ISO 10303-513:2000

• Abstract:

  This part of ISO 10303 specifies the interpretation of the generic resources for the definition of an elementary boundary representation model. The following are within the scope of this part of ISO 10303: — the definition of an elementary_brep_shape_representation, this is a representation composed of one or more manifold_solid_breps each of which is defined with elementary geometry and complete explicit topology; — the definition of the unbounded geometry of curves and surfaces used in the definition of the faces of such a B-rep model; — the definition of the topological structure of a B-rep model; — 3D geometry; — B-reps; — elementary curves, these are lines or conics; — elementary_surfaces; — geometric transformations; — polylines; — unbounded geometry; — use of topology to bound geometric entities. The following are outside the scope of this part of ISO 10303: — 2D geometry; — bounded curves other than polylines; — bounded surfaces — offset curves and surfaces. This AIC is independent of any industrial application domain.

• Status: Published
• Publication Date: 06-Sep-2000
• ICS: 25.040.40 - Industrial process measurement and control
• Technical Committee: ISO/TC 184/SC 4 - Industrial data
• Drafting Committee: ISO/TC 184/SC 4/WG 12 - STEP product modelling and resources
• Current Stage: 9093 - International Standard confirmed
• Start Date: 28-Jun-2024
• Completion Date: 29-Aug-2026

• Referred By: CR 13935:2000 - Non-destructive testing - Generic NDE data format model
• Effective Date: 25-Aug-2026

ISO 10303-513:2000 - Overview

ISO 10303-513:2000 is an Application Interpreted Construct (AIC) in the STEP family (ISO 10303) that defines an elementary boundary representation (B‑rep) for 3D product data representation and exchange. It specifies how generic integrated resources are interpreted to represent one or more manifold_solid_breps constructed from elementary geometry (lines, conics, polylines, elementary_surfaces) with explicit topology. This AIC is application‑domain independent and intended for neutral, system‑independent exchange of B‑rep solid models.

Key topics and technical requirements

• Elementary B‑rep definition: A shape_representation composed of one or more manifold_solid_breps whose faces and edges are defined by elementary geometry and explicit topology.
• Allowed geometry: Supports 3D elementary curves (lines, conics) and polylines, and elementary_surfaces (planes, spheres, cylinders, cones, toroidal variants, etc. as referenced from ISO 10303‑42).
• Unbounded geometry: Includes definitions for unbounded curves and surfaces used to define face geometry.
• Topology and bounding: Uses topological constructs (edge_loop, face_bound, connected_face_set, closed_shell) to bound geometric entities and define manifold solids.
• EXPRESS schema: The AIC provides an EXPRESS schema (aic_elementary_brep) and defines the high‑level entity elementary_brep_shape_representation with formal WHERE rules restricting items to allowed types (manifold_solid_brep, mapped_item, etc.).
• Scope exclusions: Explicitly excludes 2D geometry, bounded curves other than polylines, bounded surfaces, and offset curves/surfaces.

Practical applications and users

ISO 10303-513 is useful where precise, portable 3D B‑rep models made from elementary geometry are required:

• CAD/CAM/CAE data exchange between heterogeneous systems using STEP as a neutral format
• Product lifecycle management (PLM) and archival of solid models with explicit topology
• Interoperability for machining, simulation, inspection workflows that rely on analytic curve/surface representations
• Software vendors, systems integrators, and standards implementers creating STEP import/export, translators, or validation tools
• Quality assurance and test-suite authors implementing AIC conformance checks

Related standards

• ISO 10303‑1 (overview and principles)
• ISO 10303‑41 (product shape representation)
• ISO 10303‑42 (geometric & topological resources)
• ISO 10303‑43 (representation structures)
• ISO 10303‑514 (advanced boundary representation)
• ISO 10303‑11 / -12 (EXPRESS language references)
• ISO 10303‑202 (AIC terminology)

Keywords: ISO 10303-513, STEP, elementary B‑rep, boundary representation, manifold_solid_brep, elementary geometry, topology, EXPRESS schema, polylines, conics, 3D geometry.

INTERNATIONAL ISO
STANDARD 10303-513
First edition
2000-09-01
Industrial automation systems and
integration — Product data representation
and exchange —
Part 513:
Application interpreted construct:
Elementary boundary representation
Systèmes d'automatisation industrielle et intégration — Représentation et
échange de données de produits —
Partie 513: Construction interprétée d'application: Représentation des
limites élémentaires
Reference number
©
ISO 2000
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ii © ISO 2000 – All rights reserved

