ISO 10303-42:2003
(Main)Industrial automation systems and integration — Product data representation and exchange — Part 42: Integrated generic resource: Geometric and topological representation
Industrial automation systems and integration — Product data representation and exchange — Part 42: Integrated generic resource: Geometric and topological representation
ISO 10303-42:2003 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, ISO 10303-42:2003 specifies specialisations of the concepts of representation where the elements of representation are geometric. 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. The following are outside the scope of ISO 10303-42:2003: 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 boundary 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.
Systèmes d'automatisation industrielle et intégration — Représentation et échange de données de produits — Partie 42: Ressource générique intégrée: Représentation géométrique et topologique
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Standards Content (Sample)
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 10303-42:2003(E)
©
ISO 2003
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ISO 10303-42:2003(E)
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ISO 10303-42:2003(E)
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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ISO 10303-42:2003(E)
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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ISO 10303-42:2003(E)
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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ISO 10303-42:2003(E)
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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ISO 10303-42:2003(E)
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
...
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