ISO 10303-42:2000
(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
Systèmes d'automatisation industrielle et intégration — Représentation et échange de données de produits — Partie 42: Ressource générique intégrée: Représentation géométrique et topologique
General Information
Relations
Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 10303-42
Second edition
2000-09-01
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 10303-42:2000(E)
©
ISO 2000
---------------------- Page: 1 ----------------------
ISO 10303-42:2000(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but shall not
be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In downloading this
file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat accepts no liability in this
area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation parameters
were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the unlikely event
that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2000
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic
or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISO's member body
in the country of the requester.
ISO copyright office
Case postale 56 � CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.ch
Web www.iso.ch
Printed in Switzerland
ii © ISO 2000 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 10303-42:2000(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. . . . 10
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
c ISO 2000 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO 10303-42:2000(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. . . 45
4.4.23 curve . . . . 47
4.4.24 line . . . . . 47
4.4.25 conic . . . . 48
4.4.26 circle . . . . 49
4.4.27 ellipse. . . . 50
4.4.28 hyperbola. . . . 52
4.4.29 parabola . . . . 53
4.4.30 clothoid. . . . 55
4.4.31 bounded_curve . . . . 56
4.4.32 polyline. . . . 57
4.4.33 b_spline_curve. . . . 58
4.4.34 b_spline_curve_with_knots . . . 61
4.4.35 uniform_curve . . . . 63
4.4.36 quasi_uniform_curve . . . . . . 63
4.4.37 bezier_curve . . . . 64
4.4.38 rational_b_spline_curve . . . . 65
4.4.39 trimmed_curve . . . . 67
4.4.40 composite_curve . . . . 69
4.4.41 composite_curve_segment . . . 71
4.4.42 reparametrised_composite_curve_segment . . . 72
4.4.43 pcurve . . . . 73
4.4.44 bounded_pcurve . . . . 74
4.4.45 surface_curve. . . . 75
4.4.46 intersection_curve . . . . 77
4.4.47 seam_curve . . . . 77
4.4.48 bounded_surface_curve . . . . 78
4.4.49 composite_curve_on_surface . . . 78
4.4.50 offset_curve_2d . . . . 80
ivc ISO 2000 – All rights reserved
---------------------- Page: 4 ----------------------
ISO 10303-42:2000(E)
4.4.51 offset_curve_3d . . . . 81
4.4.52 curve_replica . . . . 82
4.4.53 surface . . . . 83
4.4.54 elementary_surface. . . . 84
4.4.55 plane . . . . 84
4.4.56 cylindrical_surface . . . . 85
4.4.57 conical_surface. . . . 86
4.4.58 spherical_surface. . . . 88
4.4.59 toroidal_surface . . . . 89
4.4.60 degenerate_toroidal_surface . . . 91
4.4.61 dupin_cyclide_surface . . . . . 93
4.4.62 swept_surface . . . . 97
4.4.63 surface_of_linear_extrusion . . . 98
4.4.64 surface_of_revolution . . . . . 98
4.4.65 surface_curve_swept_surface . . . 99
4.4.66 fixed_reference_swept_surface . . . 101
