Integrated generic resource: Geometric and topological representation ISO 10303-42:2021(E)
© ISO

Cover page
Table of contents
Copyright
Foreword
Introduction
1 Scope
2 Normative references
3 Terms, definitions and abbreviated terms
    3.1 Terms and definitions
    3.2 Abbreviated terms

4 Geometry
   4.1 General
   4.2 Fundamental concepts and assumptions
   4.3 Geometry constant definition
   4.4 Geometry type definitions
   4.5 Geometry entity definitions
   4.6 Geometry function definitions
   4.7 Geometry rule definitions
5 Topology
   5.1 General
   5.2 Fundamental concepts and assumptions
   5.3 Topology constant definition
   5.4 Topology type definitions
   5.5 Topology entity definitions
   5.6 Topology function definitions
6 Geometric model
   6.1 General
   6.2 Fundamental concepts and assumptions
   6.3 Geometric model type definitions
   6.4 Geometric model entity definitions
   6.5 Geometric model function definitions
7 Scan data 3d shape model
   7.1 General
   7.2 Fundamental concepts and assumptions
   7.3 Scan data 3d shape model type definition
   7.4 Scan data 3d shape model entity definitions
   7.5 Scan data 3d shape model function definitions

A Short names of entities
B Information object registration
C Computer interpretable listings
D EXPRESS-G diagrams
E Change history
Bibliography
Index

