Integrated generic resource: Mathematical representation | ISO 10303-51:2005(E) © ISO |
*)
SCHEMA mathematical_context_schema;
REFERENCE FROM
action_schema
--
ISO 10303-41
(action,
action_method);
REFERENCE FROM
mathematical_functions_schema
--
ISO 10303-50
(maths_space,
maths_value);
REFERENCE FROM
measure_schema
--
ISO 10303-41
(unit);
REFERENCE FROM
product_definition_schema
--
ISO 10303-41
(product_definition);
REFERENCE FROM
product_property_definition_schema
--
ISO 10303-41
(general_property,
shape_aspect);
REFERENCE FROM
representation_schema
--
ISO 10303-43
(representation_context,
representation_item);
REFERENCE FROM
support_resource_schema
--
ISO 10303-41
(identifier,
label,
text);
REFERENCE FROM
ISO13584_generic_expressions_schema
--
ISO 13584-20
(generic_expression);
(*
NOTE 1 The schemas referenced above are specified in the following part of ISO 10303:
action_schema ISO 10303-41 mathematical_functions_schema ISO 10303-50 measure_schema ISO 10303-41 product_definition_schema ISO 10303-41 product_property_definition_schema ISO 10303-41 representation_schema ISO 10303-43 support_resource_schema ISO 10303-41 ISO13584_generic_expressions_schema ISO 13584-20
NOTE 2 See Annex D for a graphical representation of this schema.
The mathematical_context_schema specifies a mapping between a physical set or space and a mathematical space.
The physical set can be:
EXAMPLE 1 The set cross sections along beam 'XB_1234' are identified by the set real values in the range [-1.0, +1.0].
EXAMPLE 2 The set of states during the activity that is 'normal start up of engine type XYZ_123' are identified by the set of real values in the range [0.0, 1.0].
EXAMPLE 3 The set of temperatures are identified by the set of real values greater that -273.15
A parameterisation can be given a name. There are two ways of providing more information about a parameterisation, as follows:
the mathematical value can be specified for each member of the physical set (provided the physical set is finite); or
a property distribution can be described with respect to the parameterisation, as described in the mathematical description of distribution schema.
EXAMPLE 1 A parameterisation is defined for the set of cross sections within beam 'XB_1234'. A description of the positions of the cross-sections within the beam for its initial undeformed state provides information about the nature of the parameterisation.
EXAMPLE 2 A parameterisation is defined for the set of states within the activity that is 'normal start up of engine type XYZ_123'. A description of the times of the states within the start up activity provides information about the nature of the parameterisation.
A mapping between a physical quantity space and a mathematical space is called a scale. A scale can be:
NOTE This part of ISO 10303 references ISO 10303-43 'Integrated generic resources: Representation structures' for entities that define a scale.
EXAMPLE 3 The International Practical Temperature Scale 1968 (IPTS-68) is a mapping between the space of temperatures and the set of real numbers greater than -273.15.
The fixed points within the scale are degrees of hotness that are identified by particular physical phenomena, such as the freezing point of gold. For each fixed point, a real value is assigned.
NOTE The list of entity data types will be extended in application resources that use the constructs of this resource.
EXPRESS specification:
*)
TYPE
space_context_select
=
EXTENSIBLE
SELECT
(action,
action_method,
general_property,
product_definition,
representation_item,
shape_aspect);
END_TYPE;
(*
NOTE The list of entity data types will be extended in application resources that use the constructs of this resource.
EXPRESS specification:
*)
TYPE
value_context_select
=
EXTENSIBLE
SELECT
(action,
action_method,
general_property,
product_definition,
representation_item,
shape_aspect);
END_TYPE;
(*
A compound_maths_space_context is a type of maths_space_context that is defined by a list of other instances of maths_space_context. The referenced maths_space is a space of tuples. The maths_space_context for each item in a tuple has the corresponding position in the list.
EXAMPLE Consider two different instances of maths_space_context, as follows:
P1: the relationship between the 2D set of points on the surface of 'my product' and R2; and
P2:the relationship between the 1D set of states in 'my activity' and R.
The relationship between
is the compound_maths_space_context defined by P1 x P2.
EXPRESS specification:
*)
ENTITY compound_maths_space_context
SUBTYPE OF (maths_space_context);
components : LIST[2:?] OF maths_space_context;
END_ENTITY;
(*
Attribute definitions:
components: the instances of maths_space_context that are components of the compound_maths_space_context. A maths_space_context for a single state of a product can be derived from the maths_space_context of the product. In this case the single state shall have a compound_maths_space_context with a components list consisting of a single reference to the maths_space_context of the product.
