constraints are specified in the following two functions:
– nmsf_curve_check;
– nmsf_surface_check.
In WR5, WR6, and WR10 below, these functions validate the curvesand surfacesofall edgesand faces
that are in the scope of a non_manifold_surface_shape_representation except for those that are in the
reference tree of an advanced_face; the geometry of an advanced_face is validated by a different set of
rules. The functions automatically assess all underlying geometry; for this they are called recursively.
EXAMPLE A pcurve may reference both a curve and a surface. Function nmsf_curve_check validates
not only the pcurve, but also this underlying geometry. It will, therefore, not only call itself, but also
nmsf_surface_check.
NOTE 5 - This part of ISO 10303 does not include a function for the validation of points and their under-
lying curvesand surfaces. This is because all curvesand surfacesofa non_manifold_surface_shape_-
representation are referenced from edgesand faces and are, thus, covered by the two existing functions
already.
NOTE 6 - An application protocol that uses this part of ISO 10303 should explicitly permit that the shape_-
representation entity may be instantiated as a non_manifold_surface_shape_representation.
EXPRESS specification:
*)
ENTITY non_manifold_surface_shape_representation
SUBTYPE OF (shape_representation);
WHERE
WR1: SIZEOF (QUERY (it <* SELF.items |
NOT (SIZEOF ([’AIC_NON_MANIFOLD_SURFACE.FACE_BASED_SURFACE_MODEL’,
’AIC_NON_MANIFOLD_SURFACE.MAPPED_ITEM’,
’AIC_NON_MANIFOLD_SURFACE.AXIS2_PLACEMENT_3D’] * TYPEOF (it)) = 1)))
=0;
WR2: SIZEOF (QUERY (it <* SELF.items |
8 �c ISO 2001 – All rights reserved
SIZEOF ([’AIC_NON_MANIFOLD_SURFACE.FACE_BASED_SURFACE_MODEL’,
’AIC_NON_MANIFOLD_SURFACE.MAPPED_ITEM’] * TYPEOF (it)) = 1)) > 0;
WR3: SIZEOF (QUERY (mi <* QUERY (it <* SELF.items |
’AIC_NON_MANIFOLD_SURFACE.MAPPED_ITEM’ IN TYPEOF (it)) |
NOT ((’AIC_NON_MANIFOLD_SURFACE.’+
’NON_MANIFOLD_SURFACE_SHAPE_REPRESENTATION’
IN TYPEOF (mi\mapped_item.mapping_source.mapped_representation))
AND
(SIZEOF(QUERY (mr_it <*
mi\mapped_item.mapping_source.mapped_representation.items |
(’AIC_NON_MANIFOLD_SURFACE.FACE_BASED_SURFACE_MODEL’
IN TYPEOF (mr_it)))) > 0 )))) = 0;
WR4: SIZEOF (QUERY (fbsm <* QUERY (it <* SELF.items |
’AIC_NON_MANIFOLD_SURFACE.FACE_BASED_SURFACE_MODEL’ IN TYPEOF (it)) |
NOT (SIZEOF (QUERY (cfs <*
fbsm\face_based_surface_model.fbsm_faces |
NOT (SIZEOF (QUERY (fa <* cfs.cfs_faces |
NOT (SIZEOF ([’AIC_NON_MANIFOLD_SURFACE.FACE_SURFACE’,
’AIC_NON_MANIFOLD_SURFACE.ORIENTED_FACE’] * TYPEOF (fa)) = 1)))