Contents

1 Scope
2 Normative references
3 Terms, definitions and abbreviated terms
    3.1 Terms and definitions
    3.2 Abbreviated terms
4 Geometry schema
     4.1 General
     4.2 Fundamental concepts and assumptions
   4.3 Geometry constant definition
          4.3.1 dummy_gri
     4.4 Geometry type definitions
          4.4.1 axis2_placement
          4.4.2 b_spline_curve_form
          4.4.3 b_spline_surface_form
          4.4.4 curve_on_surface
          4.4.5 dimension_count
          4.4.6 extent_enumeration
          4.4.7 knot_type
          4.4.8 linearly_independent_enum
          4.4.9 locally_refined_spline_type_enum
          4.4.10 pcurve_or_surface
          4.4.11 preferred_surface_curve_representation
          4.4.12 spline_knot_values
          4.4.13 surface_boundary
          4.4.14 transition_code
          4.4.15 trimming_preference
          4.4.16 trimming_select
          4.4.17 vector_or_direction
     4.5 Geometry entity definitions
          4.5.1 geometric_representation_context
          4.5.2 geometric_representation_item
          4.5.3 point
          4.5.4 cartesian_point
          4.5.5 cylindrical_point
          4.5.6 spherical_point
          4.5.7 polar_point
          4.5.8 point_on_curve
          4.5.9 point_on_surface
          4.5.10 point_in_volume
          4.5.11 point_replica
          4.5.12 degenerate_pcurve
          4.5.13 evaluated_degenerate_pcurve
          4.5.14 direction
          4.5.15 vector
          4.5.16 placement
          4.5.17 axis1_placement
          4.5.18 axis2_placement_2d
          4.5.19 axis2_placement_3d
          4.5.20 cartesian_transformation_operator
          4.5.21 cartesian_transformation_operator_3d
          4.5.22 cartesian_transformation_operator_2d
          4.5.23 curve
          4.5.24 line
          4.5.25 conic
          4.5.26 circle
          4.5.27 ellipse
          4.5.28 hyperbola
          4.5.29 parabola
          4.5.30 clothoid
          4.5.31 circular_involute
          4.5.32 bounded_curve
          4.5.33 polyline
          4.5.34 b_spline_curve
          4.5.35 b_spline_curve_with_knots
          4.5.36 uniform_curve
          4.5.37 quasi_uniform_curve
          4.5.38 bezier_curve
          4.5.39 rational_b_spline_curve
          4.5.40 local_b_spline
          4.5.41 locally_refined_spline_curve
          4.5.42 rational_locally_refined_spline_curve
          4.5.43 trimmed_curve
          4.5.44 composite_curve
          4.5.45 composite_curve_segment
          4.5.46 reparametrised_composite_curve_segment
          4.5.47 pcurve
          4.5.48 bounded_pcurve
          4.5.49 surface_curve
          4.5.50 intersection_curve
          4.5.51 seam_curve
          4.5.52 bounded_surface_curve
          4.5.53 composite_curve_on_surface
          4.5.54 offset_curve_2d
          4.5.55 offset_curve_3d
          4.5.56 curve_replica
          4.5.57 surface
          4.5.58 elementary_surface
          4.5.59 plane
          4.5.60 cylindrical_surface
          4.5.61 conical_surface
          4.5.62 spherical_surface
          4.5.63 toroidal_surface
          4.5.64 degenerate_toroidal_surface
          4.5.65 dupin_cyclide_surface
          4.5.66 swept_surface
          4.5.67 surface_of_linear_extrusion
          4.5.68 surface_of_revolution
          4.5.69 surface_curve_swept_surface
          4.5.70 fixed_reference_swept_surface
          4.5.71 bounded_surface
          4.5.72 b_spline_surface
          4.5.73 b_spline_surface_with_knots
          4.5.74 uniform_surface
          4.5.75 quasi_uniform_surface
          4.5.76 bezier_surface
          4.5.77 rational_b_spline_surface
          4.5.78 locally_refined_spline_surface
          4.5.79 rational_locally_refined_spline_surface
          4.5.80 rectangular_trimmed_surface
          4.5.81 curve_bounded_surface
          4.5.82 boundary_curve
          4.5.83 outer_boundary_curve
          4.5.84 rectangular_composite_surface
          4.5.85 surface_patch
          4.5.86 offset_surface
          4.5.87 oriented_surface
          4.5.88 surface_replica
          4.5.89 volume
          4.5.90 block_volume
          4.5.91 wedge_volume
          4.5.92 pyramid_volume
          4.5.93 tetrahedron_volume
          4.5.94 hexahedron_volume
          4.5.95 spherical_volume
          4.5.96 cylindrical_volume
          4.5.97 eccentric_conical_volume
          4.5.98 toroidal_volume
          4.5.99 ellipsoid_volume
          4.5.100 b_spline_volume
          4.5.101 b_spline_volume_with_knots
          4.5.102 bezier_volume
          4.5.103 uniform_volume
          4.5.104 quasi_uniform_volume
          4.5.105 rational_b_spline_volume
          4.5.106 locally_refined_spline_volume
          4.5.107 rational_locally_refined_spline_volume
     4.6 Geometry function definitions
          4.6.1 above_plane
          4.6.2 acyclic_curve_replica
          4.6.3 acyclic_point_replica
          4.6.4 acyclic_surface_replica
          4.6.5 associated_surface
          4.6.6 base_axis
          4.6.7 build_2axes
          4.6.8 build_axes
          4.6.9 check_geometric_dimension