4.4.67 bounded_surface . . . . 103
4.4.68 b_spline_surface . . . . 103
4.4.69 b_spline_surface_with_knots . . . 106
4.4.70 uniform_surface . . . . 108
4.4.71 quasi_uniform_surface . . . . . 109
4.4.72 bezier_surface . . . . 110
4.4.73 rational_b_spline_surface . . . 110
4.4.74 rectangular_trimmed_surface . . . 111
4.4.75 curve_bounded_surface . . . . 113
4.4.76 boundary_curve . . . . 115
4.4.77 outer_boundary_curve . . . . . 115
4.4.78 rectangular_composite_surface . . . 116
4.4.79 surface_patch. . . . 118
4.4.80 offset_surface. . . . 119
4.4.81 oriented_surface . . . . 120
4.4.82 surface_replica . . . . 121
4.4.83 volume . . . . 121
4.4.84 block_volume . . . . 122
4.4.85 wedge_volume . . . . 123
4.4.86 pyramid_volume . . . . 125
4.4.87 tetrahedron_volume . . . . . . 126
4.4.88 hexahedron_volume . . . . . . 127
4.4.89 spherical_volume. . . . 129
4.4.90 cylindrical_volume. . . . 130
4.4.91 eccentric_conical_volume . . . 131
4.4.92 toroidal_volume . . . . 132
4.4.93 ellipsoid_volume . . . . 133
4.4.94 b_spline_volume . . . . 134
4.4.95 b_spline_volume_with_knots . . . 136
4.4.96 bezier_volume . . . . 138
c ISO 2000 – All rights reserved v
---------------------- Page: 5 ----------------------
ISO 10303-42:2000(E)
4.4.97 uniform_volume . . . . 139
4.4.98 quasi_uniform_volume . . . . . 140
4.4.99 rational_b_spline_volume . . . 141
4.5 Geometryschemaruledefinition:compatible_dimension . . 142
4.6 Geometryfunctiondefinitions . . . . 143
4.6.1 dimension_of. . . . 143
4.6.2 acyclic_curve_replica . . . . . 145
4.6.3 acyclic_point_replica . . . . . . 145
4.6.4 acyclic_surface_replica . . . . 146
4.6.5 associated_surface . . . . 147
4.6.6 base_axis . . . . 147
4.6.7 build_2axes. . . . 149
4.6.8 build_axes . . . . 150
4.6.9 orthogonal_complement . . . . 150
4.6.10 first_proj_axis . . . . 151
4.6.11 second_proj_axis. . . . 152
4.6.12 cross_product. . . . 153
4.6.13 dot_product. . . . 154
4.6.14 normalise . . . . 156
4.6.15 scalar_times_vector . . . . 157
4.6.16 vector_sum . . . . 158
4.6.17 vector_difference. . . . 160
4.6.18 default_b_spline_knot_mult . . . 161
4.6.19 default_b_spline_knots . . . . . 162
4.6.20 default_b_spline_curve_weights. . . 163
4.6.21 default_b_spline_surface_weights . . . 163
4.6.22 constraints_param_b_spline . . . 164
4.6.23 curve_weights_positive . . . . 166
4.6.24 constraints_composite_curve_on_surface . . . 166
4.6.25 get_basis_surface. . . . 167
4.6.26 surface_weights_positive . . . . 168
4.6.27 volume_weights_positive . . . 169
4.6.28 constraints_rectangular_composite_surface . . . . 170
4.6.29 list_to_array . . . . 171
4.6.30 make_array_of_array . . . . . . 172
4.6.31 make_array_of_array_of_array . . . 173
4.6.32 above_plane . . . . 174
4.6.33 same_side . . . . 175
5 Topology . . . . . 177
5.1 Introduction. . . . 177
5.2 Fundamental concepts and assumptions . . . 177
5.2.1 Geometricassociations. . . . 178
5.2.2 Associationswithparameterspacegeometry . . . 179
5.2.3 Graphs,cycles,andtraversals . . . 181
5.3 Topology constant and type definitions. . . 182
vic ISO 2000 – All rights reserved
---------------------- Page: 6 ----------------------
ISO 10303-42:2000(E)
5.3.1 dummy_tri . . . . 182
5.3.2 shell. . . . . 182
5.3.3 reversible_topology_item . . . 183
