ISO/TS 10303-1652:2019 Basic geometry


Application module: Basic geometry	ISO/TS 10303-1652:2019(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 Information requirements
4.1 Required AM ARMs
4.2 ARM entity definitions
4.3 ARM subtype constraint definitions
5 Module interpreted model
5.1 Mapping specification
5.2 MIM EXPRESS short listing

A MIM short names
B Information object registration
C ARM EXPRESS-G
D MIM EXPRESS-G
E Computer interpretable listings
F Change history
Bibliography
Index

5.1 Mapping specification

In the following, "Application element" designates any entity data type defined in Clause 4, any of its explicit attributes and any subtype constraint. "MIM element" designates any entity data type defined in Clause 5.2 or imported with a USE FROM statement, from another EXPRESS schema, any of its attributes and any subtype constraint defined in Clause 5.2 or imported with a USE FROM statement.

This clause contains the mapping specification that defines how each application element of this part of ISO 10303 (see Clause 4) maps to one or more MIM elements (see Clause 5.2).

The mapping for each application element is specified in a separate subclause below. The mapping specification of an attribute of an ARM entity is a subclause of the clause that contains the mapping specification of this entity. Each mapping specification subclause contains up to five elements.

Title: The clause title contains:

the name of the considered ARM entity or subtype constraint, or
the name of the considered ARM entity attribute when this attribute refers to a type that is not an entity data type or a SELECT type that contains or may contain entity data types, or
a composite expression, <attribute name> to <referred type>, when this attribute refers to a type that is not an entity data type or a SELECT type that contains or may contain entity data types.

MIM element: This section contains, depending on the considered application element:

the name of one or more MIM entity data types;
the name of a MIM entity attribute, presented with the syntax <entity name>.<attribute name>, when the considered ARM attribute refers to a type that is not an entity data type or a SELECT type that contains or may contain entity data types;
the term PATH, when the considered ARM entity attribute refers to an entity data type or to a SELECT type that contains or may contain entity data types;
the term IDENTICAL MAPPING, when both application objects involved in an application assertion map to the same instance of a MIM entity data type;
the term NO MAPPING EXTENSION PROVIDED, when the extension to an extensible SELECT TYPE has no impact;
the syntax /SUPERTYPE(<supertype name>)/, when the considered ARM entity is mapped as its supertype;
one or more constructs /SUBTYPE(<subtype name>)/, when the mapping of the considered ARM entity is the union of the mapping of its subtypes.

When the mapping of an application element involves more than one MIM element, each of these MIM elements is presented on a separate line in the mapping specification, enclosed between parentheses or brackets.

Source: This section contains:

the ISO standard number and part number in which the MIM element is defined, for those MIM elements that are defined in a common resource document;
the ISO standard number and part number of this part of ISO 10303, for those MIM elements that are defined in the MIM schema of this part.

This section is omitted when the keywords PATH or IDENTICAL MAPPING or NO MAPPING EXTENSION PROVIDED are used in the MIM element section.

Rules: This section contains the name of one or more global rules that apply to the population of the MIM entity data types listed in the MIM element section or in the reference path. When no rule applies, this section is omitted.

A reference to a global rule may be followed by a reference to the subclause in which the rule is defined.

Constraint: This section contains the name of one or more subtype constraints that apply to the population of the MIM entity data types listed in the MIM element section or in the reference path. When no subtype constraint applies, this section is omitted.

A reference to a subtype constraint may be followed by a reference to the subclause in which the subtype constraint is defined.

Reference path: This section contains:

the reference path to its supertypes in the common resources, for each MIM element created within this part of ISO 10303;
the specification of the relationships between MIM elements, when the mapping of an application element requires to relate instances of several MIM entity data types. In such a case, each line in the reference path documents the role of a MIM element relative to the referring MIM element or to the next referred MIM element.

