ISO 10303-42:2003

INTERNATIONAL ISO
STANDARD 10303-42
Third edition
2003-04-15
Industrial automation systems and
integration — Product data
representation and exchange —
Part 42:
Integrated generic resource: Geometric
and topological representation
Systèmes d'automatisation industrielle et intégration — Représentation
et échange de données de produits —
Partie 42: Ressource générique intégrée: Représentation géométrique
et topologique
Reference number
©
ISO 2003
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ii © ISO 2003 — All rights reserved

Contents Page
1 Scope . . . . . 1
1.1 Geometry . . . . . 1
1.2 Topology . . . . . 2
1.3 GeometricShapeModels . . . . 2
2 Normativereferences . . . . 3
3 Terms,definitions,symbolsandabbreviations . . . 3
3.1 Terms defined in ISO 10303-1 . . . . 3
3.2 Othertermsanddefinitions. . . . 4
3.3 Symbols. . . . . . 9
3.4 Abbreviations. . . . . . . 12
4 Geometry . . . . . 13
4.1 Introduction. . . . 14
4.2 Fundamental concepts and assumptions . . . 14
4.2.1 Space dimensionality . . . . . . 14
4.2.2 Geometricrelationships . . . . 15
4.2.3 Parametrisation of analytic curves and surfaces . . 15
4.2.4 Curves . . . . 15
4.2.5 Surfaces . . . . 15
4.2.6 Preferredform . . . . 16
4.3 Geometryconstantandtypedefinitions . . . 16
4.3.1 dummy_gri . . . . 16
4.3.2 dimension_count . . . . 17
4.3.3 b_spline_curve_form. . . . 17
4.3.4 b_spline_surface_form . . . . . 18
4.3.5 extent_enumeration . . . . 19
4.3.6 knot_type. . . . 19
4.3.7 preferred_surface_curve_representation . . . 20
4.3.8 transition_code . . . . 21
4.3.9 trimming_preference . . . . . . 21
4.3.10 axis2_placement . . . . 22
4.3.11 curve_on_surface. . . . 22
4.3.12 pcurve_or_surface . . . . 23
4.3.13 surface_boundary . . . . 23
4.3.14 trimming_select . . . . 23
4.3.15 vector_or_direction. . . . 24
4.4 Geometry entity definitions . . . . . . 24
4.4.1 geometric_representation_context . . . 24
4.4.2 geometric_representation_item . . . 25
4.4.3 point . . . . 27
4.4.4 cartesian_point . . . . 27
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4.4.5 cylindrical_point . . . . 28
4.4.6 spherical_point . . . . 29
4.4.7 polar_point . . . . 30
4.4.8 point_on_curve. . . . 31
4.4.9 point_on_surface . . . . 32
4.4.10 point_in_volume . . . . 32
4.4.11 point_replica . . . . 33
4.4.12 degenerate_pcurve . . . . 34
4.4.13 evaluated_degenerate_pcurve . . . 35
4.4.14 direction . . . . 35
4.4.15 vector . . . . 36
4.4.16 placement. . . . 37
4.4.17 axis1_placement . . . . 37
4.4.18 axis2_placement_2d . . . . . . 38
4.4.19 axis2_placement_3d . . . . . . 39
4.4.20 cartesian_transformation_operator . . . 41
4.4.21 cartesian_transformation_operator_3d. . . 43
4.4.22 cartesian_transformation_operator_2d. . . 46
4.4.23 curve . . . . 47
4.4.24 line . . . . . 47
4.4.25 conic . . . . 48
4.4.26 circle . . . . 49
4.4.27 ellipse. . . . 49
4.4.28 hyperbola. . . . 52
4.4.29 parabola . . . . 53
4.4.30 clothoid. . . . 55
4.4.31 circular_involute . . . . 56
4.4.32 bounded_curve . . . . 58
4.4.33 polyline. . . . 59
4.4.34 b_spline_curve. . . . 59
4.4.35 b_spline_curve_with_knots . . . 62