Contents Page
1 Scope . . . . . 1
2 Normativereferences . . . . 2
3 Terms,definitions,andabbreviations . . . . 2
3.1 Terms defined in ISO 10303-1 . . . . 3
3.2 Terms defined in ISO 10303-42 . . . 3
3.3 Terms defined in ISO 10303-202 . . . 3
3.4 Terms defined in ISO 10303-514 . . . 4
3.5 Otherdefinitions . . . . 4
3.6 Abbreviations. . . . 4
4 EXPRESSshortlisting . . . . 4
4.1 Fundamental concepts and assumptions . . . 6
4.2 aic_elementary_brep schema entity definition: elementary_brep_shape_representation 7
Annex A (normative) Short names of entities. . . 12
AnnexB(normative) Informationobjectregistration . . . 13
B.1 Documentidentification . . . . 13
B.2 Schemaidentification. . . . 13
AnnexC(informative) Computer-interpretablelistings . . . 14
AnnexD(informative) EXPRESS-Gdiagrams . . . 15
AnnexE(informative) AICconformancerequirementsandtestpurposes . . 20
E.1 AICconformancerequirements:elementaryB-rep . . . 20
E.2 TestpurposesforelementaryB-repAIC . . . 21
E.3 AbstracttestcasesforelementaryB-rep . . . 25
E.4 ContextsdefinedfortestcasesofelementaryB-rep . . . 41
Index . . . . . 56
Figures
Figure D.1 aic_elementary_boundary_representation EXPRESS-G diagram, page 1 of 4 . 16
Figure D.2 aic_elementary_boundary_representation EXPRESS-G diagram, page 2 of 4 . 17
Figure D.3 aic_elementary_boundary_representation EXPRESS-G diagram, page 3 of 4 . 18
Figure D.4 aic_elementary_boundary_representation EXPRESS-G diagram, page 4 of 4 . 19
Tables
Table A.1 Short names of entities . . . . . . 12
c ISO 2000 — All rights reserved iii

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 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.
International Standard ISO 10303-513 was prepared by Technical Committee ISO/TC 184, Industrial
automation systems and integration, Subcommittee SC 4, Industrial da.ta.
A complete list of parts of ISO 10303 is available from the Internet:

This part of ISO 10303 is a member of the application interpreted constructs series.
Annexes A and B form a normative part of this part of ISO 10303. Annexes C, D and E are for
information only.
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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 construct series.
An application interpreted construct (AIC) provides a logical grouping of interpreted constructs that
supportsa 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 definition ofa boundary representa-
tion solid with elementary geometry and explicit topology.
c ISO 2000— All rights reserved v

INTERNATIONAL STANDARD ISO 10303-513:2000(E)
Industrial automation systems and integration —
Product data representation and exchange —
Part 513 :
Application interpreted construct:
Elementary boundary representation
1Scope
This part of ISO 10303 specifies the interpretation of the generic resources for the definition of an ele-
mentary boundary representation model.
The following are within the scope of this part of ISO 10303:
— the definition of an elementary_brep_shape_representation, this is a representation composed
of one or more manifold_solid_breps each of which is defined with elementary geometry and
complete explicit topology;
— the definition of the unbounded geometry of curves and surfaces used in the definition of the faces
of such a B-rep model;
— the definition of the topological structure of a B-rep model;
— 3D geometry;
— B-reps;
— elementary curves, these are linesor conics;
— elementary_surfaces;
— geometric transformations;
— polylines;
— unbounded geometry;
— use of topology to bound geometric entities.
The following are outside the scope of this part of ISO 10303:
— 2D geometry;
— bounded curves other than polylines;
— bounded surfaces;
c ISO 2000 — All rights reserved 1

— offset curves and surfaces.
This AIC is independent of any industrial application 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: 1995, Information technology - Abstract Syntax Notation One (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/TR 10303-12: 1997, Industrial automation systems and integration - Product data representation
and exchange - Part 12 : Description methods: The EXPRESS-I 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.
ISO 10303-514: 1999, Industrial automation systems and integration - Product data representation and
exchange - Part 514: Application interpreted construct: Advanced boundary representation.
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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.
— application;
— application context;
— application protocol;
— implementation method;
— integrated resource;
— interpretation;
— product data.
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.
— arcwise connected;
— boundary;
— bounds;
— coordinate space;
— curve;
— open curve;
— orientable;
— surface;
— topological sense.
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.
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— AIC.
3.4 Terms defined in ISO 10303-514
For the purposes of this part of ISO 10303, the following terms defined in ISO 10303-514 apply.
— manifold solid.
3.5 Other definitions
For the purposes of this part of ISO 10303 the following definitions apply:
3.5.1
elementary B-rep shape representation
a shape representation made up of one or more manifold solid B-reps. Each constituent B-rep is required
to have its faces and edges defined by elementary geometry.
3.5.2
elementary geometry
geometry composed of lines, polylines, conicsand elementary_surfaces.
3.6 Abbreviations
For the purposes of this part of ISO 10303, the following abbreviations apply:
AIC application interpreted construct
AP application protocol
B-rep boundary representation solid model
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 manifold solid models with faces having elementary geometry and explicitly defined
edges and vertices. The faces of the B-rep models are bounded by polylines, lines or conics.
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The highest level entity in this AIC is the elementary_brep_shape_representation. This is a shape_-
representation (see: ISO 10303-41) consisting of manifold_solid_brepsand mapped_itemsdefined
as translated or transformed copies of manifold_solid_breps having elementary geometry.
EXPRESS specification:
*)
SCHEMA aic_elementary_brep;
USE FROM geometry_schema(axis2_placement_3d,
cartesian_point,
cartesian_transformation_operator_3d,
circle,
conical_surface,
cylindrical_surface,
degenerate_toroidal_surface,
direction,
ellipse,
hyperbola,
line,
parabola,
plane,
polyline,
spherical_surface,
toroidal_surface,
vector);
USE FROM geometric_model_schema(manifold_solid_brep,
brep_with_voids);
REFERENCE FROM geometric_model_schema(msb_shells);
USE FROM topology_schema(closed_shell,
connected_face_set,
edge_curve,
edge_loop,
face_bound,
face_outer_bound,
face_surface,
oriented_closed_shell,
vertex_loop,
vertex_point);
USE FROM representation_schema(mapped_item);
USE FROM product_property_representation_schema(shape_representation);
(*
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NOTE 2 The connected_face_set entity is explicitly interfaced (i.e. included in the USE FROM lists) to allow
rules in the elementary_brep_shape_representation entity to access attributes of this entity. For the use of this
AIC this entity shall only be instantiated as one of its subtypes.
NOTE 3 The schemas referenced above can be found in the following parts of ISO 10303:
geometry_schema ISO 10303-42
geometric_model_schema ISO 10303-42
topology_schema ISO 10303-42
representation_schema ISO 10303-43
product_property_representation_schema ISO 10303-41
4.1 Fundamental concepts and assumptions
The following entities are intended to be independently instantiated in the application protocol schemas
that use this AIC:
— axis2_placement_3d;
— brep_with_voids;
— cartesian_point;
— cartesian_transformation_operator_3d;
— circle;
— closed_shell;
— conical_surface;
— cylindrical_surface;
— degenerate_toroidal_surface;
— direction;
— edge_curve;
— edge_loop;
— elementary_face;
— ellipse;
— face_bound;
— face_outer_bound;
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— face_surface;
— hyperbola;
— line;
— manifold_solid_brep;
— mapped_item;
— oriented_closed_shell;
— parabola;
— plane;
— polyline;
— representation_map;
— spherical_surface;
— toroidal_surface;
— vector;
— vertex_loop;
— vertex_point.
An application protocol that uses this AIC shall require that all the above entities are supported.
An application protocol that uses this AIC shall permit the shape_representation entity to be instantiated
as an elementary_brep_shape_representation.
4.2 aic_elementary_brep schema entity definition:
elementary_brep_shape_representation
The elementary_brep_shape_representation is a type of shape_representation in which the repre-
sentation items are specialisations of manifold_solid_brep entities. These differ from the more general
B-rep in having only explicit geometric forms for their faces and edges. The face geometry is restricted
to elementary_surfaces, and the edge curves to lines, polylinesor conics.
c ISO 2000 — All rights reserved 7