A defined_maths_space_context is a type of maths_space_context that is defined by reference to a representation_context, unit or both.
NOTE A defined_maths_space_context can be instantiated as a representation_context_defined_maths_space_context, a unit_defined_maths_space_context or both.
EXPRESS specification:
*)
ENTITY defined_maths_space_context
SUBTYPE OF (maths_space_context);
END_ENTITY;
(*
An explicitly_enumerated_maths_space_context is a type of maths_space_context that is defined by specifying the instances of maths_value_context that are members of the maths_space_context.
NOTE An explicitly_enumerated_maths_space_context can only be specified for a discrete maths_space with a finite number of members.
EXPRESS specification:
*)
ENTITY explicitly_enumerated_maths_space_context
SUBTYPE OF (maths_space_context);
members : SET[1:?] OF maths_value_context;
END_ENTITY;
(*
Attribute definitions:
members: the instances of maths_value_context that are members of the maths_space_context.
EXPRESS specification:
*)
ENTITY maths_space_context
SUPERTYPE OF (ONEOF (compound_maths_space_context,
defined_maths_space_context,
explicitly_enumerated_maths_space_context));
id : identifier;
name : label;
description :
OPTIONAL
text;
abstract_space : maths_space;
physical_space : space_context_select;
END_ENTITY;
(*
Attribute definitions:
id: the identifier for the maths_space_context.
name: the label by which the maths_space_context is known.
description: the text that characterizes the maths_space_context. The value of this attribute need not be specified.
abstract_space: the maths_space that has each member corresponding to one member of the physical_space.
NOTE 1 This schema references the ABSTRACT entity type maths_space from ISO 10303-50, but not an entity type that is a SUBTYPE. An Application Module that uses this part of ISO 10303 should reference or define at least one SUBTYPE.
NOTE 2 Each of the subtypes of maths_function defined in ISO 10303-50 requires that a maths_space be a tuple_space.
physical_space: the physical space that has each member corresponding to one members of the abstract_space.
EXPRESS specification:
*)
ENTITY maths_value_context;
id : identifier;
name : label;
description :
OPTIONAL
text;
abstract_value : maths_value;
physical_value : value_context_select;
END_ENTITY;
(*
Attribute definitions:
id: the identifier for the maths_value_context.
name: the label by which the maths_value_context is known.
description: the text that characterizes the maths_value_context. The value of this attribute need not be specified.
abstract_value: the maths_value that corresponds to the physical_value.
physical_value: the physical value that corresponds to the maths_value.
EXPRESS specification:
*)
ENTITY membership_of_maths_space_context;
space_context : maths_space_context;
value_context : maths_value_context;
END_ENTITY;
(*
Attribute definitions:
space_context: the maths_space_context that has the maths_value_context as a member.
value_context: the maths_value_context that is a member of the maths_space_context.
A normalized_maths_space_context is a type of defined_maths_space_context that is defined by a reference physical value.
Let:
p be a physical value;
p0 be the reference physical value;
v be the maths value.
An instance of normalized_maths_space_context specifies that:
p = p0.v
EXPRESS specification:
*)
ENTITY normalized_maths_space_context
SUBTYPE OF (defined_maths_space_context);
normalization_basis : value_context_select;
END_ENTITY;
(*
Attribute definitions:
normalization_basis: the reference physical value that defines the maths_space_context.
EXPRESS specification:
*)
ENTITY representation_context_defined_maths_space_context
SUBTYPE OF (defined_maths_space_context);
representation_basis : representation_context;
END_ENTITY;
(*
Attribute definitions:
representation_basis: the representation_context that defines the maths_space_context.
EXPRESS specification:
*)
ENTITY unit_defined_maths_space_context
SUBTYPE OF (defined_maths_space_context);
unit_basis : unit;
END_ENTITY;
(*
Attribute definitions:
unit_basis: the unit that defines the maths_space_context.
NOTE This schema references the SELECT type unit from ISO 10303-41, but not the entity types that are selected by unit. An Application Module that uses this part of ISO 10303 should reference at least one of these entity types.
*)
END_SCHEMA; -- mathematical_context_schema
(*
© ISO 2005 — All rights reserved