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Application module:
Elemental geometric shape |
ISO/TS 10303-1004:2021(E)
© ISO
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This clause specifies the information requirements for the
Elemental geometric shape
application module. The information requirements are specified as the
Application Reference Model (ARM) of this application module.
NOTE 1 A graphical representation of the information
requirements is given in
Annex C.
NOTE 2 The mapping specification is specified in
5.1. It shows how
the information requirements are met by using common resources and
constructs defined or imported in the MIM schema of this application
module.
This clause defines the information requirements to which implementations shall
conform using the EXPRESS language as defined in ISO 10303-11.
The following begins the
Elemental_geometric_shape_arm
schema and identifies the necessary external references.
EXPRESS specification:
*)
SCHEMA Elemental_geometric_shape_arm;
(*
The following EXPRESS interface statements specify the elements
imported from the ARMs of other application modules.
EXPRESS specification:
*)
USE FROM
Elemental_topology_arm;
--
ISO/TS 10303-1005
USE FROM
Foundation_representation_arm;
--
ISO/TS 10303-1006
(*
NOTE 1
The schemas referenced above are specified in the following
part of ISO 10303:
| Elemental_topology_arm |
ISO/TS 10303-1005 |
| Foundation_representation_arm |
ISO/TS 10303-1006 |
NOTE 2
See Annex C,
Figures
C.1and C.2
for a graphical representation of this schema.
This subclause specifies the ARM types
for this application module. The ARM types and
definitions are specified below.
The cartesian_transformation type allows for the designation of the data
types
Cartesian_transformation_2d and Cartesian_transformation_3d.
The cartesian_transformation type is a mechanism to refer to an instance of either a 2D or 3D cartesian transformation operator.
EXPRESS specification:
*)
TYPE
cartesian_transformation =
SELECT
(Cartesian_transformation_2d,
Cartesian_transformation_3d);
END_TYPE;
(*
The geometric_model_item type allows for the designation of the data
types
Detailed_geometric_model_element and Detailed_topological_model_element.
EXPRESS specification:
*)
TYPE
geometric_model_item =
SELECT
(Detailed_geometric_model_element,
Detailed_topological_model_element);
END_TYPE;
(*
The template_definition_select type is an
extensible list of alternate data types
that allows for the designation of the data
type Geometric_model.
NOTE
The list of entity data types may be
extended in application modules that use the constructs of
this module.
EXPRESS specification:
*)
TYPE
template_definition_select =
EXTENSIBLE
SELECT
(Geometric_model);
END_TYPE;
(*
This subclause specifies the ARM entities for this
module. Each ARM application entity is an atomic element that
embodies a unique application concept and contains attributes
specifying the data elements of the entity. The ARM
entities and definitions are specified below.
An Axis1_placement is a type of
Detailed_geometric_model_element
that defines the position of a single axis in three-dimensional space.
EXPRESS specification:
*)
ENTITY Axis1_placement
SUBTYPE OF (Axis_placement);
axis :
OPTIONAL
Direction;
WHERE
WR1: SELF\Axis_placement.dim = 3;
WR2: SIZEOF(axis\Direction.direction_ratios) = 3;
END_ENTITY;
(*
Attribute definitions:
axis:
the direction of the axis.
Formal propositions:
WR1:
The dimensionality of the Axis_placement_2d shall be 3.
WR2:
The number of dimension ratios of the axis shall be 3.
An Axis_placement
is a type of
Detailed_geometric_model_element
that locates and orient a geometric item with respect to the coordinate system of its
Geometric_coordinate_space.
NOTE
An Axis_placement might be used as a local right-handed, 2D or 3D, coordinate system within its
Geometric_coordinate_space.