4.4.36 uniform_curve . . . . 64
4.4.37 quasi_uniform_curve . . . . . . 65
4.4.38 bezier_curve . . . . 65
4.4.39 rational_b_spline_curve . . . . 67
4.4.40 trimmed_curve . . . . 68
4.4.41 composite_curve . . . . 71
4.4.42 composite_curve_segment . . . 73
4.4.43 reparametrised_composite_curve_segment . . . 74
4.4.44 pcurve . . . . 75
4.4.45 bounded_pcurve . . . . 76
4.4.46 surface_curve. . . . 76
4.4.47 intersection_curve . . . . 78
4.4.48 seam_curve . . . . 79
4.4.49 bounded_surface_curve . . . . 79
4.4.50 composite_curve_on_surface . . . 80
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4.4.51 offset_curve_2d . . . . 81
4.4.52 offset_curve_3d . . . . 83
4.4.53 curve_replica . . . . 84
4.4.54 surface . . . . 85
4.4.55 elementary_surface. . . . 85
4.4.56 plane . . . . 86
4.4.57 cylindrical_surface . . . . 87
4.4.58 conical_surface. . . . 88
4.4.59 spherical_surface. . . . 90
4.4.60 toroidal_surface . . . . 91
4.4.61 degenerate_toroidal_surface . . . 92
4.4.62 dupin_cyclide_surface . . . . . 94
4.4.63 swept_surface . . . . 98
4.4.64 surface_of_linear_extrusion . . . 99
4.4.65 surface_of_revolution . . . . . 100
4.4.66 surface_curve_swept_surface . . . 101
4.4.67 fixed_reference_swept_surface . . . 103
4.4.68 bounded_surface . . . . 105
4.4.69 b_spline_surface . . . . 105
4.4.70 b_spline_surface_with_knots . . . 108
4.4.71 uniform_surface . . . . 110
4.4.72 quasi_uniform_surface . . . . . 110
4.4.73 bezier_surface . . . . 111
4.4.74 rational_b_spline_surface . . . 112
4.4.75 rectangular_trimmed_surface . . . 113
4.4.76 curve_bounded_surface . . . . 115
4.4.77 boundary_curve . . . . 117
4.4.78 outer_boundary_curve . . . . . 117
4.4.79 rectangular_composite_surface . . . 117
4.4.80 surface_patch. . . . 119
4.4.81 offset_surface. . . . 120
4.4.82 oriented_surface . . . . 122
4.4.83 surface_replica . . . . 122
4.4.84 volume . . . . 123
4.4.85 block_volume . . . . 124
4.4.86 wedge_volume . . . . 125
4.4.87 pyramid_volume . . . . 127
4.4.88 tetrahedron_volume . . . . . . 128
4.4.89 hexahedron_volume . . . . . . 129
4.4.90 spherical_volume. . . . 130
4.4.91 cylindrical_volume. . . . 131
4.4.92 eccentric_conical_volume . . . 132
4.4.93 toroidal_volume . . . . 134
4.4.94 ellipsoid_volume . . . . 135
4.4.95 b_spline_volume . . . . 135
4.4.96 b_spline_volume_with_knots . . . 138
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4.4.97 bezier_volume . . . . 139
4.4.98 uniform_volume . . . . 140
4.4.99 quasi_uniform_volume . . . . . 141
4.4.100 rational_b_spline_volume . . . 142
4.5 Geometryschemaruledefinition:compatible_dimension . . 143
4.6 Geometryfunctiondefinitions . . . . 144
4.6.1 dimension_of. . . . 145
4.6.2 acyclic_curve_replica . . . . . 146
4.6.3 acyclic_point_replica . . . . . . 147
4.6.4 acyclic_surface_replica . . . . 147
4.6.5 associated_surface . . . . 148
4.6.6 base_axis . . . . 149
4.6.7 build_2axes. . . . 150
4.6.8 build_axes . . . . 151
4.6.9 orthogonal_complement . . . . 152
4.6.10 first_proj_axis . . . . 152
4.6.11 second_proj_axis. . . . 154
4.6.12 cross_product. . . . 155
4.6.13 dot_product. . . . 156