EXPRESS specification:
*)
ENTITY elementary_brep_shape_representation
SUBTYPE OF (shape_representation);
WHERE
WR1 : SIZEOF (QUERY (it <* SELF.items |
NOT (SIZEOF ([’AIC_ELEMENTARY_BREP.MANIFOLD_SOLID_BREP’,
’AIC_ELEMENTARY_BREP.FACETED_BREP’,
’AIC_ELEMENTARY_BREP.MAPPED_ITEM’,
’AIC_ELEMENTARY_BREP.AXIS2_PLACEMENT_3D’] *
TYPEOF(it)) = 1))) = 0;
WR2 : SIZEOF (QUERY (it <* SELF.items |
SIZEOF([’AIC_ELEMENTARY_BREP.MANIFOLD_SOLID_BREP’,
’AIC_ELEMENTARY_BREP.MAPPED_ITEM’] * TYPEOF(it)) =1 )) > 0;
WR3 : SIZEOF (QUERY (msb <* QUERY (it <* SELF.items |
’AIC_ELEMENTARY_BREP.MANIFOLD_SOLID_BREP’ IN TYPEOF(it)) |
NOT (SIZEOF (QUERY (csh <* msb_shells(msb) |
NOT (SIZEOF (QUERY(fcs <* csh.cfs_faces |
NOT(’AIC_ELEMENTARY_BREP.FACE_SURFACE’ IN TYPEOF(fcs)))) = 0
)))=0
)))=0;
WR4 : SIZEOF (QUERY (msb <* QUERY (it <* SELF.items |
’AIC_ELEMENTARY_BREP.MANIFOLD_SOLID_BREP’ IN TYPEOF(it)) |
NOT (SIZEOF (QUERY (csh <* msb_shells(msb) |
NOT (SIZEOF (QUERY(fcs <* csh\connected_face_set.cfs_faces |
NOT((’AIC_ELEMENTARY_BREP.ELEMENTARY_SURFACE’ IN
TYPEOF(fcs\face_surface.face_geometry))
))) = 0
)))=0
)))=0;
WR5 : SIZEOF (QUERY (msb <* QUERY (it <* SELF.items |
’AIC_ELEMENTARY_BREP.MANIFOLD_SOLID_BREP’ IN TYPEOF(it)) |
NOT (SIZEOF (QUERY (csh <* msb_shells(msb) |
NOT (SIZEOF (QUERY(fcs <* csh\connected_face_set.cfs_faces |
NOT (SIZEOF(QUERY (elp_fbnds <* QUERY (bnds <* fcs.bounds |
’AIC_ELEMENTARY_BREP.EDGE_LOOP’ IN TYPEOF(bnds.bound)) |
NOT (SIZEOF (QUERY (oe <* elp_fbnds.bound\path.edge_list |
NOT(’AIC_ELEMENTARY_BREP.EDGE_CURVE’ IN
TYPEOF(oe.edge_element)))) = 0
)))=0
)))=0
))) = 0
))) = 0;
WR6 : SIZEOF (QUERY (msb <* QUERY (it <* SELF.items |
’AIC_ELEMENTARY_BREP.MANIFOLD_SOLID_BREP’ IN TYPEOF(it)) |
NOT (SIZEOF (QUERY (csh <* msb_shells(msb) |
NOT (SIZEOF (QUERY(fcs <* csh\connected_face_set.cfs_faces |
NOT (SIZEOF(QUERY (elp_fbnds <* QUERY (bnds <* fcs.bounds |
’AIC_ELEMENTARY_BREP.EDGE_LOOP’ IN TYPEOF(bnds.bound)) |
NOT (SIZEOF (QUERY (oe <* elp_fbnds.bound\path.edge_list |
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NOT (SIZEOF ([’AIC_ELEMENTARY_BREP.LINE’,
’AIC_ELEMENTARY_BREP.CONIC’,
’AIC_ELEMENTARY_BREP.POLYLINE’] *
TYPEOF(oe.edge_element\edge_curve.edge_geometry)) = 1 )
)) = 0
))) = 0
)))=0
)))=0
)))=0;
WR7 : SIZEOF (QUERY (msb <* QUERY (it <* SELF.items |
’AIC_ELEMENTARY_BREP.MANIFOLD_SOLID_BREP’ IN TYPEOF(it)) |
NOT (SIZEOF (QUERY (csh <* msb_shells(msb) |
NOT (SIZEOF (QUERY(fcs <* csh\connected_face_set.cfs_faces |
NOT (SIZEOF(QUERY (elp_fbnds <* QUERY (bnds <* fcs.bounds |
’AIC_ELEMENTARY_BREP.EDGE_LOOP’ IN TYPEOF(bnds.bound)) |
NOT (SIZEOF (QUERY (oe <* elp_fbnds.bound\path.edge_list |
NOT((’AIC_ELEMENTARY_BREP.VERTEX_POINT’ IN TYPEOF(oe.edge_start))
AND (’AIC_ELEMENTARY_BREP.VERTEX_POINT’ IN
TYPEOF(oe.edge_end))
))) = 0
))) = 0
))) = 0
)))=0
)))=0;
WR8 : SIZEOF (QUERY (msb <* QUERY (it <* SELF.items |
’AIC_ELEMENTARY_BREP.MANIFOLD_SOLID_BREP’ IN TYPEOF(it)) |
NOT (SIZEOF (QUERY (csh <* msb_shells(msb) |
NOT (SIZEOF (QUERY(fcs <* csh\connected_face_set.cfs_faces |
NOT (SIZEOF(QUERY (elp_fbnds <* QUERY (bnds <* fcs.bounds |
’AIC_ELEMENTARY_BREP.EDGE_LOOP’ IN TYPEOF(bnds.bound)) |
NOT (SIZEOF (QUERY (oe <* elp_fbnds.bound\path.edge_list |
(’AIC_ELEMENTARY_BREP.POLYLINE’ IN
TYPEOF(oe.edge_element\edge_curve.edge_geometry)) AND
(NOT (SIZEOF (oe\oriented_edge.edge_element\
edge_curve.edge_geometry\polyline.points) >= 3))
)) = 0
))) = 0
)))=0
)))=0
)))=0;
WR9 : SIZEOF (QUERY (msb <* QUERY (it <* items |
’AIC_ELEMENTARY_BREP.MANIFOLD_SOLID_BREP’ IN TYPEOF(it)) |
’AIC_ELEMENTARY_BREP.ORIENTED_CLOSED_SHELL’ IN TYPEOF
(msb\manifold_solid_brep.outer)))
=0;
WR10 : SIZEOF (QUERY (brv <* QUERY (it <* items |
’AIC_ELEMENTARY_BREP.BREP_WITH_VOIDS’ IN TYPEOF(it)) |
NOT (SIZEOF (QUERY (csh <* brv\brep_with_voids.voids |
csh\oriented_closed_shell.orientation)) = 0))) = 0;
WR11 : SIZEOF (QUERY (mi <* QUERY (it <* items |