          4.6.10 constraints_composite_curve_on_surface
          4.6.11 constraints_param_b_spline
          4.6.12 constraints_param_local_b_spline
          4.6.13 constraints_rectangular_composite_surface
          4.6.14 constraints_scaling
          4.6.15 cross_product
          4.6.16 curve_weights_positive
          4.6.17 default_b_spline_curve_weights
          4.6.18 default_b_spline_knot_mult
          4.6.19 default_b_spline_knots
          4.6.20 default_b_spline_surface_weights
          4.6.21 dimension_of
          4.6.22 dot_product
          4.6.23 first_proj_axis
          4.6.24 geometric_dimensionalities_in_contexts
          4.6.25 get_basis_surface
          4.6.26 increasing_values_in_list
          4.6.27 list_to_array
          4.6.28 make_array_of_array
          4.6.29 make_array_of_array_of_array
          4.6.30 normalise
          4.6.31 orthogonal_complement
          4.6.32 same_side
          4.6.33 scalar_times_vector
          4.6.34 second_proj_axis
          4.6.35 surface_weights_positive
          4.6.36 vector_difference
          4.6.37 vector_sum
          4.6.38 volume_weights_positive
          4.6.39 weights_positive
     4.7 Geometry rule definition
          4.7.1 compatible_dimension
5 Topology schema
     5.1 General
     5.2 Fundamental concepts and assumptions
   5.3 Topology constant definition
          5.3.1 dummy_tri
     5.4 Topology type definitions
          5.4.1 list_of_reversible_topology_item
          5.4.2 reversible_topology
          5.4.3 reversible_topology_item
          5.4.4 set_of_reversible_topology_item
          5.4.5 shell
          5.4.6 tri_id_attribute_select
     5.5 Topology entity definitions
          5.5.1 topological_representation_item
          5.5.2 vertex
          5.5.3 vertex_point
          5.5.4 edge
          5.5.5 edge_curve
          5.5.6 oriented_edge
          5.5.7 seam_edge
          5.5.8 subedge
          5.5.9 path
          5.5.10 subpath
          5.5.11 oriented_path
          5.5.12 open_path
          5.5.13 loop
          5.5.14 vertex_loop
          5.5.15 edge_loop
          5.5.16 poly_loop
          5.5.17 face_bound
          5.5.18 face_outer_bound
          5.5.19 face
          5.5.20 face_surface
          5.5.21 oriented_face
          5.5.22 subface
          5.5.23 connected_face_set
          5.5.24 vertex_shell
          5.5.25 wire_shell
          5.5.26 open_shell
          5.5.27 oriented_open_shell
          5.5.28 closed_shell
          5.5.29 oriented_closed_shell
          5.5.30 connected_face_sub_set
          5.5.31 connected_edge_set
          5.5.32 connected_edge_sub_set
          5.5.33 volume_with_faces
          5.5.34 volume_with_parametric_boundary
          5.5.35 volume_with_shell
          5.5.36 connected_volume_set
          5.5.37 connected_volume_sub_set
     5.6 Topology function definitions
          5.6.1 boolean_choose
          5.6.2 closed_shell_reversed
          5.6.3 conditional_reverse
          5.6.4 edge_curve_pcurves
          5.6.5 edge_reversed
          5.6.6 face_bound_reversed
          5.6.7 face_reversed
          5.6.8 get_tri_in_representations
          5.6.9 list_face_loops
          5.6.10 list_loop_edges
          5.6.11 list_of_topology_reversed
          5.6.12 list_shell_edges
          5.6.13 list_shell_faces
          5.6.14 list_shell_loops
          5.6.15 list_to_set
          5.6.16 mixed_loop_type_set
          5.6.17 open_shell_reversed
          5.6.18 path_head_to_tail
          5.6.19 path_reversed
          5.6.20 set_of_topology_reversed
          5.6.21 shell_reversed
          5.6.22 topology_reversed
          5.6.23 valid_tri_ids
          5.6.24 vertex_point_pcurves
6 Geometric model schema
     6.1 General
     6.2 Fundamental concepts and assumptions
     6.3 Geometric model type definitions
          6.3.1 angular_deviation
          6.3.2 boolean_operand
          6.3.3 boolean_operator
          6.3.4 bounded_primitive_2d
          6.3.5 chordal_deviation
          6.3.6 csg_primitive
          6.3.7 csg_select
          6.3.8 edge_or_curve
          6.3.9 face_or_surface
          6.3.10 geometric_set_select
          6.3.11 length_to_height_ratio
          6.3.12 maximum_edge_length
          6.3.13 path_or_composite_curve
          6.3.14 surface_model
          6.3.15 tessellated_facet_long_short_edge_ratio
          6.3.16 tessellated_edge_or_vertex
          6.3.17 tessellation_accuracy_parameter_item
          6.3.18 wireframe_model
     6.4 Geometric model entity definitions
          6.4.1 solid_model
          6.4.2 manifold_solid_brep
          6.4.3 brep_with_voids
          6.4.4 faceted_brep
          6.4.5 brep_2d
          6.4.6 csg_solid
          6.4.7 boolean_result
          6.4.8 block
          6.4.9 right_angular_wedge
          6.4.10 rectangular_pyramid
          6.4.11 faceted_primitive
          6.4.12 tetrahedron
          6.4.13 convex_hexahedron
          6.4.14 sphere
          6.4.15 right_circular_cone
          6.4.16 right_circular_cylinder
          6.4.17 eccentric_cone