4.6.14 normalise . . . . 157
4.6.15 scalar_times_vector . . . . 158
4.6.16 vector_sum . . . . 159
4.6.17 vector_difference. . . . 161
4.6.18 default_b_spline_knot_mult . . . 162
4.6.19 default_b_spline_knots . . . . . 163
4.6.20 default_b_spline_curve_weights. . . 164
4.6.21 default_b_spline_surface_weights . . . 165
4.6.22 constraints_param_b_spline . . . 165
4.6.23 curve_weights_positive . . . . 167
4.6.24 constraints_composite_curve_on_surface . . . 168
4.6.25 get_basis_surface. . . . 168
4.6.26 surface_weights_positive . . . . 169
4.6.27 volume_weights_positive . . . 170
4.6.28 constraints_rectangular_composite_surface . . . . 171
4.6.29 list_to_array . . . . 172
4.6.30 make_array_of_array . . . . . . 173
4.6.31 make_array_of_array_of_array . . . 174
4.6.32 above_plane . . . . 175
4.6.33 same_side . . . . 176
5 Topology . . . . . 178
5.1 Introduction. . . . 178
5.2 Fundamental concepts and assumptions . . . 178
5.2.1 Geometricassociations. . . . 179
5.2.2 Associationswithparameterspacegeometry . . . 180
5.2.3 Graphs,cycles,andtraversals . . . 182
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5.3 Topology constant and type definitions. . . 183
5.3.1 dummy_tri . . . . 183
5.3.2 shell. . . . . 183
5.3.3 reversible_topology_item . . . 184
5.3.4 list_of_reversible_topology_item . . . 184
5.3.5 set_of_reversible_topology_item . . . 185
5.3.6 reversible_topology . . . . . . 185
5.4 Topology entity definitions . . . . . . 185
5.4.1 topological_representation_item . . . 185
5.4.2 vertex . . . . 186
5.4.3 vertex_point . . . . 187
5.4.4 edge. . . . . 187
5.4.5 edge_curve . . . . 189
5.4.6 oriented_edge . . . . 190
5.4.7 seam_edge . . . . 191
5.4.8 subedge. . . . 192
5.4.9 path . . . . . 192
5.4.10 oriented_path. . . . 193
5.4.11 open_path . . . . 194
5.4.12 loop. . . . . 195
5.4.13 vertex_loop . . . . 196
5.4.14 edge_loop . . . . 197
5.4.15 poly_loop. . . . 198
5.4.16 face_bound . . . . 199
5.4.17 face_outer_bound . . . . 199
5.4.18 face . . . . . 200
5.4.19 face_surface . . . . 202
5.4.20 oriented_face . . . . 203
5.4.21 subface . . . . 204
5.4.22 connected_face_set. . . . 205
5.4.23 vertex_shell. . . . 206
5.4.24 wire_shell . . . . 206
5.4.25 open_shell . . . . 208
5.4.26 oriented_open_shell . . . . . . 210
5.4.27 closed_shell . . . . 211
5.4.28 oriented_closed_shell . . . . 213
5.4.29 connected_face_sub_set . . . . 214
5.4.30 connected_edge_set . . . . 215
5.5 Topology function definitions . . . . 215
5.5.1 conditional_reverse. . . . 215
5.5.2 topology_reversed . . . . 216
5.5.3 edge_reversed . . . . 217
5.5.4 path_reversed. . . . 218
5.5.5 face_bound_reversed . . . . . . 218
5.5.6 face_reversed . . . . 219
5.5.7 shell_reversed . . . . 220
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5.5.8 closed_shell_reversed . . . . 220
5.5.9 open_shell_reversed . . . . 221
5.5.10 set_of_topology_reversed . . . 222
5.5.11 list_of_topology_reversed . . . 223
5.5.12 boolean_choose . . . . 223
5.5.13 path_head_to_tail . . . . 224
5.5.14 list_face_loops . . . . 225
5.5.15 list_loop_edges. . . . 225