5.3.4 list_of_reversible_topology_item . . . 183
5.3.5 set_of_reversible_topology_item . . . 184
5.3.6 reversible_topology . . . . . . 184
5.4 Topology entity definitions . . . . . . 184
5.4.1 topological_representation_item . . . 184
5.4.2 vertex . . . . 185
5.4.3 vertex_point . . . . 186
5.4.4 edge. . . . . 186
5.4.5 edge_curve . . . . 188
5.4.6 oriented_edge . . . . 189
5.4.7 seam_edge . . . . 190
5.4.8 subedge. . . . 191
5.4.9 path . . . . . 191
5.4.10 oriented_path. . . . 192
5.4.11 open_path . . . . 193
5.4.12 loop. . . . . 194
5.4.13 vertex_loop . . . . 195
5.4.14 edge_loop . . . . 196
5.4.15 poly_loop. . . . 197
5.4.16 face_bound . . . . 198
5.4.17 face_outer_bound . . . . 198
5.4.18 face . . . . . 199
5.4.19 face_surface . . . . 201
5.4.20 oriented_face . . . . 202
5.4.21 subface . . . . 203
5.4.22 connected_face_set. . . . 204
5.4.23 vertex_shell. . . . 205
5.4.24 wire_shell . . . . 205
5.4.25 open_shell . . . . 207
5.4.26 oriented_open_shell . . . . . . 209
5.4.27 closed_shell . . . . 210
5.4.28 oriented_closed_shell . . . . 212
5.4.29 connected_face_sub_set . . . . 213
5.4.30 connected_edge_set . . . . 214
5.5 Topology function definitions . . . . 214
5.5.1 conditional_reverse. . . . 214
5.5.2 topology_reversed . . . . 215
5.5.3 edge_reversed . . . . 216
5.5.4 path_reversed. . . . 217
5.5.5 face_bound_reversed . . . . . . 217
5.5.6 face_reversed . . . . 218
5.5.7 shell_reversed . . . . 219
5.5.8 closed_shell_reversed . . . . 219
c ISO 2000 – All rights reserved vii
---------------------- Page: 7 ----------------------
ISO 10303-42:2000(E)
5.5.9 open_shell_reversed . . . . 220
5.5.10 set_of_topology_reversed . . . 221
5.5.11 list_of_topology_reversed . . . 222
5.5.12 boolean_choose . . . . 222
5.5.13 path_head_to_tail . . . . 223
5.5.14 list_face_loops . . . . 224
5.5.15 list_loop_edges. . . . 224
5.5.16 list_shell_edges. . . . 225
5.5.17 list_shell_faces . . . . 225
5.5.18 list_shell_loops. . . . 226
5.5.19 mixed_loop_type_set . . . . . . 227
5.5.20 list_to_set. . . . 228
5.5.21 edge_curve_pcurves . . . . 228
5.5.22 vertex_point_pcurves . . . . . . 230
6 Geometricmodels . . . . . 231
6.1 Introduction. . . . 231
6.2 Fundamental concepts and assumptions . . . 232
6.3 Geometricmodeltypedefinitions . . . 232
6.3.1 boolean_operand . . . . 232
6.3.2 boolean_operator . . . . 233
6.3.3 csg_primitive . . . . 233
6.3.4 csg_select. . . . 234
6.3.5 geometric_set_select . . . . 234
6.3.6 surface_model . . . . 235
6.3.7 wireframe_model. . . . 235
6.4 Geometric model entity definitions. . . 235
6.4.1 solid_model . . . . 235
6.4.2 manifold_solid_brep . . . . 236
6.4.3 brep_with_voids . . . . 239
6.4.4 faceted_brep . . . . 239
6.4.5 brep_2d. . . . 240
6.4.6 csg_solid . . . . 241
6.4.7 boolean_result . . . . 242
6.4.8 block . . . . 243
6.4.9 right_angular_wedge . . . . . . 244
6.4.10 rectangular_pyramid . . . . . . 245
6.4.11 faceted_primitive. . . . 246
6.4.12 tetrahedron . . . . 247
6.4.13 convex_hexahedron . . . . . . 248
6.4.14 sphere. . . . 249
6.4.15 right_circular_cone. . . . 250
6.4.16 right_circular_cylinder. . . . . 251
6.4.17 eccentric_cone . . . . 252
6.4.18 torus . . . . 253
6.4.19 ellipsoid . . . . 254
viiic ISO 2000 – All rights reserved