          6.4.18 torus
          6.4.19 ellipsoid
          6.4.20 cyclide_segment_solid
          6.4.21 half_space_solid
          6.4.22 boxed_half_space
          6.4.23 box_domain
          6.4.24 primitive_2d
          6.4.25 circular_area
          6.4.26 elliptic_area
          6.4.27 rectangular_area
          6.4.28 polygonal_area
          6.4.29 area_with_outer_boundary
          6.4.30 half_space_2d
          6.4.31 rectangled_half_space
          6.4.32 rectangle_domain
          6.4.33 swept_face_solid
          6.4.34 extruded_face_solid
          6.4.35 revolved_face_solid
          6.4.36 surface_curve_swept_face_solid
          6.4.37 swept_area_solid
          6.4.38 extruded_area_solid
          6.4.39 revolved_area_solid
          6.4.40 surface_curve_swept_area_solid
          6.4.41 swept_disk_solid
          6.4.42 trimmed_volume
          6.4.43 solid_replica
          6.4.44 shell_based_surface_model
          6.4.45 face_based_surface_model
          6.4.46 shell_based_wireframe_model
          6.4.47 edge_based_wireframe_model
          6.4.48 geometric_set
          6.4.49 geometric_curve_set
          6.4.50 sectioned_spine
          6.4.51 geometric_set_replica
          6.4.52 tessellated_shape_representation
          6.4.53 tessellated_item
          6.4.54 repositioned_tessellated_item
          6.4.55 tessellated_structured_item
          6.4.56 coordinates_list
          6.4.57 tessellated_vertex
          6.4.58 tessellated_edge
          6.4.59 tessellated_connecting_edge
          6.4.60 tessellated_face
          6.4.61 triangulated_face
          6.4.62 cubic_bezier_tessellated_edge
          6.4.63 cubic_tessellated_connecting_edge
          6.4.64 complex_triangulated_face
          6.4.65 cubic_bezier_triangulated_face
          6.4.66 tessellated_solid
          6.4.67 tessellated_shell
          6.4.68 tessellated_wire
          6.4.69 tessellated_surface_set
          6.4.70 triangulated_surface_set
          6.4.71 complex_triangulated_surface_set
          6.4.72 tessellated_curve_set
          6.4.73 tessellated_geometric_set
          6.4.74 tessellated_point_set
          6.4.75 tessellated_shape_representation_with_accuracy_parameters
     6.5 Geometric model function definitions
          6.5.1 acyclic_set_replica
          6.5.2 acyclic_solid_replica
          6.5.3 build_transformed_set
          6.5.4 constraints_geometry_shell_based_surface_model
          6.5.5 constraints_geometry_shell_based_wireframe_model
          6.5.6 msb_shells
7 Scan data 3d shape model schema
     7.1 General
     7.2 Fundamental concepts and assumptions
     7.3 Scan data 3d shape model type definition
          7.3.1 point_cloud_set_or_superset
     7.4 Scan data 3d shape model entity definitions
          7.4.1 scan_data_shape_representation
          7.4.2 scanned_data_item
          7.4.3 point_cloud_dataset
          7.4.4 point_cloud_dataset_with_normals
          7.4.5 point_cloud_dataset_with_colours
          7.4.6 point_cloud_dataset_with_intensities
          7.4.7 point_cloud_superdataset
          7.4.8 triangulated_point_cloud_dataset
          7.4.9 scan_3d_model
          7.4.10 scanner_property
          7.4.11 scanner_basic_properties
     7.5 Scan data 3d shape model function definition
          7.5.1 consistent_sizes
Annex A Short names of entities
Annex B Information object registration
   B.1 Document identification
   B.2 Schema identification
Annex C Computer interpretable listings
Annex D EXPRESS-G diagrams
Annex E Change history
      E.1 General
      E 2 Changes made in edition 2
            E 2.1 Summary of changes
            E 2.5 Changes made to schema geometry_schema
            E 2.7 Changes made to schema topology_schema
            E 2.9 Changes made to schema geometric_model_schema
      E 3 Changes made in edition 3
            E 3.1 Summary of changes
            E 3.5 Changes made to schema geometry_schema
            E 3.7 Changes made to schema topology_schema
            E 3.9 Changes made to schema geometric_model_schema
      E 4 Changes made in edition 4
            E 4.1 Summary of changes
            E 4.5 Changes made to schema geometry_schema
            E 4.7 Changes made to schema geometric_model_schema
      E 5 Changes made in edition 5
            E 5.1 Summary of changes
            E 5.5 Changes made to schema geometry_schema
            E 5.7 Changes made to schema topology_schema
            E 5.9 Changes made to schema geometric_model_schema
            E 5.11 Changes made to schema scan_data_3d_shape_model_schema
      E 6 Changes made in edition 6
            E 6.1 Summary of changes
            E 6.3 Changes made to schema geometry_schema
            E 6.5 Changes made to schema topology_schema
      E 7 Changes made in edition 7
            E 7.1 Summary of changes
            E 7.3 Changes made to schema geometric_model_schema
            E 7.5 Changes made to schema geometry_schema
            E 7.7 Changes made to schema topology_schema
            E 7.9 Changes made to schema scan_data_3d_shape_model_schema
Bibliography
Index