’AIC_ELEMENTARY_BREP.MAPPED_ITEM’ IN TYPEOF(it)) |
NOT (’AIC_ELEMENTARY_BREP.ELEMENTARY_BREP_SHAPE_REPRESENTATION’ IN
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TYPEOF(mi\mapped_item.mapping_source.
mapped_representation)))) = 0;
WR12 : SIZEOF (QUERY (msb <* QUERY (it <* SELF.items |
’AIC_ELEMENTARY_BREP.MANIFOLD_SOLID_BREP’ IN TYPEOF(it)) |
NOT (SIZEOF (QUERY (csh <* msb_shells(msb) |
NOT (SIZEOF (QUERY(fcs <* csh\connected_face_set.cfs_faces |
NOT (SIZEOF(QUERY (vlp_fbnds <* QUERY (bnds <* fcs.bounds |
’AIC_ELEMENTARY_BREP.VERTEX_LOOP’ IN TYPEOF(bnds.bound)) |
NOT((’AIC_ELEMENTARY_BREP.VERTEX_POINT’ IN
TYPEOF(vlp_fbnds\face_bound.bound\vertex_loop.loop_vertex)) AND
(’AIC_ELEMENTARY_BREP.CARTESIAN_POINT’ IN
TYPEOF(vlp_fbnds\face_bound.bound\vertex_loop.
loop_vertex\vertex_point.vertex_geometry))
))) = 0))) = 0))) = 0))) =0;
END_ENTITY;
(*
Formal propositions:
WR1: The items attribute of the representation supertype shall contain manifold_solid_breps, mapped_-
itemsand axis2_placement_3ds only. The use of faceted_breps is excluded by this rule since an in-
stance of faceted_brep would also be of type manifold_solid_brep.
WR2: At least one item in the items set shall be a manifold_solid_brep entity or a mapped_item (see
also WR11).
WR3: All faces used in constructing a manifold_solid_brep shall be of type face_surface.
NOTE 1 The call to function msb_shells in WR3, and later rules, is correct since, although the generic type of the
argument ‘msb’ is representation_item, ‘msb’ has been selected by QUERY to be of type manifold_solid_brep.
WR4: For each manifold_solid_brep in the items set, the associated surface for each face shall be an
elementary_surface.
WR5: For each manifold_solid_brep in the items set, the edges used to define the boundaries shall all
be of type edge_curve.
WR6: For each manifold_solid_brep in the items set, each curve used to define the face bounds shall
be either a conic,a line,or a polyline.
WR7: For each manifold_solid_brep in the items set, the edges used to define the boundaries shall all
be trimmed by vertices of type vertex_point.
WR8: For each manifold_solid_brep in the items set, each polyline used to define part of the face
bounds shall contain 3 or more points.
WR9: For each manifold_solid_brep in the items set, the outer shell attribute shall not be of type
oriented_closed_shell.
WR10: If a brep_with_voids is included in the items set, each shell in the voids set shall be an ori-
ented_closed_shell with orientation value FALSE.
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WR11: If a mapped_item is included in the items set, the mapped_representation of the map-
ping_source attribute shall be an elementary_brep_shape_representation.
NOTE If a cartesian_transformation_operator_3d is included as
mapped_item.mapping_target with an axis2_placement_3d that corresponds to the original coordinate system
as mapped_representation.mapping_origin, the resulting mapped_item is a transformed copy of the elementary_-
brep_shape_representation. The precise definition of the transformation, including translation, rotation, scaling
and, if appropriate, mirroring, is given by the transformation operator.
WR12: For each manifold_solid_brep in the items set, any vertex_loop used to define a face bound
shall reference a vertex_point with the geometry defined by a cartesian_point.
EXPRESS specification:
*)
END_SCHEMA; -- end AIC_ELEMENTARY_BREP SCHEMA
(*
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Annex A
(normative)
Short names of entities
Table A.1 provides the short names of entities specified in this part of ISO 10303. Requirements on the
use of the short names are found in the implementation methods included in ISO 10303.
Table A.1 – Short names of entities
Entity name Short name
ELEMENTARY_BREP_SHAPE_REPRESENTATION EBSR
12c ISO 2000 — All rights reserved