5.5.16 list_shell_edges. . . . 226
5.5.17 list_shell_faces . . . . 226
5.5.18 list_shell_loops. . . . 227
5.5.19 mixed_loop_type_set . . . . . . 228
5.5.20 list_to_set. . . . 229
5.5.21 edge_curve_pcurves . . . . 229
5.5.22 vertex_point_pcurves . . . . . . 231
6 Geometricmodels . . . . . 232
6.1 Introduction. . . . 232
6.2 Fundamental concepts and assumptions . . . 233
6.3 Geometricmodeltypedefinitions . . . 233
6.3.1 boolean_operand . . . . 233
6.3.2 boolean_operator . . . . 234
6.3.3 csg_primitive . . . . 234
6.3.4 csg_select. . . . 235
6.3.5 geometric_set_select . . . . 235
6.3.6 surface_model . . . . 236
6.3.7 wireframe_model. . . . 236
6.4 Geometric model entity definitions. . . 236
6.4.1 solid_model . . . . 236
6.4.2 manifold_solid_brep . . . . 237
6.4.3 brep_with_voids . . . . 240
6.4.4 faceted_brep . . . . 240
6.4.5 brep_2d. . . . 241
6.4.6 csg_solid . . . . 242
6.4.7 boolean_result . . . . 243
6.4.8 block . . . . 244
6.4.9 right_angular_wedge . . . . . . 245
6.4.10 rectangular_pyramid . . . . . . 246
6.4.11 faceted_primitive. . . . 247
6.4.12 tetrahedron . . . . 248
6.4.13 convex_hexahedron . . . . . . 249
6.4.14 sphere. . . . 250
6.4.15 right_circular_cone. . . . 251
6.4.16 right_circular_cylinder. . . . . 252
6.4.17 eccentric_cone . . . . 253
6.4.18 torus . . . . 254
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6.4.19 ellipsoid . . . . 255
6.4.20 cyclide_segment_solid . . . . 256
6.4.21 half_space_solid . . . . 257
6.4.22 boxed_half_space . . . . 259
6.4.23 box_domain . . . . 259
6.4.24 primitive_2d . . . . 260
6.4.25 circular_area . . . . 261
6.4.26 elliptic_area . . . . 261
6.4.27 rectangular_area . . . . 262
6.4.28 polygonal_area . . . . 262
6.4.29 half_space_2d . . . . 263
6.4.30 rectangled_half_space . . . . . 264
6.4.31 rectangle_domain . . . . 264
6.4.32 swept_face_solid . . . . 265
6.4.33 extruded_face_solid . . . . . . 266
6.4.34 revolved_face_solid . . . . . . 266
6.4.35 surface_curve_swept_face_solid. . . 268
6.4.36 swept_area_solid . . . . 270
6.4.37 extruded_area_solid . . . . 270
6.4.38 revolved_area_solid . . . . 271
6.4.39 surface_curve_swept_area_solid. . . 272
6.4.40 swept_disk_solid . . . . 273
6.4.41 trimmed_volume. . . . 275
6.4.42 solid_replica . . . . 276
6.4.43 shell_based_surface_model . . . 277
6.4.44 face_based_surface_model. . . 277
6.4.45 shell_based_wireframe_model. . . 278
6.4.46 edge_based_wireframe_model. . . 279
6.4.47 geometric_set. . . . 280
6.4.48 geometric_curve_set . . . . 281
6.4.49 sectioned_spine. . . . 281
6.4.50 geometric_set_replica . . . . . 282
6.5 Geometricmodelfunctiondefinitions . . . 283
6.5.1 acyclic_solid_replica. . . . 283
6.5.2 acyclic_set_replica . . . . 284
6.5.3 constraints_geometry_shell_based_surface_model . . 285
6.5.4 constraints_geometry_shell_based_wireframe_model. . 285
6.5.5 build_transformed_set . . . . 286
6.5.6 msb_shells . . . . 287
Annex A (normative) Short names of entities. . . 289
AnnexB(normative) Informationobjectregistration . . . 297
B.1 Documentidentification . . . . 297
B.2 Schemaidentification. . . . 297
AnnexC(informative) Computer-interpretablelistings . . . 298