= 0))) = 0))) = 0;
WR5: SIZEOF (QUERY (fbsm <* QUERY (it <* SELF.items |
’AIC_NON_MANIFOLD_SURFACE.FACE_BASED_SURFACE_MODEL’ IN TYPEOF (it)) |
NOT (SIZEOF (QUERY (cfs <*
fbsm\face_based_surface_model.fbsm_faces |
NOT (SIZEOF (QUERY (f_sf <* QUERY (fa <* cfs.cfs_faces |
(’AIC_NON_MANIFOLD_SURFACE.FACE_SURFACE’ IN TYPEOF (fa))) |
NOT ((’AIC_NON_MANIFOLD_SURFACE.ADVANCED_FACE’ IN TYPEOF (f_sf))
OR
(nmsf_surface_check(f_sf\face_surface.face_geometry))))) = 0)))
= 0))) = 0;
WR6: SIZEOF (QUERY (fbsm <* QUERY (it <* SELF.items |
’AIC_NON_MANIFOLD_SURFACE.FACE_BASED_SURFACE_MODEL’ IN TYPEOF (it)) |
NOT (SIZEOF (QUERY (cfs <*
fbsm\face_based_surface_model.fbsm_faces |
NOT (SIZEOF (QUERY (o_fa <* QUERY (fa <* cfs.cfs_faces |
(’AIC_NON_MANIFOLD_SURFACE.ORIENTED_FACE’ IN TYPEOF (fa))) |
NOT ((’AIC_NON_MANIFOLD_SURFACE.ADVANCED_FACE’ IN TYPEOF
(o_fa\oriented_face.face_element))
OR
(nmsf_surface_check
(o_fa\oriented_face.face_element\face_surface.face_geometry)))))
= 0))) = 0))) = 0;
WR7: SIZEOF (QUERY (fbsm <* QUERY (it <* SELF.items |
’AIC_NON_MANIFOLD_SURFACE.FACE_BASED_SURFACE_MODEL’ IN TYPEOF (it)) |
NOT (SIZEOF (QUERY (cfs <*
fbsm\face_based_surface_model.fbsm_faces |
NOT (SIZEOF (QUERY (fa <* cfs.cfs_faces |
NOT ((’AIC_NON_MANIFOLD_SURFACE.ADVANCED_FACE’ IN TYPEOF (fa))
OR
(SIZEOF (QUERY (bnds <* fa.bounds |
NOT (SIZEOF ([’AIC_NON_MANIFOLD_SURFACE.EDGE_LOOP’,
’AIC_NON_MANIFOLD_SURFACE.VERTEX_LOOP’]
�c ISO 2001 – All rights reserved 9
* TYPEOF (bnds.bound)) = 1))) = 0)))) = 0))) = 0))) = 0;
WR8: SIZEOF (QUERY (fbsm <* QUERY (it <* SELF.items|
’AIC_NON_MANIFOLD_SURFACE.FACE_BASED_SURFACE_MODEL’ IN TYPEOF (it)) |
NOT (SIZEOF (QUERY (cfs <*
fbsm\face_based_surface_model.fbsm_faces |
NOT (SIZEOF (QUERY (fa <* cfs.cfs_faces |
NOT ((’AIC_NON_MANIFOLD_SURFACE.ADVANCED_FACE’ IN TYPEOF (fa))
OR
(SIZEOF (QUERY (elp_fbnds <* QUERY (bnds <* fa.bounds |
’AIC_NON_MANIFOLD_SURFACE.EDGE_LOOP’ IN TYPEOF (bnds.bound)) |
NOT (SIZEOF (QUERY (oe <* elp_fbnds\path.edge_list |
NOT (’AIC_NON_MANIFOLD_SURFACE.EDGE_CURVE’ IN TYPEOF
(oe.edge_element)))) = 0))) = 0)))) = 0))) = 0))) = 0;
WR9: SIZEOF (QUERY (fbsm <* QUERY (it <* SELF.items |
’AIC_NON_MANIFOLD_SURFACE.FACE_BASED_SURFACE_MODEL’ IN TYPEOF (it)) |
NOT (SIZEOF (QUERY (cfs <*
fbsm\face_based_surface_model.fbsm_faces |
NOT (SIZEOF (QUERY (fa <* cfs.cfs_faces |
NOT ((’AIC_NON_MANIFOLD_SURFACE.ADVANCED_FACE’ IN TYPEOF (fa))
OR
(SIZEOF (QUERY (elp_fbnds <* QUERY (bnds <* fa.bounds |
’AIC_NON_MANIFOLD_SURFACE.EDGE_LOOP’ IN TYPEOF (bnds.bound)) |
NOT (SIZEOF (QUERY (oe_cv <* QUERY (oe <*
elp_fbnds\path.edge_list |