Annex B
(normative)
Information object registration
B.1 Document identification
To provide for unambiguous identification of an information object in an open system, the object identi-
fier
{ iso standard 10303 part(513) version(1) }
is assigned to this part of ISO 10303. The meaning of this value is defined in ISO/IEC 8824-1, and is
described in ISO 10303-1.
B.2 Schema identification
To provide for unambiguous identification of the aic_elementary_brep in an open information system,
the object identifier
{ iso standard 10303 part(513) version(1) object(1) aic-elementary-brep(1) }
is assigned to the aic_elementary_brep schema (see clause 4). The meaning of this value is defined in
ISO/IEC 8824-1, and is described in ISO 10303-1.
c ISO 2000 — All rights reserved 13

Annex C
(informative)
Computer-interpretable listings
This annex provides a listing of the EXPRESS entity names and corresponding short names as speci-
fied in this Part of ISO 10303 without comments or other explanatory text. This annex is available in
computer-interpretable form and can be found at the following URLs:
Short names: http://www.mel.nist.gov/div826/subject/apde/snr/
EXPRESS: http://www.mel.nist.gov/step/parts/part513/is/
If there is difficulty accessing these sites contact ISO Central Secretariat or contact the ISO TC 184/SC4
Secretariat directly at: [e-mail].
NOTE – The information provided in computer-interpretable form at the above URLs is informative. The infor-
mation that is contained in the body of this part of ISO 10303 is normative.
14c ISO 2000 — All rights reserved

Annex D
(informative)
EXPRESS-G diagrams
Figures D.1 through D.4 correspond to the EXPRESS generated from the short listing given in clause 4
using the interface specifications of ISO 10303-11. The diagrams use the EXPRESS-G graphical nota-
tion for the EXPRESS language. EXPRESS-G is defined in annex D of ISO 10303-11.
NOTE 1 The following select types are interfaced into the AIC expanded listing according to the implicit inter-
face rules of ISO 10303-11. These select types are not used by other entities in this part of ISO 10303.
— geometric_set_select;
— pcurve_or_surface;
— reversible_topology;
— shell;
— trimming_select;
— vector_or_direction.
NOTE 2 The implicit interface rules of ISO 10303-11 also introduce some entities whose instantiation is prohib-
ited by rules on the elementary_brep_shape_representation. These entities are marked""in the EXPRESS-G
diagrams.
c ISO 2000 — All rights reserved 15