---------------------- Page: 8 ----------------------
ISO 10303-42:2000(E)
6.4.20 cyclide_segment_solid . . . . 255
6.4.21 half_space_solid . . . . 256
6.4.22 boxed_half_space . . . . 257
6.4.23 box_domain . . . . 258
6.4.24 primitive_2d . . . . 259
6.4.25 circular_area . . . . 259
6.4.26 elliptic_area . . . . 260
6.4.27 rectangular_area . . . . 260
6.4.28 polygonal_area . . . . 261
6.4.29 half_space_2d . . . . 261
6.4.30 rectangled_half_space . . . . . 262
6.4.31 rectangle_domain . . . . 263
6.4.32 swept_face_solid . . . . 263
6.4.33 extruded_face_solid . . . . . . 264
6.4.34 revolved_face_solid . . . . . . 265
6.4.35 surface_curve_swept_face_solid. . . 266
6.4.36 swept_area_solid . . . . 268
6.4.37 extruded_area_solid . . . . 268
6.4.38 revolved_area_solid . . . . 269
6.4.39 surface_curve_swept_area_solid. . . 270
6.4.40 trimmed_volume. . . . 271
6.4.41 solid_replica . . . . 273
6.4.42 shell_based_surface_model . . . 273
6.4.43 face_based_surface_model. . . 274
6.4.44 shell_based_wireframe_model. . . 275
6.4.45 edge_based_wireframe_model. . . 276
6.4.46 geometric_set. . . . 277
6.4.47 geometric_curve_set . . . . 277
6.4.48 sectioned_spine. . . . 278
6.4.49 geometric_set_replica . . . . . 279
6.5 Geometricmodelfunctiondefinitions . . . 280
6.5.1 acyclic_solid_replica. . . . 280
6.5.2 acyclic_set_replica . . . . 281
6.5.3 constraints_geometry_shell_based_surface_model . . 281
6.5.4 constraints_geometry_shell_based_wireframe_model. . 282
6.5.5 build_transformed_set . . . . 283
6.5.6 msb_shells . . . . 284
Annex A (normative) Short names of entities. . . 286
AnnexB(normative) Informationobjectregistration . . . 294
B.1 Documentidentification . . . . 294
B.2 Schemaidentification. . . . 294
AnnexC(informative) Computer-interpretablelistings . . . 295
AnnexD(informative) EXPRESS-Gdiagrams . . . 296
c ISO 2000 – All rights reserved ix
---------------------- Page: 9 ----------------------
ISO 10303-42:2000(E)
Bibliography . . . . . 317
Index . . . . . 318
Figures
Figure 1 Spherical_point attributes . . . . . 30
Figure 2 Axis2_placement_3d . . . . 41
Figure 3 (a) Cartesian_transformation_operator_3d . . . 44
Figure 3 (b) Cartesian_transformation_operator_3d . . . 45
Figure 3 (c) Cartesian_transformation_operator_3d . . . 46
Figure4 Circle . . . . . 50
Figure 5 Ellipse . . . . . 51
Figure6 Hyperbola. . . . 53
Figure7 Parabola . . . . 54
Figure8 Clothoidcurve. . . . 57
Figure9 B-splinecurve . . . . 60
Figure10 Composite_curve . . . . 71
Figure11 Conical_surface . . . . 87
Figure12 Crosssectionofdegenerate_toroidal_surface. . . 92
Figure 13 Cross-sections of a Dupin cyclide with C=0. . . 94
Figure14 ADupinringcyclide . . . . 95
Figure15 ADupinhornedcyclide. . . . 95
Figure16 ADupinspindlecyclide. . . . 96
Figure17 Fixed_reference_swept_surface. . . 102
Figure 18 Curve bounded surface . . . . . . 114
Figure19 Wedge_volumeanditsattributes . . . 124
Figure20 Edgecurve . . . . 187
Figure 21 Right angular wedge and its attributes . . . 244
Figure 22 Convex_hexahedron. . . . 250
Figure23 Crosssectionofcyclide_segment_solid . . . 256
Figure24 Revolvedfacesolid . . . . 265
FigureD.1 Geometry_schemaEXPRESS-Gdiagram1of13 . . 297
FigureD.2 Geometry_schemaEXPRESS-Gdiagram2of13 . . 298