’AIC_NON_MANIFOLD_SURFACE.EDGE_CURVE’ IN TYPEOF (oe.edge_element)) |
NOT (SIZEOF ([’AIC_NON_MANIFOLD_SURFACE.B_SPLINE_CURVE’,
’AIC_NON_MANIFOLD_SURFACE.CONIC’,
’AIC_NON_MANIFOLD_SURFACE.CURVE_REPLICA’,
’AIC_NON_MANIFOLD_SURFACE.LINE’,
’AIC_NON_MANIFOLD_SURFACE.OFFSET_CURVE_3D’,
’AIC_NON_MANIFOLD_SURFACE.PCURVE’,
’AIC_NON_MANIFOLD_SURFACE.POLYLINE’,
’AIC_NON_MANIFOLD_SURFACE.SURFACE_CURVE’] *
TYPEOF (oe_cv.edge_element\edge_curve.edge_geometry))
= 1))) = 0))) = 0)))) = 0))) = 0))) = 0;
WR10: SIZEOF (QUERY (fbsm <* QUERY (it <* SELF.items |
’AIC_NON_MANIFOLD_SURFACE.FACE_BASED_SURFACE_MODEL’ IN TYPEOF (it)) |
NOT (SIZEOF (QUERY (cfs <*
fbsm\face_based_surface_model.fbsm_faces |
NOT (SIZEOF (QUERY (fa <* cfs.cfs_faces |
NOT ((’AIC_NON_MANIFOLD_SURFACE.ADVANCED_FACE’ IN TYPEOF (fa))
OR
(SIZEOF (QUERY (elp_fbnds <* QUERY (bnds <* fa.bounds |
’AIC_NON_MANIFOLD_SURFACE.EDGE_LOOP’ IN TYPEOF (bnds.bound)) |
NOT (SIZEOF (QUERY (oe <* elp_fbnds\path.edge_list |
NOT (nmsf_curve_check (oe.edge_element\edge_curve.edge_geometry))))
= 0))) = 0)))) = 0))) = 0))) = 0;
WR11: SIZEOF (QUERY(fbsm <* QUERY (it <* SELF.items |
’AIC_NON_MANIFOLD_SURFACE.FACE_BASED_SURFACE_MODEL’ IN TYPEOF (it)) |
NOT (SIZEOF (QUERY (cfs <*
fbsm\face_based_surface_model.fbsm_faces |
NOT (SIZEOF (QUERY (fa <* cfs.cfs_faces |
10 �c ISO 2001 – All rights reserved
NOT ((’AIC_NON_MANIFOLD_SURFACE.ADVANCED_FACE’ IN TYPEOF (fa))
OR
(SIZEOF (QUERY (elp_fbnds <* QUERY (bnds <* fa.bounds |
’AIC_NON_MANIFOLD_SURFACE.EDGE_LOOP’ IN TYPEOF (bnds.bound)) |
NOT (SIZEOF (QUERY (oe <* elp_fbnds\path.edge_list|
NOT ((’AIC_NON_MANIFOLD_SURFACE.VERTEX_POINT’ IN TYPEOF
(oe.edge_element.edge_start))
AND
(’AIC_NON_MANIFOLD_SURFACE.VERTEX_POINT’ IN
TYPEOF (oe.edge_element.edge_end)))))
= 0))) = 0)))) = 0))) = 0))) = 0;
WR12: SIZEOF (QUERY (fbsm <* QUERY (it <* SELF.items |
’AIC_NON_MANIFOLD_SURFACE.FACE_BASED_SURFACE_MODEL’ IN TYPEOF (it)) |
NOT (SIZEOF (QUERY (cfs <*
fbsm\face_based_surface_model.fbsm_faces |
NOT (SIZEOF (QUERY (fa <* cfs.cfs_faces |
NOT ((’AIC_NON_MANIFOLD_SURFACE.ADVANCED_FACE’ IN TYPEOF (fa))
OR
(SIZEOF (QUERY (elp_fbnds <* QUERY (bnds <* fa.bounds |
’AIC_NON_MANIFOLD_SURFACE.EDGE_LOOP’ IN TYPEOF (bnds.bound)) |
NOT (SIZEOF (QUERY (oe <* elp_fbnds\path.edge_list |
NOT ((SIZEOF ([’AIC_NON_MANIFOLD_SURFACE.CARTESIAN_POINT’,
’AIC_NON_MANIFOLD_SURFACE.DEGENERATE_PCURVE’,
’AIC_NON_MANIFOLD_SURFACE.POINT_ON_CURVE’,
’AIC_NON_MANIFOLD_SURFACE.POINT_ON_SURFACE’] * TYPEOF
(oe.edge_element.edge_start\vertex_point.vertex_geometry)) = 1)
AND
(SIZEOF ([’AIC_NON_MANIFOLD_SURFACE.CARTESIAN_POINT’,