elementary_
brep_shape_
coordinate_
space_
representation
geometric_
e
e dimension
solid_model
representation
shape_
_context
e
representation
e e e
e context_ context_ e
dimension_
type
identifier
manifold_
count
name
e
solid_brep
representation
representation
e
_context context_ e
mapped_
of_items
representation
e e
faceted_
brep_with_ items
brep * S[1:?]
voids
mapping_
outer
e origin representation
voidse
_map
1,4 (2) S[0:?] representation
e
e e e
mapping_
_item
mapping_
e
source
e
orientation
closed_ oriented_
e e
target
name
e
shell closed_shell
e
mapped_
e
e
closed_
item
shell_element
connected_
shell
1 face_set
e
e e
1,5 (2) cfs_faces
topological_ geometric_
S[1:?]
representation representation
e e
_item _item
open_
e 2,1
3,2
shell *
face 1
placement
e
open_ vector_or_
2,2
direction
shell_
face_bound4,34,1
element
e 1,1 (3,4)
vector
curve
oriented_
e e
2,3axis1 e
open_ e
vertex
3,1
scale
e
shell *
e
direction
surfaceaxis2
orientationee
2,4
2,7
e e
cartesian_
direction_edge
edge_curve e
2,5 transformation
ratios L[2:3]
_operator
loop 2,8
uL[3:3]
face_surface
(DER)
2,6
axis3
path 2,9
e point
e
vertex_point
e
cartesian_
1,2 (2) e
transformation
cartesian_ _operator_3d
length_
e
pointmeasure
e
1,3 (3,4)
coordinates
e
* excluded by rule on
L[1:3]
local_origin
elementary_brep_shape_representation
Figure D.1 – aic_elementary_boundary_representation EXPRESS-G
diagram, page 1 of 4
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reversible_
topology
e
2,8 (1)
face_geometry
face_
e
dsurface
reversible_
same_sense
e
3,4
e topology_item
oriented_
surface
eface *
face_orientation
face
e
element
e e
2,1 (1)
1,4
2,2 (1) closed_shell
bounds S[1:?]e e
face_outer e
e
face_bound
_bound e
1,5
orientation
boundopen_shell
e
2,6 (1)
e e
e
2,5 (1)
loop
path path_
e
element
edge_list
L[1:?]
d oriented_
path *
e
vertex_
e
loop
orientation
e
edge_
e
e
orientation
loop_vertexoriented_loop
d
edge
2,3 (1)
edge_element
d ee
e
edge_start
e 1
vertex
edge
e e
edge_end
e
e
e
vertex_
e2,4 (1)
2,9 (1)
pointe
edge_
2,7 (1)
curve
vertex_
geometry
edge_
same_
geometrysensee
1,2
point
4,2 curve
* entity is implicitly interfaced but
excluded by rules
Figure D.2 – aic_elementary_boundary_representation EXPRESS-G
diagram, page 2 of 4
c ISO 2000 — All rights reserved 17

1,2
point
4,2
trimming_
curve
select
pcurve_or_
geometric_
surface
set_select
3,2 (1) 1,3
cartesian_
e point
e e
e
3,1 (1)
placement
surface
location
e
3,4 (2)
1,1
direction
e
e
axis
axis2_
position
elementary_ e
ref_direction
placement_
surface
3d
e
pL[3:3](DER)
3,3 (4)
e
toroidal_
surface
major_
minor_ radius
e e e e
radius
e e
conical_ spherical_ cylindrical_
positive_ positive_
plane
surface
surface surface
length_ length_
measure measure
e
degenerate_
radius
semi_angle
radius radius
toroidal_
d d d
e surface
plane_
positive_ positive_
length_
angle_
measure
length_ length_ select_outer
measure
measure measure
e
Figure D.3 – aic_elementary_boundary_representation EXPRESS-G
diagram, page 3 of 4
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4,2 (2,3)
d
e
curve 4,1 (1)
d
bounded_
curve
d
1,3
pnt
cartesian_
line
d
point
polyline
dir
d
points
e
LIST[2:?] vector 4,3 (1)
d
orientation
1,3
’$
magnitude
cartesian_
point
1,1 direction d
length_
&%measure
d
position axis2_
d
conic
placement
3,3
axis2_placement_
3d
d d d d
ellipse parabola hyperbola
circle
semi_imag_
radius semi_axis_1 semi_axis_2 focal_dist semi_axis
axis
d d d d d d
positive_ positive_ positive_
length_
length_ length_ measure length_
measure measure measure
Figure D.4 – aic_elementary_boundary_representation EXPRESS-G
diagram, page 4 of 4
c ISO 2000 — All rights reserved 19

Annex E
(informative)
AIC conformance requirements and test purposes
E.1 AIC conformance requirements: elementary B-rep
Any application protocol that uses this AIC may require conformance to the AIC conformance require-
ments defined below when instantiating an elementary_brep_shape_representation.
Conformance to this AIC means that all the defined types and entity types defined in the EXPRESS listing
are supported. The only legitimate use, within the context of this AIC, for a geometric or topological
entity instance is for the purpose of defining an elementary_brep_shape_representation.
The following entities are instantiableas part of the definition of an elementary_brep_shape_representation:
— axis2_placement_3d;
— brep_with_voids;
— cartesian_point;
— cartesian_transformation_operator_3d;
— circle;
— closed_shell;
— conical_surface;
— cylindrical_surface;
— degenerate_toroidal_surface;
— direction;
— edge_curve;
— edge_loop;
— elementary_face;
— ellipse;
— face_bound;
20c ISO 2000 — All rights reserved

— face_outer_bound;
— face_surface;
— hyperbola;
— line;
— manifold_solid_brep;
— mapped_item;
— oriented_closed_shell;
— parabola;
— plane;
— polyline;
— representation_map;
— spherical_surface;
— toroidal_surface;
— vector;
— vertex_loop;
— vertex_point.
E.2 Test purposes for elementary B-rep AIC
This clause defines conformance test purposes which are appropriate for the elementary B-rep AIC. The
test purposes are based on the constructs found in clause 4 of this part of ISO 10303.
E.2.1 elementary_brep_shape_representation
The following test purposes are derived from the definition of this entity:
EB1: representation as shape_representation as
elementary_brep_shape_representation. (see E.3.1).
EB2: elementary_brep_shape_representation with context as geometric_context with items as
manifold_solid_brep. (see E.3.1).
c ISO 2000 — All rights reserved 21