For the expression of reference paths and of the constraints between MIM elements, the following notational conventions apply:

[]	enclosed section constrains multiple MIM elements or sections of the reference path are required to satisfy an information requirement;
()	enclosed section constrains multiple MIM elements or sections of the reference path are identified as alternatives within the mapping to satisfy an information requirement;
{}	enclosed section constrains the reference path to satisfy an information requirement;
<>	enclosed section constrains at one or more required reference path;
\|\|	enclosed section constrains the supertype entity;
->	the attribute, whose name precedes the -> symbol, references the entity or select type whose name follows the -> symbol;
<-	the entity or select type, whose name precedes the <- symbol, is referenced by the entity attribute whose name follows the <- symbol;
[i]	the attribute, whose name precedes the [i] symbol, is an aggregate; any element of that aggregate is referred to;
[n]	the attribute, whose name precedes the [n] symbol, is an ordered aggregate; member n of that aggregate is referred to;
=>	the entity, whose name precedes the => symbol, is a supertype of the entity whose name follows the => symbol;
<=	the entity, whose name precedes the <= symbol, is a subtype of the entity whose name follows the <= symbol;
=	the string, select, or enumeration type is constrained to a choice or value;
\	the reference path expression continues on the next line;
*	one or more instances of the relationship entity data type may be assembled in a relationship tree structure. The path between the relationship entity and the related entities, is enclosed with braces;
--	the text following is a comment or introduces a clause reference;
*>	the select or enumeration type, whose name precedes the > symbol, is extended into the select or enumeration type whose name follows the > symbol;
<*	the select or enumeration type, whose name precedes the <* symbol, is an extension of the select or enumeration type whose name follows the <* symbol;
!{}	section enclosed by {} indicates a negative constraint placed on the mapping.

The definition and use of mapping templates are not supported in the present version of the application modules. However, use of predefined templates /MAPPING_OF/, /SUBTYPE/, and /SUPERTYPE/ is supported.

5.1.1 Bounded_curve

MIM element:	bounded_curve
Source:	ISO 10303-42
Reference path:	bounded_curve <= curve <= geometric_representation_item <= representation_item

5.1.2 Bounded_surface

MIM element:	bounded_surface
Source:	ISO 10303-42
Reference path:	bounded_surface <= surface <= geometric_representation_item <= representation_item

5.1.3 Circle

MIM element:	circle
Source:	ISO 10303-42
Reference path:	circle <= conic <= curve <= geometric_representation_item <= representation_item

5.1.3.1 radius

MIM element:	circle.radius
Reference path:	circle.radius -> positive_length_measure

5.1.4 Conic

MIM element:	conic
Source:	ISO 10303-42
Reference path:	conic <= curve <= geometric_representation_item <= representation_item

5.1.4.1 Conic to Axis_placement (as position)

MIM element:	conic.position
Reference path:	conic.position -> axis2_placement = (axis2_placement_3d) (axis2_placement_2d)

5.1.5 Conical_surface

MIM element:	conical_surface
Source:	ISO 10303-42
Reference path:	conical_surface <= elementary_surface <= surface <= geometric_representation_item <= representation_item

5.1.5.1 radius

MIM element:	conical_surface.radius
Reference path:	conical_surface.radius -> length_measure

5.1.5.2 semi_angle

MIM element:	conical_surface.semi_angle
Reference path:	conical_surface.semi_angle -> plane_angle_measure

5.1.5.3 Conical_surface to Axis_placement_3d (as position)

MIM element:	elementary_surface.position
Reference path:	elementary_surface.position -> axis2_placement_3d

5.1.6 Curve

MIM element:	curve
Source:	ISO 10303-42
Reference path:	curve <= geometric_representation_item

5.1.7 Cylindrical_point

MIM element:	cylindrical_point
Source:	ISO 10303-42

5.1.7.1 r

MIM element:

cylindrical_point.r

5.1.7.2 theta

MIM element:

cylindrical_point.theta

5.1.7.3 z

MIM element:

cylindrical_point.z

5.1.8 Cylindrical_surface

MIM element:	cylindrical_surface
Source:	ISO 10303-42
Reference path:	cylindrical_surface <= elementary_surface <= surface <= geometric_representation_item <= representation_item