’AIC_NON_MANIFOLD_SURFACE.DEGENERATE_PCURVE’,
’AIC_NON_MANIFOLD_SURFACE.POINT_ON_CURVE’,
’AIC_NON_MANIFOLD_SURFACE.POINT_ON_SURFACE’] * TYPEOF
(oe.edge_element.edge_end\vertex_point.vertex_geometry)) = 1
)))) = 0))) = 0)))) = 0))) = 0))) = 0;
WR13: SIZEOF (QUERY (fbsm <* QUERY (it <* SELF.items |
’AIC_NON_MANIFOLD_SURFACE.FACE_BASED_SURFACE_MODEL’ IN TYPEOF (it)) |
NOT (SIZEOF (QUERY (cfs <*
fbsm\face_based_surface_model.fbsm_faces |
NOT (SIZEOF (QUERY (fa <* cfs.cfs_faces |
NOT ((’AIC_NON_MANIFOLD_SURFACE.ADVANCED_FACE’ IN TYPEOF (fa))
OR
(SIZEOF (QUERY (vlp_fbnds <* QUERY (bnds <* fa.bounds |
’AIC_NON_MANIFOLD_SURFACE.VERTEX_LOOP’ IN TYPEOF (bnds.bound)) |
NOT (’AIC_NON_MANIFOLD_SURFACE.VERTEX_POINT’ IN TYPEOF
(vlp_fbnds\vertex_loop.loop_vertex)))) = 0)))) = 0)))
= 0))) = 0;
WR14: SIZEOF (QUERY (fbsm <* QUERY (it <* SELF.items |
’AIC_NON_MANIFOLD_SURFACE.FACE_BASED_SURFACE_MODEL’ IN TYPEOF (it)) |
NOT (SIZEOF (QUERY (cfs <*
fbsm\face_based_surface_model.fbsm_faces |
NOT (SIZEOF (QUERY (fa <* cfs.cfs_faces |
NOT ((’AIC_NON_MANIFOLD_SURFACE.ADVANCED_FACE’ IN TYPEOF (fa))
OR
�c ISO 2001 – All rights reserved 11
(SIZEOF (QUERY (vlp_fbnds <* QUERY (bnds <* fa.bounds |
’AIC_NON_MANIFOLD_SURFACE.VERTEX_LOOP’ IN TYPEOF (bnds.bound)) |
NOT (SIZEOF ([’AIC_NON_MANIFOLD_SURFACE.CARTESIAN_POINT’,
’AIC_NON_MANIFOLD_SURFACE.DEGENERATE_PCURVE’,
’AIC_NON_MANIFOLD_SURFACE.POINT_ON_CURVE’,
’AIC_NON_MANIFOLD_SURFACE.POINT_ON_SURFACE’] * TYPEOF
(vlp_fbnds\vertex_loop.loop_vertex\vertex_point.vertex_geometry))
= 1))) = 0)))) = 0))) = 0))) = 0;
END_ENTITY;
(*
Formal propositions:
WR1: The items in a non_manifold_surface_shape_representation shall be face_based_surface_-
models, mapped_items, or axis2_placement_3ds.
NOTE 7 - Axis2_placement_3d is a valid mapped_item.mapping_target. To include another repre-
sentation into the list of items of a non_manifold_surface_shape_representation (see WR3 for valid
mapped_items), the mapped_item.mapping_source.mapping_origin may be any entity that is geometri-
cally founded in the geometric_representation_context of the mapped_representation. If this entity is an
axis2_placement_3d, the operator that maps the mapped_representation into the non_manifold_surface_-
shape_representation corresponds to a transformation matrix with only translation and rotation enabled. If
a cartesian_transformation_operator_3d is used as mapping_origin, scaling and mirroring are possible.
WR2: At least one of the items in a non_manifold_surface_shape_representation shall be either a
face_based_surface_model or a mapped_item.