EB3: elementary_brep_shape_representation with context as geometric_context with items as
mapped_item; (see E.3.6).
EB4: elementary_brep_shape_representation with context as geometric_context with items as
two or more items as manifold_solid_brep,or mapped_item,or axis2_placement_3d, including
at least one axis2_placement_3d. (see E.3.6)
E.2.2 manifold_solid_brep
The following test purposes are derived from the definition of this entity:
EB5: manifold_solid_brep with outer (voids absent) as closed_shell.(NOT oriented_closed_-
shell subtype.) (see E.3.1).
EB6: manifold_solid_brep as brep_with_voids subtype with outer as closed_shell and voids as
a SET of one oriented_closed_shell. (voids present) (see E.3.2)
EB7: manifold_solid_brep as brep_with_voids subtype with outer as closed_shell and voids as
a SET of more than one oriented_closed_shell. (voids present) (see E.3.2).
E.2.3 oriented_closed_shell
The following test purpose is derived from the definition of this entity and the constraints imposed on the
elementary_brep_shape_representation:
EB8: oriented_closed_shell with orientation = FALSE. (see E.3.2).
E.2.4 closed_shell
The following test purpose is derived from the definition of this entity and the constraints imposed on the
elementary_brep_shape_representation:
EB9: closed_shell with cfs_faces as a SET of one face_surface. (see E.3.2).
EB10: closed_shell with cfs_faces as a SET of more than one face_surface. (see E.3.1).
E.2.5 face
The following test purposes are derived from the definition of this entity and the constraints imposed on
the elementary_brep_shape_representation:
EB11: face as face_surface with bounds as SET of one face_bound as face_outer_bound with
orientation = TRUE. (see E.3.1).
22c ISO 2000 — All rights reserved

EB12: face as face_surface with bounds as SET of one face_bound as face_outer_bound with
bound as edge_loop (not oriented_path)and orientation = FALSE. (see E.3.1).
EB13: face as face_surface with bounds as SET of at least two face_bounds with bound as
edge_loop and orientation = TRUE. (see E.3.1).
EB14: face as face_surface with bounds as SET of at least two face_bounds with bound as
edge_loop and orientation = FALSE. (see E.3.1).
EB15: face as face_surface with bounds as SET of at least two face_bounds (including one ver-
tex_loop). (see E.3.5).
E.2.6 face_surface
The following test purposes are derived from the definition of this entity and the constraints imposed on
the elementary_brep_shape_representation:
EB16: face_surface with face_geometry as surface. (see E.3.1).
EB17: face_surface with same_sense = TRUE. (see E.3.1).
EB18: face_surface with same_sense = FALSE. (see E.3.5).
E.2.7 surface
The following test purposes are derived from the definition of this entity and the constraints imposed on
the face_surface:
EB19: surface as elementary_surface. (see E.3.1).
E.2.8 elementary_surface
The following test purposes are derived from the definition of this entity and the constraints imposed on
the face_surface:
EB20: elementary_surface with position as axis2_placement_3d with axis present. (see E.3.1).
EB21: elementary_surface with position as axis2_placement_3d with axis absent. (see E.3.4).
EB22: elementary_surface with position as axis2_placement_3d with ref_direction present.
(see E.3.1).
EB23: elementary_surface with position as axis2_placement_3d with ref_direction absent. (see
E.3.4).
c ISO 2000 — All rights reserved 23

EB24: elementary_surface as plane. (see E.3.1).
EB25: elementary_surface as cylindrical_surface. (see E.3.1).
EB26: elementary_surface as conical_surface. (see E.3.5).
EB27: elementary_surface as spherical_surface. (see E.3.1).
EB28: elementary_surface as toroidal_surface. (see E.3.3).
E.2.9 loop
The following test purposes are derived from the definition of this entity and the constraints imposed on
the face_surface:
EB29: loop as edge_loop. (see E.3.1).
EB30: loop as vertex_loop with loop_vertex as vertex_point with vertex_geometry as cartesian_-
point. (see E.3.2).
E.2.10 edge
The following test purposes are derived from the definition of this entity and the constraints imposed on
the face_surface:
EB31: edge as edge_curve with edge_start as vertex_point and edge_end as vertex_point.(see
E.3.1).
EB32: edge as oriented_edge with orientation TRUE. (see E.3.1).
EB33: edge as oriented_edge with orientation FALSE. (see E.3.3).
E.2.11 edge_curve
The following test purposes are derived from the definition of this entity and the constraints imposed on
the face_surface:
EB34: edge_curve with edge_geometry as line. (see E.3.3).
EB35: edge_curve with edge_geometry as polyline. (see E.3.4).
EB36: edge_curve with edge_geometry as conic. (see E.3.1).
EB37: edge_curve with same_sense = TRUE. (see E.3.1).
EB38: edge_curve with same_sense = FALSE. (see E.3.5)>
24c ISO 2000 — All rights reserved