Figures

Figure 1 — Schema level diagram of relationships among ISO 10303-42 schemas and other resource schemas
Figure 2 — Spherical point attributes
Figure 3 — Axis2_placement_3d
Figure 4a — Cartesian_transformation_operator_3d
Figure 4b — Cartesian_transformation_operator_3d
Figure 4c — Cartesian_transformation_operator_3d
Figure 5 — Circle
Figure 6 — Ellipse
Figure 7 — Hyperbola
Figure 8 — parabola
Figure 9 — Clothoid
Figure 10 — Circular_involute
Figure 11 — B_spline_curve
Figure 12 — local_b_spline equation
Figure 13 — Composite_curve
Figure 14 — Conical_surface
Figure 15 — Cross section of degenerate_toroidal_surface
Figure 16 — Cross-sections of a Dupin cyclide with C = 0
Figure 17 — A Dupin ring cyclide
Figure 18 — A Dupin horned cyclide
Figure 19 — A Dupin spindle cyclide
Figure 20 — Fixed_reference_swept_surface
Figure 21 — Mesh for a locally refined spline surface of degree 2
Figure 22 — Curve_bounded_surface
Figure 23 — Wedge_volume and its attributes
Figure 24 — Hexahedron_volume and its attributes
Figure 25 — Edge_curve
Figure 26 — Right angular wedge and its attributes
Figure 27 — Convex_hexahedron
Figure 28 — Cyclide_segment_solid
Figure 29 — Cross section of cyclide_segment_solid
Figure 30 — Revolved face solid
Figure 31 — Use of pnindex to locate coordinates
Figure 32 — Ordering of points for complex_triangulated_face
Figure 33 — Relationship between control points and triangular surface
Figure D.1 — EXPRESS-G diagram of the geometry_schema (1 of 16)
Figure D.2 — EXPRESS-G diagram of the geometry_schema (2 of 16)
Figure D.3 — EXPRESS-G diagram of the geometry_schema (3 of 16)
Figure D.4 — EXPRESS-G diagram of the geometry_schema (4 of 16)
Figure D.5 — EXPRESS-G diagram of the geometry_schema (5 of 16)
Figure D.6 — EXPRESS-G diagram of the geometry_schema (6 of 16)
Figure D.7 — EXPRESS-G diagram of the geometry_schema (7 of 16)
Figure D.8 — EXPRESS-G diagram of the geometry_schema (8 of 16)
Figure D.9 — EXPRESS-G diagram of the geometry_schema (9 of 16)
Figure D.10 — EXPRESS-G diagram of the geometry_schema (10 of 16)
Figure D.11 — EXPRESS-G diagram of the geometry_schema (11 of 16)
Figure D.12 — EXPRESS-G diagram of the geometry_schema (12 of 16)
Figure D.13 — EXPRESS-G diagram of the geometry_schema (13 of 16)
Figure D.14 — EXPRESS-G diagram of the geometry_schema (14 of 16)
Figure D.15 — EXPRESS-G diagram of the geometry_schema (15 of 16)
Figure D.16 — EXPRESS-G diagram of the geometry_schema (16 of 16)
Figure D.17 — EXPRESS-G diagram of the topology_schema (1 of 5)
Figure D.18 — EXPRESS-G diagram of the topology_schema (2 of 5)
Figure D.19 — EXPRESS-G diagram of the topology_schema (3 of 5)
Figure D.20 — EXPRESS-G diagram of the topology_schema (4 of 5)
Figure D.21 — EXPRESS-G diagram of the topology_schema (5 of 5)
Figure D.22 — EXPRESS-G diagram of the geometric_model_schema (1 of 11)
Figure D.23 — EXPRESS-G diagram of the geometric_model_schema (2 of 11)
Figure D.24 — EXPRESS-G diagram of the geometric_model_schema (3 of 11)
Figure D.25 — EXPRESS-G diagram of the geometric_model_schema (4 of 11)
Figure D.26 — EXPRESS-G diagram of the geometric_model_schema (5 of 11)
Figure D.27 — EXPRESS-G diagram of the geometric_model_schema (6 of 11)
Figure D.28 — EXPRESS-G diagram of the geometric_model_schema (7 of 11)
Figure D.29 — EXPRESS-G diagram of the geometric_model_schema (8 of 11)
Figure D.30 — EXPRESS-G diagram of the geometric_model_schema (9 of 11)
Figure D.31 — EXPRESS-G diagram of the geometric_model_schema (10 of 11)
Figure D.32 — EXPRESS-G diagram of the geometric_model_schema (11 of 11)
Figure D.33 — EXPRESS-G diagram of the scan_data_3d_shape_model_schema (1 of 2)
Figure D.34 — EXPRESS-G diagram of the scan_data_3d_shape_model_schema (2 of 2)

Tables

Table 1 — Geometry mathematical symbology
Table 2 — Topology symbol definitions
Table C.1 — EXPRESS listings


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