WR3: If there is a mapped_item in a non_manifold_surface_shape_representation,the mapped_-
representation of its mapping_source shall be a non_manifold_surface_shape_representation.This
shape_representation shall include at least one face_based_surface_model.
WR4: A face shall be instantiated as either a face_surface, its subtype advanced_face,oran oriented_-
face.
WR5: All basis geometry that via a face_surface is referenced by surfaces shall be either within the
reference tree of an advanced_face or shall be valid curvesand surfaces.
The basis_surface of an offset_surface shall be either an elementary_surface, b_spline_surface, off-
set_surface, swept_surface,or surface_replica.
The parent_surface of a surface_replica shall be either an elementary_surface, b_spline_surface,
offset_surface, swept_surface,or surface_replica.
The swept_curve of a swept_surface shall be either a line, conic, pcurve, surface_curve, offset_-
curve_3d, b_spline_curve, polyline,or curve_replica.
The attribute self_intersect shall be set to FALSE or UNKNOWN for b_spline_surfacesand offset_-
surfaces.
NOTE 8 - A surface is validated against these constraints by the function nmsf_surface_check.
WR6: All basis geometry that is referenced via an oriented_face.face_element shall be either within
the reference tree of an advanced_face or shall be valid curvesand surfaces.
12 �c ISO 2001 – All rights reserved
The basis_surface of an offset_surface shall be either an elementary_surface, b_spline_surface, off-
set_surface, swept_surface,or surface_replica.
The parent_surface of a surface_replica shall be either an elementary_surface, b_spline_surface,
offset_surface, swept_surface,or surface_replica.
The swept_curve of a swept_surface shall be either a line, conic, pcurve, surface_curve, offset_-
curve_3d, b_spline_curve, polyline,or curve_replica.
The attribute self_intersect shall be set to FALSE or UNKNOWN for b_spline_surfacesand offset_-
surfaces.
NOTE 9 - A surface is validated against these constraints by the function nmsf_surface_check.
WR7: The bound of a face_bound that is referenced by a face that is referenced either directly by a
connected_face_set or via an oriented_face shall be either within the reference tree of an advanced_-
face or shall be an edge_loop or a vertex_loop.
WR8: The geometry of a bounding edge that is the edge_element of an oriented_edge that is referenced
by a face that is referenced either directly by a connected_face_set or via an oriented_face shall be
either within the reference tree of an advanced_face or shall be an edge_curve.
WR9: The curve used to define the geometry of an edge that is the edge_geometry of an edge_curve
of an edge that is referenced by a face that is referenced either directly by a connected_face_set or via
an oriented_face shall be either a b_spline_curve,a conic,a curve_replica,a line,an offset_curve_3d,
a pcurve,a polyline,a surface_curve,ora curve in the reference tree of an advanced_face.
WR10: All basis geometry that is referenced by curves shall be either within the reference tree of an
advanced_face or shall be valid curvesand surfaces.
The parent_curve of a curve_replica shall be either a line, conic, pcurve, surface_curve, offset_-
curve_3d, b_spline_curve, polyline,or curve_replica.
The basis_curve of an offset_curve_3d shall be either a line, conic, pcurve, surface_curve, offset_-
curve_3d, b_spline_curve,or curve_replica.
The curve_3d of a surface_curve shall be either a line, conic, offset_curve_3d, b_spline_curve, poly-
line,or curve_replica.
The basis_surface of a surface_curve shall be either a b_spline_surface, elementary_surface, offset_-
surface, surface_replica,or swept_surface.
Polylines shall contain at least three cartesian_points.
The attribute self_intersect shall be set to FALSE or UNKNOWN for b_spline_curvesand offset_-
curve_3ds.
NOTE 10 - A curve is validated against these constraints by the function nmsf_curve_check.
WR11: The edge_start and edge_end of an edge shall be either within the reference tree of an ad-
vanced_face or shall be vertex_points.
WR12: The vertex_geometry of a vertex that is part of an edge_loop shall be either within the refer-
ence tree of an advanced_face or shall be a cartesian_point, point_on_curve, point_on_surface,or
degenerate_pcurve.
�c ISO 2001 – All rights reserved 13
WR13: The loop_vertex of a vertex_loop shall be either within the reference tree of an advanced_face
or shall be a vertex_point.