E.2.12 conic
The following test purposes are derived from the definition of this entity and the constraints imposed on
the face_surface:
EB39: conic as circle. (see E.3.1).
EB40: conic as ellipse. (see E.3.1).
EB41: conic as hyperbola. (see E.3.5).
EB42: conic as parabola. (see E.3.5).
E.2.13 polyline
The following test purpose is derived from the definition of this entity and the constraints imposed on the
face_surface:
EB43: polyline with points as a LIST of 3 or more cartesian_points. (see E.3.4).
E.2.14 cartesian_transformation_operator_3d
The following test purposes are derived from the definitions of this entity, the mapped_item entity, and
the constraints imposed on the elementary_brep_shape_representation:
EB44: mapped_item with mapping_target as cartesian_transformation_operator_3d. (see E.3.7)
EB45: cartesian_transformation_operator as cartesian_transformation_operator_3d with scale
as REAL not equal to 1.0. (see E.3.7).
E.3 Abstract test cases for elementary B-rep
The post-processor abstract test cases in this clause are fully documented in EXPRESS-I.
A simple textual description is provided for each pre-processor test case to enable the creation of a model
similar to that described in the EXPRESS-I documentation of the post-processor test. For each test case
a number of relevant test purposes is identified.
NOTE Many of the test purposes are applicable to more than one test case, but the criteria are only defined with
the first such test case. This applies in particular to many of the purposes documented in test case eb1.
E.3.1 Test case eb1
Test case eb1 is the most basic test case consisting of the faces needed to define a single solid cylinder
with hemispherical base and elliptic top. All geometry is explicitly defined with no defaults and no sense
reversals of geometry required. The definition of the faces is provided by the cylinder_sphere_shell
context using the original parameters.
c ISO 2000 — All rights reserved 25

E.3.1.1 Test purpose coverage
The AIM test purposes addressed by this test case are listed below.
EB1 representation as shape_representation as elementary_brep_shape_representation;
EB2 elementary_brep_shape_representation with context as geometric_representation_contextwith items
as manifold_solid_brep;
EB5 manifold_solid_brep with outer (voids absent) as closed_shell (NOT oriented_closed_shell sub-
type);
EB10 closed_shell with cfs_faces as a SET of more than one face_surface;
EB11 face as face_surface with bounds as a SET of one face_bound as face_outer_bound with orienta-
tion TRUE;
EB12 face as face_surface with bounds as a SET of one face_bound as face_outer_bound with orienta-
tion FALSE;
EB13 face as face_surface with bounds as a SET of more than one face_bound with bound as an
edge_loop and orientation TRUE;
EB14 face as face_surface with bounds as a SET of more than one face_bound with bound as an
edge_loop and orientation FALSE;
EB16 face_surface with face_geometry as surface;
EB17 face_surface with same_sense = TRUE;
EB19 surface as elementary_surface;
EB20 elementary_surface with position as axis2_placement_3d with axis present;
EB22 elementary_surface with position as axis2_placement_3d with ref_direction present;
EB24 elementary_surface as plane;
EB25 elementary_surface as cylindrical_surface;
EB27 elementary_surface as spherical_surface;
EB29 loop as edge_loop;
EB31 edge as edge_curve with edge_start as vertex_point and edge_end as vertex_point;
EB32 edge as oriented_edge with orientation as TRUE;
EB36 edge_curve with edge_geometry as conic;
EB37 edge_curve with same_sense as TRUE;
EB39 conic as a circle;
EB40 conic as an ellipse.
E.3.1.2 Preprocessor input specification
Create an elementary_brep_shape_representation consisting of a single manifold_solid_brep.The
manifold_solid_brep should be in the form of a solid cylinder with a hemi-spherical base and a sloping
planar top. The centre of the hemisphere is at the origin and the Z axis is the axis of the cylinder. The
B-rep object is defined by a single closed shell with 3 faces. A suitable set of dimensions is defined in
the EXPRESS-I specification below.
NOTE The cylinder_sphere_shell context is used, in its simplest form with default values, to define the faces
of the B-rep.
26c ISO 2000 — All rights reserved

E.3.1.3 Postprocessor input specification
*)
TEST_CASE example_ebrep_1; WITH aic_elementary_brep;
REALIZATION
LOCAL
shell_object : closed_shell ;
cysp_solid : manifold_solid_brep ;
ebsr : elementary_brep_shape_representation ;
its_units : named_unit ;
its_context : representation_context ;
END_LOCAL;
CALL cylinder_sphere_shell ; -- uses default values, so no WITH
IMPORT (shell_object := @cyspshell; ) ;
END_CALL;
cysp_solid := manifold_solid_brep (’cysp_solid’, shell_object) ;
its_units := length_unit() || si_unit (’milli’, ’metre’) ;
its_context := geometric_representation_context
(’context_1’, ’context_for_cylinder_sphere’, 3) ||
global_unit_assigned_context ( [its_units] ) ;
ebsr := elementary_brep_shape_representation
( ’ebsr’, [cysp_solid], its_context );
END_REALIZATION;
END_TEST_CASE;
(*
E.3.1.4 Postprocessor verdict criteria
EB1: All WRs on elementary_brep_shape_representation shall be verified.
EB2: Length units shall be correctly interpreted, model re-created shall contain no polyloopsor
vertex_loops.
EB5: Shell normals shall point out of solid.
EB10: Faces shall be connected along edges, no other face intersections shall occur.
EB11: Face geometry shall be correctly trimmed by face_bound.
c ISO 2000 — All rig
...