EXPRESS specification:
*)
ENTITY Axis_placement
ABSTRACT SUPERTYPE
OF (ONEOF (Axis_placement_2d,
Axis_placement_3d,
Axis1_placement))
SUBTYPE OF (Detailed_geometric_model_element);
location : Cartesian_point;
DERIVE
dim : INTEGER := SIZEOF(location\Cartesian_point.coordinates);
END_ENTITY;
(*
Attribute definitions:
location:
the
Cartesian_point
that defines the position of the Axis_placement in the geometric space.
dim:
the dimensionality of the Axis_placement. It is equal to the number of coordinates of the location.
An Axis_placement_2d is a type of
Axis_placement that is two-dimensional.
EXPRESS specification:
*)
ENTITY Axis_placement_2d
SUBTYPE OF (Axis_placement);
ref_direction :
OPTIONAL
Direction;
WHERE
WR1: SELF\Axis_placement.dim = 2;
WR2: SIZEOF(ref_direction\Direction.direction_ratios) = 2;
END_ENTITY;
(*
Attribute definitions:
ref_direction:
the direction used to determine the direction of the local X axis.
The value of this attribute need not be specified.
If ref_direction is omitted, this directions is taken from the geometric coordinate system
Formal propositions:
WR1:
The dimensionality of the Axis_placement_2d shall be two.
WR2:
The dimensionality of the ref_direction shall be two.
An Axis_placement_3d is a type of
Axis_placement
that is three-dimensional.
The third direction of the coordinate system is defined
by the vector product of axis and ref_direction.
EXPRESS specification:
*)
ENTITY Axis_placement_3d
SUBTYPE OF (Axis_placement);
axis :
OPTIONAL
Direction;
ref_direction :
OPTIONAL
Direction;
WHERE
WR1: SELF\Axis_placement.dim = 3;
WR2: SIZEOF(axis\Direction.direction_ratios) = 3;
WR3: SIZEOF(ref_direction\Direction.direction_ratios) = 3;
END_ENTITY;
(*
Attribute definitions:
axis:
the
Direction
that defines the second axis of the Axis_placement. The value of this attribute need not be specified.
ref_direction:
the direction used to determine the direction of the local X axis.
The value of this attribute need not be specified.
If axis or ref_direction is omitted, these directions are taken from the geometric coordinate system
Formal propositions:
WR1:
The dimensionality of the Axis_placement_3d shall be three.
WR2:
The dimensionality of the axis shall be three.
WR3:
The dimensionality of the ref_direction shall be three.
Informal propositions:
IP1:
If both axis and ref_direction are provided
then the vector product of axis and ref_direction shall not be a null vector.
A Cartesian_point is a type of
Point
that defines a point by a list of up to 3 cartesian coordinates.
EXPRESS specification:
*)
ENTITY Cartesian_point
SUBTYPE OF (Point);
coordinates : LIST[1:3] OF length_measure;
END_ENTITY;
(*
Attribute definitions:
coordinates:
the list of up to 3 length measure values that define the cartesian coordinates of the point.
A Cartesian_transformation_2d is a type of
Detailed_geometric_model_element.
It is defined in a 2D geometric space by a 2*2 matrix and a cartesian point.
Let be:
- M, the 2*2 multiplication matrix of the cartesian transformation;
- A, the point of the cartesian transformation;
- P, a point in the geometric space;
- Q, the result of the application of the transformation to P.
The coordinates of Q shall be obtained by the formula: Q = M*P + A
EXPRESS specification:
*)
ENTITY Cartesian_transformation_2d
SUBTYPE OF (Detailed_geometric_model_element);
multiplication_matrix : ARRAY[1:2] OF Direction;
translation : Cartesian_point;
scale :
OPTIONAL
REAL;
WHERE
WR1: SIZEOF(multiplication_matrix[1]\Direction.direction_ratios)=2;
WR2: SIZEOF(multiplication_matrix[2]\Direction.direction_ratios)=2;
WR3: SIZEOF(translation.coordinates)=2;
END_ENTITY;
(*
Attribute definitions:
multiplication_matrix:
the array of two instances of
Direction
that defines the multiplication matrix of the transformation.
translation:
the
Cartesian_point
that defines the position of the result of the application of the transformation to the origin of the geometric space.
scale:
the scaling value specified for the transformation.