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AnnexD(informative) EXPRESS-Gdiagrams . . . 299
Bibliography . . . . . 320
Index . . . . . 321
Figures
Figure 1 Spherical_point attributes . . . . . 30
Figure 2 Axis2_placement_3d . . . . 41
Figure 3 (a) Cartesian_transformation_operator_3d . . . 43
Figure 3 (b) Cartesian_transformation_operator_3d . . . 44
Figure 3 (c) Cartesian_transformation_operator_3d . . . 45
Figure4 Circle . . . . . 50
Figure 5 Ellipse . . . . . 51
Figure6 Hyperbola. . . . 53
Figure7 Parabola . . . . 54
Figure8 Clothoidcurve. . . . 57
Figure9 Circularinvolutecurve . . . . 58
Figure10 B-splinecurve . . . . 61
Figure11 Composite_curve . . . . 72
Figure12 Conical_surface . . . . 89
Figure13 Crosssectionofdegenerate_toroidal_surface. . . 93
Figure 14 Cross-sections of a Dupin cyclide with C=0. . . 96
Figure15 ADupinringcyclide . . . . 97
Figure16 ADupinhornedcyclide. . . . 98
Figure17 ADupinspindlecyclide. . . . 99
Figure18 Fixed_reference_swept_surface. . . 104
Figure 19 Curve bounded surface . . . . . . 116
Figure20 Wedge_volumeanditsattributes . . . 125
Figure21 Edgecurve . . . . 188
Figure 22 Right angular wedge and its attributes . . . 245
Figure 23 Convex_hexahedron. . . . 251
Figure24 Cyclide_segment_solid . . . . 257
Figure25 Crosssectionofcyclide_segment_solid . . . 258
Figure26 Revolvedfacesolid . . . . 267
FigureD.1 Geometry_schemaEXPRESS-Gdiagram1of13 . . 300
FigureD.2 Geometry_schemaEXPRESS-Gdiagram2of13 . . 301
FigureD.3 Geometry_schemaEXPRESS-Gdiagram3of13 . . 302
FigureD.4 Geometry_schemaEXPRESS-Gdiagram4of13 . . 303
FigureD.5 Geometry_schemaEXPRESS-Gdiagram5of13 . . 304
FigureD.6 Geometry_schemaEXPRESS-Gdiagram6of13 . . 305
FigureD.7 Geometry_schemaEXPRESS-Gdiagram7of13 . . 306
FigureD.8 Geometry_schemaEXPRESS-Gdiagram8of13 . . 307
FigureD.9 Geometry_schemaEXPRESS-Gdiagram9of13 . . 308
FigureD.10 Geometry_schemaEXPRESS-Gdiagram10of13. . 309
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FigureD.11 Geometry_schemaEXPRESS-Gdiagram11of13. . 310
FigureD.12 Geometry_schemaEXPRESS-Gdiagram12of13. . 311
FigureD.13 Geometry_schemaEXPRESS-Gdiagram13of13. . 312
Figure D.14 Topology_schema EXPRESS-G diagram 1 of 3 . . . 313
Figure D.15 Topology_schema EXPRESS-G diagram 2 of 3 . . . 314
Figure D.16 Topology_schema EXPRESS-G diagram 3 of 3 . . . 315
FigureD.17 Geometric_model_schemaEXPRESS-Gdiagram1of4. . 316
FigureD.18 Geometric_model_schemaEXPRESS-Gdiagram2of4. . 317
FigureD.19 Geometric_model_schemaEXPRESS-Gdiagram3of4. . 318
FigureD.20 Geometric_model_schemaEXPRESS-Gdiagram4of4. . 319
Tables
Table1 Geometrymathematicalsymbology . . . 9
Table 2 Topology symbol definitions . . . 11
Table A.1 Short names of entities . . . . . . 289
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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 document may be the subject
of patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 10303-42 was prepared by Technical Committee ISO/ TC 184, Industrial automation systems and
integration, Subcommittee SC 4, Industrial data.