5.1.8.1 radius

MIM element:	cylindrical_surface.radius
Reference path:	cylindrical_surface.radius -> positive_length_measure

5.1.8.2 Cylindrical_surface to Axis_placement_3d (as position)

MIM element:	elementary_surface.position
Reference path:	elementary_surface.position -> axis2_placement_3d

5.1.9 Degenerate_pcurve

MIM element:	degenerate_pcurve
Source:	ISO 10303-42

5.1.9.1 Degenerate_pcurve to Definitional_representation (as reference_to_curve)

Reference path:

degenerate_pcurve.reference_to_curve ->
definitional_representation

5.1.9.2 Degenerate_pcurve to Surface (as basis_surface)

Reference path:

degenerate_pcurve.basis_surface ->
surface

5.1.10 Ellipse

MIM element:	ellipse
Source:	ISO 10303-42
Reference path:	ellipse <= conic <= curve <= geometric_representation_item <= representation_item

5.1.10.1 first_semi_axis

MIM element:	ellipse.semi_axis_1
Reference path:	ellipse.semi_axis_1 -> positive_length_measure

5.1.10.2 second_semi_axis

MIM element:	ellipse.semi_axis_2
Reference path:	ellipse.semi_axis_2 -> positive_length_measure

5.1.11 Extruded_surface

MIM element:	surface_of_linear_extrusion
Source:	ISO 10303-42
Reference path:	surface_of_linear_extrusion <= swept_surface <= surface <= geometric_representation_item <= representation_item

5.1.11.1 Extruded_surface to Direction (as extrusion_axis)

MIM element:	surface_of_linear_extrusion.extrusion_axis.orientation
Reference path:	surface_of_linear_extrusion.extrusion_axis -> vector vector.orientation -> direction

5.1.12 Hyperbola

MIM element:	hyperbola
Source:	ISO 10303-42
Reference path:	hyperbola <= conic <= curve <= geometric_representation_item <= representation_item

5.1.12.1 imaginary_semi_axis

MIM element:	hyperbola.semi_imag_axis
Reference path:	hyperbola.semi_imag_axis -> positive_length_measure

5.1.12.2 semi_axis

MIM element:	hyperbola.semi_axis
Reference path:	hyperbola.semi_axis -> positive_length_measure

5.1.13 Line

MIM element:	line
Source:	ISO 10303-42
Reference path:	line <= curve

5.1.13.1 Line to Cartesian_point (as point)

MIM element:	line.pnt
Reference path:	line.pnt -> cartesian_point

5.1.13.2 Line to Direction (as line_direction)

MIM element:	line.dir.orientation
Reference path:	line.dir -> vector vector.orientation -> direction

5.1.14 Parabola

MIM element:	parabola
Source:	ISO 10303-42
Reference path:	parabola <= conic <= curve <= geometric_representation_item <= representation_item

5.1.14.1 focal_distance

MIM element:	parabola.focal_dist
Reference path:	parabola.focal_dist -> positive_length_measure

5.1.15 Plane

MIM element:	plane
Source:	ISO 10303-42

5.1.15.1 Plane to Axis_placement_3d (as position)

MIM element:	elementary_surface.position
Reference path:	plane <= elementary_surface elementary_surface.position -> axis2_placement_3d

5.1.16 Point_on_curve

MIM element:	point_on_curve
Source:	ISO 10303-42

5.1.16.1 Point_on_curve to Curve (as supporting_curve)

MIM element:	PATH
Reference path:	point_on_curve.basis_curve -> curve

5.1.17 Point_on_surface

#1: If the point is defined from the evaluation of the surface function for a given parameter pair.