The value of this attribute need not be specified.
Formal propositions:
WR1:
The first element of the matrix shall refer to a two-dimensional
Direction.
WR2:
The second element of the matrix shall refer to a two-dimensional
Direction.
WR3:
The translation point shall have two coordinates.
A Cartesian_transformation_3d is a type of
Detailed_geometric_model_element
that is a geometric transformation defined in a 3D geometric space by a 3*3 matrix and a cartesian point.
Let be:
- M, the 3*3 multiplication matrix of the cartesian transformation;
- A, the point of the cartesian transformation;
- P, a point in the geometric space;
- Q, the result of the application of the transformation to P.
The coordinates of Q shall be obtained by the formula: Q = M*P + A
EXPRESS specification:
*)
ENTITY Cartesian_transformation_3d
SUBTYPE OF (Detailed_geometric_model_element);
multiplication_matrix : ARRAY[1:3] OF Direction;
translation : Cartesian_point;
scale :
OPTIONAL
REAL;
WHERE
WR1: SIZEOF(multiplication_matrix[1]\Direction.direction_ratios)=3;
WR2: SIZEOF(multiplication_matrix[2]\Direction.direction_ratios)=3;
WR3: SIZEOF(multiplication_matrix[3]\Direction.direction_ratios)=3;
WR4: SIZEOF(translation.coordinates)=3;
END_ENTITY;
(*
Attribute definitions:
multiplication_matrix:
the array of three instances of
Direction
that defines the multiplication matrix of the transformation.
translation:
the
Cartesian_point
that defines the position of the result of the application of the transformation to the origin of the geometric space.
scale:
the scaling value specified for the transformation.
The value of this attribute need not be specified.
Formal propositions:
WR1:
The first element of the matrix shall refer to a three-dimensional
Direction.
WR2:
The second element of the matrix shall refer to a three-dimensional
Direction.
WR3:
The third element of the matrix shall refer to a three-dimensional
Direction.
WR4:
The translation point shall have three coordinates.
A Detailed_geometric_model_element is a type of
Representation_item.
It identifies a geometric construct.
Only non-abstract specializations of the Detailed_geometric_model_element entity data type can be instantiated.
A Detailed_geometric_model_element is either a
Cartesian_point
or a
Direction
or an
Axis_placement
or a
Cartesian_transformation_2d
or a
Cartesian_transformation_3d
or a
Geometric_placement_operation
or a specialization defined elsewhere.
EXPRESS specification:
*)
ENTITY Detailed_geometric_model_element
ABSTRACT SUPERTYPE
OF (ONEOF (Direction,
Axis_placement,
Cartesian_transformation_2d,
Cartesian_transformation_3d,
Geometric_placement_operation,
Point))
SUBTYPE OF (Representation_item);
END_ENTITY;
(*
Informal propositions:
IP1:
A Detailed_geometric_model_element shall be an item of a
Geometric_model
or serve to create an item of a
Geometric_model.
IP2:
The instances of
Geometric_model
that contain the Detailed_geometric_model_element shall all have the same space dimensionality.
A Direction is a type of
Detailed_geometric_model_element
that defines a 2 or 3 dimensional vector.
NOTE 1
A Direction is not located in a geometric space but is used in the definition of geometric entities like
Axis_placement.
EXPRESS specification:
*)
ENTITY Direction
SUBTYPE OF (Detailed_geometric_model_element);
direction_ratios : LIST[2:3] OF REAL;
END_ENTITY;
(*
Attribute definitions:
direction_ratios:
the list of 2 or 3 length measure values that define the direction ratios of the Direction.
NOTE 2
The direction ratios of a Direction may not be normalised, and the actual magnitudes
of the components have no effect upon the direction being defined; only the ratios x:y:z or x:y are
significant.