WR14: The vertex_geometry of a vertex that is part of a vertex_loop shall be either within the refer-
ence tree of an advanced_face or shall be a cartesian_point, point_on_curve, point_on_surface,or
degenerate_pcurve.
Informal propositions:
IP1: The portion of a b_spline_curve that is within the topological domain of a non_manifold_-
surface_shape_representation shall not self-intersect.
IP2: The portion of a b_spline_surface that is within the topological domain of a non_manifold_-
surface_shape_representation shall not self-intersect.
IP3: The portion of an offset_curve_3d that is within the topological domain of a non_manifold_-
surface_shape_representation shall not self-intersect.
IP4: The portion of an offset_surface that is within the topological domain of a non_manifold_-
surface_shape_representation shall not self-intersect.
IP5: If a face has only one connected outer bound, the corresponding loop shall be represented as face_-
outer_bound. If the outer bound is not connected, face_outer_bound shall not be used.
4.3 aic_non_manifold_surface function definitions
This section describes functions required to formulate constraints for the aic_non_manifold_surface
schema. These functions are used in the specification of the entity non_manifold_surface_shape_-
representation.
4.3.1 nmsf_curve_check
The nmsf_curve_check function checks a curve instance for validity in the context of a non_manifold_-
surface_shape_representation. All geometry that is referenced by this curve instance, such as other
curvesand surfaces, are also validated.
EXAMPLE One of the constraints that is validated by this function is whether the self-intersection flag of a
b_spline_curve instance is set to TRUE, FALSE, or UNKNOWN; only FALSE and UNKNOWN are valid.
Where appropriate an instance is investigated recursively. This means if a curve references another
curve as a basis curve or parent curve, the nmsf_curve_check function is called again. If a surface is
referenced, the nmsf_surface_check function is called. The recursive process terminates at entity types
that do not reference any curvesor surfaces.
The following curve types and their subtypes are within the scope of the non_manifold_surface_-
shape_representation and are, thus, valid input to this function:
14 �c ISO 2001 – All rights reserved
– b_spline_curve;
– conic;
– curve_replica;
– line;
– offset_curve_3d;
– pcurve;
– polyline;
– surface_curve.
Four of these curve types reference basis or parent curves. The lists below indicate the valid references.
NOTE 1 - This function applies to those entity types that are marked in the lists below a recursive process
to check their entity references for valid instantiations.
The parent_curve of a curve_replica shall be of one of the following types:
– b_spline_curve;
– conic;
– curve_replica (recursive);
– line;
– offset_curve_3d (recursive);
– pcurve (recursive);
– polyline;
– surface_curve (recursive).
The basis_curve of an offset_curve_3d shall be of one of the following types:
– b_spline_curve;
– conic;
– curve_replica (recursive);
�c ISO 2001 – All rights reserved 15
– line;
– offset_curve_3d (recursive);
– pcurve (recursive);
– surface_curve (recursive).
The one instance in the set of items of a definitional_representation that is referenced as reference_-
to_curve by a pcurve shall be of one of the following types:
– b_spline_curve;
– conic;
– curve_replica (recursive);
– line;
– polyline.
The curve_3d of a surface_curve shall be of one of the following types:
– b_spline_curve;
– conic;
– curve_replica (recursive);
– line;
– offset_curve_3d (recursive);
– polyline;
– surface_curve (recursive).
Pcurve and surface_curve reference surfaces. Function nmsf_surface_check is called for validation
of these surfaces. The non_manifold_surface_shape_representation requires the same constraints on
valid surface references for pcurvesand surface_curves as specified in ISO 10303-42.
A valid polyline shall consist of at least three cartesian_points.
The attribute self_intersect shall for B-spline and offset geometry be set to FALSE or UNKNOWN.
16 �c ISO 2001 – All rights reserved
This function returns TRUE, if the types of all referenced geometries are within the scope of the non_-
manifold_surface_shape_representation and if all constraints are fulfilled, otherwise the function re-
turns FALSE.
NOTE 2 - This function does not check the correctness of references with respect to requirements specified
by ISO 10303-42. Only additional requirements due to the scope of the non_manifold_surface_shape_re-
presentation are checked.
EXPRESS specification:
*)
FUNCTION nmsf_curve_check (cv : representation_item) : BOOLEAN;
(* This function verifies the validity ofa curve in the context of a
non-manifold surface model. Representation_items are
valid input, however, they are supposed to be curves; otherwise
this function will return false.