MIM element:	(point_on_surface)
Source:	ISO 10303-42

#2: If the Point_on_surface identifies a point where a curve on the surface collapses.

MIM element:	(degenerate_pcurve)
Source:	ISO 10303-42

5.1.17.1 Point_on_surface to Surface (as supporting_surface)

#1: If the point is defined from the evaluation of the surface function for a given parameter pair.

MIM element:	PATH
Reference path:	point_on_surface.basis_surface -> surface

#2: If the Point_on_surface identifies a point where a curve on the surface collapses.

MIM element:	PATH
Reference path:	degenerate_pcurve.basis_surface -> surface

5.1.18 Polar_point

MIM element:	polar_point
Source:	ISO 10303-42

5.1.18.1 r

MIM element:

polar_point.r

5.1.18.2 theta

MIM element:

polar_point.theta

5.1.19 Spherical_point

MIM element:	spherical_point
Source:	ISO 10303-42

5.1.19.1 phi

MIM element:

spherical_point.phi

5.1.19.2 r

MIM element:

spherical_point.r

5.1.19.3 theta

MIM element:

spherical_point.theta

5.1.20 Spherical_surface

MIM element:	spherical_surface
Source:	ISO 10303-42
Reference path:	spherical_surface <= elementary_surface <= surface <= geometric_representation_item <= representation_item

5.1.20.1 radius

MIM element:	spherical_surface.radius
Reference path:	spherical_surface.radius -> positive_length_measure

5.1.20.2 Spherical_surface to Axis_placement_3d (as position)

MIM element:	elementary_surface.position
Reference path:	elementary_surface.position -> axis2_placement_3d

5.1.21 Surface

#1: If no orientation is specified for the Surface.

MIM element:	surface
Source:	ISO 10303-42
Reference path:	surface <= geometric_representation_item

#2: If an orientation is specified for the Surface.

MIM element:	oriented_surface
Source:	ISO 10303-42
Reference path:	oriented_surface <= surface surface <= geometric_representation_item

5.1.22 Surface_of_revolution

MIM element:	surface_of_revolution
Source:	ISO 10303-42
Reference path:	surface_of_revolution <= swept_surface <= surface <= geometric_representation_item <= representation_item

5.1.22.1 Surface_of_revolution to Cartesian_point (as axis_point)

MIM element:	surface_of_revolution.axis_position.location
Reference path:	surface_of_revolution.axis_position -> axis1_placement <= placement placement.location -> cartesian_point

5.1.22.2 Surface_of_revolution to Direction (as axis_direction)

MIM element:	surface_of_revolution.axis_position.axis
Reference path:	surface_of_revolution.axis_position -> axis1_placement axis1_placement.z -> direction

5.1.23 Swept_surface

MIM element:	swept_surface
Source:	ISO 10303-42
Reference path:	swept_surface <= surface <= geometric_representation_item <= representation_item

5.1.23.1 Swept_surface to Curve (as swept_curve)

MIM element:	swept_surface.swept_curve
Reference path:	swept_surface.swept_curve -> curve

5.1.24 Toroidal_surface

MIM element:	toroidal_surface
Source:	ISO 10303-42
Reference path:	toroidal_surface <= elementary_surface <= surface <= geometric_representation_item <= representation_item

5.1.24.1 minor_radius

MIM element:	toroidal_surface.minoor_radius
Reference path:	toroidal_surface.minor_radius -> positive_length_measure

5.1.24.2 radius

MIM element:	toroidal_surface.major_radius
Reference path:	toroidal_surface.major_radius -> positive_length_measure

5.1.24.3 Toroidal_surface to Axis_placement_3d (as position)

MIM element:	elementary_surface.position
Reference path:	elementary_surface.position -> axis2_placement_3d

5.1.25 alternate_geometry_items

It maps to ONEOF constraint defined directly in the geometric_representation_item entity.

Constraint:	geometric_representation_item
Source:	ISO 10303-42