A Geometric_coordinate_space is a type of
Numerical_representation_context
that defines a coordinate space where geometric elements can be defined. It is either two or three-dimensional.
There shall be at least two units specified for the Geometric_coordinate_space: one length unit and one plane angle unit.
The length unit applies to each coordinate direction.
EXAMPLE
The length unit millimetre and the angle unit radian are examples of units that may assigned to a Geometric_coordinate_space.
NOTE
The origin for coordinate values is implicitly defined as being the cartesian point whose coordinates are all zero.
EXPRESS specification:
*)
ENTITY Geometric_coordinate_space
SUBTYPE OF (Numerical_representation_context);
dimension_count : INTEGER;
WHERE
WR1: dimension_count >0;
END_ENTITY;
(*
Attribute definitions:
dimension_count:
the dimensionality of the geometric space.
Formal propositions:
WR1:
The dimensionality shall be greater than zero.
A Geometric_model is a type of
Representation
dedicated to the description of geometric constructs.
The Geometric_model is founded in a
Geometric_coordinate_space.
The items of a Geometric_model are instances of
Detailed_geometric_model_element
and
Detailed_topological_model_element.
EXPRESS specification:
*)
ENTITY Geometric_model
SUBTYPE OF (Representation);
version_id :
OPTIONAL
STRING;
model_extent :
OPTIONAL
length_measure;
SELF\Representation.context_of_items : Geometric_coordinate_space;
SELF\Representation.items : SET[1:?] OF geometric_model_item;
END_ENTITY;
(*
Attribute definitions:
version_id:
the text that specifies the version identifier of the Geometric_model. The value of this attribute need not be specified.
model_extent:
the
length_measure
that specifies the radius of a sphere that encloses all elements of the geometric model.
The centre of the sphere is located at the origin of the
Geometric_coordinate_space
of the Geometric_model.
The value of this attribute need not be specified.
context_of_items:
the
Geometric_coordinate_space
in which the Geometric_model is defined.
items:
the instances of
Detailed_geometric_model_element
and
Detailed_topological_model_element
that are included in the Geometric_model.
A Geometric_operator_transformation is a type of
Geometric_placement_operation that results in a Cartesian transformation.
EXPRESS specification:
*)
ENTITY Geometric_operator_transformation
SUBTYPE OF (Geometric_placement_operation);
target : cartesian_transformation;
END_ENTITY;
(*
Attribute definitions:
target:
the
cartesian_transformation
that identifies the target of the transformation.
A Geometric_placement is a type of
Geometric_placement_operation that results in an axis placement in a coordinate space.
EXPRESS specification:
*)
ENTITY Geometric_placement
SUBTYPE OF (Geometric_placement_operation);
target : Axis_placement;
END_ENTITY;
(*
Attribute definitions:
target:
the
Axis_placement
that identifies the target of the placement.
A Geometric_placement_operation is a type of
Detailed_geometric_model_element.
A Geometric_placement_operation may be a
Geometric_placement
or a
Geometric_operator_transformation.
EXPRESS specification:
*)
ENTITY Geometric_placement_operation
ABSTRACT SUPERTYPE
OF (ONEOF (Geometric_placement,
Geometric_operator_transformation))
SUBTYPE OF (Detailed_geometric_model_element);
source : Axis_placement;
template_definition : template_definition_select;
END_ENTITY;
(*
Attribute definitions:
source:
the
Axis_placement
that identifies the source of the operation.
template_definition:
the value from
template_definition_select.
A Point is a type of
Detailed_geometric_model_element.
A Point is a location in a Cartesian coordinate space.
EXPRESS specification:
*)
ENTITY Point
SUBTYPE OF (Detailed_geometric_model_element);
END_ENTITY;
(*
*)
END_SCHEMA; -- Elemental_geometric_shape_arm
(*
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