This third edition cancels and replaces the second edition (ISO 10303-42:2000) of which it constitutes
a minor technical revision. The first edition (ISO 10303-42:1994) is provisionally retained to support
continued use and maintenance of implementations based on the first edition and to satisfy normative
references in other parts of ISO 10303.
The corrections published in ISO 10303-42:2000/Cor.1:2001 are incorporated in this edition.
This International Standard is organised as a series of parts, each published separately. The structure of
this International Standard is decribed in ISO 10303-1.
Each part of this International Standard is a member of one of the following series: decription meth-
ods, implementation methods, conformance testing methodology and framework, integrated generic re-
sources, integrated application resources, application protocols, abstract test suites, application inter-
preted constructs, and application modules. This part is a member of the integrated generic resources
series.
A complete list of parts of ISO 10303 is available from Internet:

Should further parts of ISO 10303 be published, they will follow the same numbering pattern.
This part of ISO 10303 is a member of the integrated resources series. The integrated resources specify
a single conceptual product data model.
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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 products throughout
their life cycle. This mechanism is suitable not only for neutral file exchange, but also as a basis for
implementing and sharing product databases and as a basis for archiving.
This part of ISO 10303 specifies the integrated resources used for geometric and topological representa-
tion. Their primary application is for explicit representation of the shape or geometric form of a
productmodel. Theshaperepresentationpresentedherehasbeendesignedto facilitate stable and
efficient communication when mapped to a physical file.
The geometry in clause 4 is exclusively the geometry of parametric curves and surfaces. It includes
the curve and surface entities and other entities, functions and data types necessary for their definition.
A common scheme has been used for the definition of both two-dimensional and three-dimensional
geometry. All geometry is defined in a coordinate system which is established as part of the context of
the item which it represents. These concepts are fully defined in ISO 10303 Part 43.
The topology in clause 5 is concerned with connectivity relationships between objects rather than with
the precise geometric form of objects. This clause contains the basic topological entities and specialised
subtypes of these. In some cases the subtypes have geometric associations. Also included are functions,
particularly constraint functions, and data types necessary for the definitions of the topological entities.
The geometric models in clause 6 provide basic resources for the communication of data describing
the precise size and shape of three-dimensional solid objects. The geometric shape models provide a
complete representation of the shape which in many cases includes both geometric and topological data.
Included here are the two classical types of solid model, constructive solid geometry (CSG) and boundary
representation (B-rep). Other entities, providing a rather less complete description of the geometry of a
product, and with less consistency constraints, are also included.
This edition incorporates modifications that are upwardly compatible with the previous editions. Modi-
fications to EXPRESS specifications are upwardly compatible if:
— instances encoded according to ISO 10303-21 and that conform to an ISO 10303 application proto-
col based on the previous edition of this part, also conform to a revision of that application protocol
based on this edition;
— interfaces that conform to ISO 10303-22 and to an ISO 10303 application protocol based on the
previous edition of this part, also conform to a revision of that application protocol based on this
edition;
— the mapping tables of ISO 10303 application protocols based on the previous edition of this part
remain valid in a revision of that application protocol based on this edition.
Technical modifications to ISO 10303-42:1994 are categorised as follows:
c ISO 2003— All rights reserved xiii

— changes to the EXPRESS declarations,
— new EXPRESS declarations.
The following EXPRESS declarations were modified in creating edition 2:
geometry schema:
— axis1_placement;
— base_axis;
— build_axes;
— build_2axes;
— cartesian_transformation_operator_3d;
— cartesian_transformation_operator_2d;
— composite_curve_segment;
— constraints_param_b_spline;
— cross_product;
— curve_bounded_surface;
— default_b_spline_curve_weights;
— default_b_spline_knot_mult;
— default_b_spline_knots;
— default_b_spline_surface_weights;
— geometric_representation_item;
— get_basis_surface;
— list_to_array;
— make_array_of_array;
— orthogonal_complement;
—point;
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— rectangular_composite_surface;
— scalar_times_vector;
— surface_of_revolution;
— surface_patch;
— swept_surface;
— trimmed_curve;
— vector_sum;
— vector_difference;
topology schema:
—edge;
— edge_reversed;
— face_bound_reversed;
— face_reversed;
— face_surface;
— mixed_loop_type_set;
— path_head_to_tail;
— path_reversed;
— shell_reversed;
geometric model schema:
— boolean_operand;
— build_transformed_set;
— csg_primitive;
— csg_solid;
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— revolved_area_solid;
— revolved_face_solid;
— solid_model;
— swept_area_solid;
— swept_face_solid.