*)
(* complex subtypes of curve that are both bounded_curve and
oneof conic, curve_replica, line, or offset_curve_3d are not
valid
*)
IF SIZEOF ([’AIC_NON_MANIFOLD_SURFACE.BOUNDED_CURVE’,
’AIC_NON_MANIFOLD_SURFACE.CONIC’,
’AIC_NON_MANIFOLD_SURFACE.CURVE_REPLICA’,
’AIC_NON_MANIFOLD_SURFACE.LINE’,
’AIC_NON_MANIFOLD_SURFACE.OFFSET_CURVE_3D’] * TYPEOF(cv)) > 1
THEN RETURN(FALSE);
ELSE
(* b_spline_curves shall not self-intersect
*)
IF ((’AIC_NON_MANIFOLD_SURFACE.B_SPLINE_CURVE’ IN TYPEOF (cv)) AND
(cv\b_spline_curve.self_intersect = FALSE) OR
(cv\b_spline_curve.self_intersect = UNKNOWN))
THEN RETURN(TRUE);
ELSE
(* conics and lines are valid curve types
*)
IF SIZEOF ([’AIC_NON_MANIFOLD_SURFACE.CONIC’,
’AIC_NON_MANIFOLD_SURFACE.LINE’] * TYPEOF (cv)) = 1 THEN
RETURN(TRUE);
ELSE
(* a curve_replica shall reference a valid curve
*)
IF ’AIC_NON_MANIFOLD_SURFACE.CURVE_REPLICA’ IN TYPEOF(cv) THEN
RETURN (nmsf_curve_check(cv\curve_replica.parent_curve));
�c ISO 2001 – All rights reserved 17
ELSE
(* an offset_curve_3d shall not self-intersect and
shall reference a valid curve; a polyline is not a
valid basis_curve
*)
IF ((’AIC_NON_MANIFOLD_SURFACE.OFFSET_CURVE_3D’ IN TYPEOF (cv))
AND
((cv\offset_curve_3d.self_intersect = FALSE) OR
(cv\offset_curve_3d.self_intersect = UNKNOWN))
AND
(NOT (’AIC_NON_MANIFOLD_SURFACE.POLYLINE’ IN TYPEOF
(cv\offset_curve_3d.basis_curve)))) THEN
RETURN (nmsf_curve_check(cv\offset_curve_3d.basis_curve));
ELSE
(* a pcurve shall reference a valid curve and a valid
basis_surface
*)
IF ’AIC_NON_MANIFOLD_SURFACE.PCURVE’ IN TYPEOF(cv) THEN
RETURN ((nmsf_curve_check
(cv\pcurve.reference_to_curve\representation.items[1]))
AND
(nmsf_surface_check(cv\pcurve.basis_surface)));
ELSE
(* a surface_curve references a curve_3d and one or
two pcurves or one or two surfaces or one of
each; all of these references shall be valid
*)
IF ’AIC_NON_MANIFOLD_SURFACE.SURFACE_CURVE’ IN TYPEOF(cv) THEN
(* if the curve reference is correct, check also the rest
*)
IF nmsf_curve_check(cv\surface_curve.curve_3d) THEN
REPEAT i := 1 TO SIZEOF
(cv\surface_curve.associated_geometry);
(* do for one or two associated_geometrys:
*)
IF ’AIC_NON_MANIFOLD_SURFACE.SURFACE’ IN
TYPEOF (cv\surface_curve.associated_geometry[i]) THEN
IF NOT nmsf_surface_check
(cv\surface_curve.associated_geometry[i]) THEN
RETURN(FALSE);
END_IF;
ELSE
IF ’AIC_NON_MANIFOLD_SURFACE.PCURVE’ IN TYPEOF
(cv\surface_curve.associated_geometry[i]) THEN
IF NOT nmsf_curve_check
(cv\surface_curve.associated_geometry[i]) THEN
RETURN(FALSE);
18 �c ISO 2001 – All rights reserved
END_IF;
END_IF;
END_IF;
END_REPEAT;
RETURN(TRUE);
END_IF;
ELSE
(* a polyline shall have at least 3 points
*)
IF ’AIC_NON_MANIFOLD
...
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