FigureD.3 Geometry_schemaEXPRESS-Gdiagram3of13 . . 299
FigureD.4 Geometry_schemaEXPRESS-Gdiagram4of13 . . 300
FigureD.5 Geometry_schemaEXPRESS-Gdiagram5of13 . . 301
FigureD.6 Geometry_schemaEXPRESS-Gdiagram6of13 . . 302
FigureD.7 Geometry_schemaEXPRESS-Gdiagram7of13 . . 303
FigureD.8 Geometry_schemaEXPRESS-Gdiagram8of13 . . 304
FigureD.9 Geometry_schemaEXPRESS-Gdiagram9of13 . . 305
FigureD.10 Geometry_schemaEXPRESS-Gdiagram10of13. . 306
FigureD.11 Geometry_schemaEXPRESS-Gdiagram11of13. . 307
FigureD.12 Geometry_schemaEXPRESS-Gdiagram12of13. . 308
FigureD.13 Geometry_schemaEXPRESS-Gdiagram13of13. . 309
Figure D.14 Topology_schema EXPRESS-G diagram 1 of 3 . . . 310
xc ISO 2000 – All rights reserved
---------------------- Page: 10 ----------------------
ISO 10303-42:2000(E)
Figure D.15 Topology_schema EXPRESS-G diagram 2 of 3 . . . 311
Figure D.16 Topology_schema EXPRESS-G diagram 3 of 3 . . . 312
FigureD.17 Geometric_model_schemaEXPRESS-Gdiagram1of4. . 313
FigureD.18 Geometric_model_schemaEXPRESS-Gdiagram2of4. . 314
FigureD.19 Geometric_model_schemaEXPRESS-Gdiagram3of4. . 315
FigureD.20 Geometric_model_schemaEXPRESS-Gdiagram4of4. . 316
Tables
Table1 Geometrymathematicalsymbology . . . 9
Table 2 Topology symbol definitions . . . 11
Table A.1 Short names of entities . . . . . . 286
c ISO 2000 – All rights reserved xi
---------------------- Page: 11 ----------------------
ISO 10303-42:2000(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 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.
AttentionisdrawntothepossibilitythatsomeoftheelementsofthispartofISO10303maybesubject to
patent rights. ISO shall not be held responsible for any or all such patent rights.
International Standard ISO 10303-42 was prepared by Technical Committee ISO/TC 184, Industrial
automation systems and integration, Subcommittee SC 4, Industrial data.
This second edition constitutes a technical revision of the first edition (ISO 10303-42:1994), which
is provisionally retained in order to support the continued use and maintenance of implementations
based of the first edition and to satisfy the normative references of other parts of ISO 10303.
It incorporates the corrections published in ISO 10303-42:1994/Cor.1:1999, 10303-42:1994/Cor.2:1999
1)
and ISO 10303-42:1994/Cor.3:–
This International Standard is organised as a series of parts, each published separately. The structure of
this International Standard is described in ISO 10303-1. The numbering of the parts of this International
Standard reflects its structure:
— Parts 11 to 14 specify the description methods;
— Parts 21 to 29 specify the implementation methods;
— Parts 31 to 35 specify the conformance testing methodology and framework;
— Parts 41 to 50 specify the integrated generic resources;
— Parts 101 to 107 specify the integrated application resources;
— Parts 201 to 237 specify the application protocols;
1)
To be published
xiic ISO 2000 – All rights reserved
---------------------- Page: 12 ----------------------
ISO 10303-42:2000(E)
— Parts 301 to 307 specify the abstract test suites;
— parts 501 to 520 specify the application interpreted constructs.
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 pat
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.