The following EXPRESS declarations were added in edition 2:
geometry schema:
— above_plane;
— b_spline_volume;
— b_spline_volume_with_knots;
— bezier_volume;
— block_volume;
—clothoid;
— cylindrical_point;
— cylindrical_volume;
— dummy_gri;
— dupin_cyclide_surface;
— eccentric_conical_volume;
— ellipsoid_volume;
— oriented_surface;
— hexahedron_volume;
— make_array_of_array_of_array;
— point_in_volume;
— polar_point;
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— pyramid_volume;
— quasi_uniform_volume;
— rational_b_spline_volume;
—same_side;
— spherical_point;
— spherical_volume;
— surface_boundary;
— surface_curve_swept_surface;
— tetrahedron_volume;
— toroidal_volume;
— volume;
— wedge_volume;
topology schema:
— closed_shell_reversed;
— connected_face_sub_set;
— dummy_tri;
— open_shell_reversed;
— seam_edge;
— subedge;
geometric model schema:
— brep_2d;
— circular_area;
— convex_hexahedron;
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— cyclide_segment_solid;
— eccentric_cone;
— ellipsoid;
— elliptic_area;
— faceted_primitive;
— half_space_2d;
— polygonal_area;
— primitive_2d;
— rectangular_area;
— rectangular_pyramid;
— sectioned_spine;
— surface_curve_swept_area_solid;
— surface_curve_swept_face_solid;
— tetrahedron;
— trimmed_volume.
Technical corrigendum 1 modified the folowing EXPRESS declarations:
— surface_of_revolution (geometry schema)
— first_proj_axis (geometry schema)
— list_to_array (FUNCTION geometry schema)
— make_array_of_array (FUNCTION geometry schema)
— make_array_of_array_of_array (FUNCTION geometry schema)
— revolved_face_solid (geometric_model schema)
— revolved_area_solid (geometric_model schema)
— box_domain (geometric_model schema)
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— rectangle_domain (geometric_model schema)
— build_transformed_set (FUNCTION geometric_model schema)
This revision (edition 3) corrects the definition of path_head_to_tail function and adds the following
new EXPRESS declarations:
— circular_involute (geometry schema)
— swept_disk_solid (geometric_model schema)
Several components of this part of ISO 10303 are available in electronic form. This access is provided
through the specification of Universal Resource Locators (URL’s) that identify the location of these files
on the internet. If there is difficulty in accessing these files, contact the ISO Central Secretariat or the
ISO SC4 Secretariat directly at: sc4sec@tc184-sc4.org.
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INTERNATIONAL STANDARD ISO 10303-42:2003(E)
Industrial automation systems and integration —
Product data representation and exchange —
Part 42:
Integrated generic resource:
Geometric and topological representation
1Scope
This part of ISO 10303 specifies the resource constructs for the explicit geometric and topological
representation of the shape of a product. The scope is determined by the requirements for the explicit
representation of an ideal product model; tolerances and implicit forms of representation in terms of
features are out of scope. The geometry in clause 4 and the topology in clause 5 are available for use
independently and are also extensively used by the various forms of geometric shape model in clause 6.
In addition, this part of ISO 10303 specifies specialisations of the concepts of representation where the
elements of representation are geometric.
1.1 Geometry
The following are within the scope of the geometry schema:
— definition of points, vectors, parametric curves and parametric surfaces;
— definition of finite volumes with internal parametrisation;
— definition of transformation operators;
— points defined directly by their coordinate values or in terms of the parameters of an existing curve
or surface;
— definition of conic curves and elementary surfaces;
— definition of curves defined on a parametric surface;
— definition of general parametric spline curves, surfaces and volumes;
— definition of point, curve and surface replicas;
— definition of offset curves and surfaces;
— definition of intersection curves.
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The following are outside the scope of this part of ISO 10303:
— all other forms of procedurally defined curves and surfaces;
— curves and surfaces which do not have a parametric form of representation;
— any form of explicit representation of a ruled surface.
NOTE For a ruled surface the geometry is critically dependent upon the parametrisation of the bound-
ary curves and the method of associating pairs of points on the two curves. A ruled surface with B-spline
boundary curves can however be exactly represented by the B-spline surface entity.
1.2 Topology
The following are within the scope of the topology schema:
— definition of the fundamental topological entities vertex, edge, and face, each with a specialised
subtype to enable it to be associated with the geometry of a point, curve, or surface, respectively;
— collections of the basic entities to form topological structures of path, loop and shell and constraints
to ensure the integrity of these structures;
— orientation of topological entities.
1.3 Geometric Shape Models
The following are within the scope of the geometric model schema:
— data describing the precise geometric form of three-dimensional solid objects;
— constructive solid geometry (CSG) models;
— CSG models in two-dimensional space;
— definition of CSG primitives and half-spaces;
— creation of solid models by sweeping operations;
— manifold boundary representation (B-rep) models;
— constraints to ensure the integrity of B-rep models;
— surface models;
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— wireframe models;
— geometric sets;
— creation of a replica of a solid model in a new location.
The following are outside the scope of this part of ISO 10303:
— non-manifold boundary representation models;
— spatial occupancy forms of solid models (such as octree models);
— assemblies and mechanisms.
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 documen
t
(including any amendments) applies.
ISO/IEC 8824-1:1998, 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 10303-41:2000, Industrial automation systems and integration— Product data representation and
exchange— Part 41: Integrated generic resource: Fundamentals of product description and support
ISO 10303-43:2000, Industrial automation systems and integration— Product data representation and
exchange— Part 43: Integrated generic resource: Representation structures
3 Terms, definitions, symbols 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.
— integrated resource.
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3.2 Other terms and definitions
For the purposes of this part of ISO 10303, the following terms and definitions apply. A number of
informal definitions are also given here which will later be used to describe and constrain the topological
entities. They are not intended to be mathematically rigourous. The definitions are given in alphabetical,
not logical order.
3.2.1
arcwise connected
an entity is arcwise connected if any two arbitrary points in its domain can be connected by a curve that
lies entirely within the domain.
3.2.2
axi-symmetric
an entity is axi-symmetric if it has an axis of symmetry such that the object is invariant under all rotations
about this axis.
3.2.3
bounds
the topological entities of lower dimensionality which mark the limits of a topological entity. The bounds
of a face are loops, and the bounds of an edge are vertices.
3.2.4
boundary
m
the set of mathematical points x in a domain X contained in R for which there is an open ball U
m
in R containing x such that the intersection U\X is homeomorphic to an open set in the closed d
d
-dimensional half-space R ,for some dm, where the homeomorphism carries x into the origin in+
d
R .
+
d d
NOTE 1 R is defined to be the set of all mathematical points(x;:::;x in R with x0.1d)1+
NOTE 2 For this purpose, the word “open” has its usual mathematical meaning. It does not relate to “open
surface” as defined elsewhere in this part of ISO 10303.
3.2.5
boundary representation solid model (B-rep)
a type of geometric model in which the size and shape of the solid is defined in terms of the faces, edges
and vertices which make up its boundary.
3.2.6
closed curve
a curve such that both end points are the same.
3.2.7
closed surface
a connected 2-manifold that divides space into exactly two connected components, one of which is finite.
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3.2.8
completion of a topological entity
a set consisting of the entity in question together with all the faces, edges and vertices referenced, directly
or indirectly, in the definition of the bounds of that entity.
3.2.9
connected
equivalent to arcwise connected (see 3.2.1).
3.2.10
connected component
a maximal connected subset of a domain.
3.2.11
const
...