Integrated generic resource: Mathematical representation | ISO 10303-51:2005(E) © ISO |
*)
SCHEMA mathematical_description_of_distribution_schema;
REFERENCE FROM
mathematical_context_schema
--
ISO 10303-51
(maths_space_context);
REFERENCE FROM
mathematical_functions_schema
--
ISO 10303-50
(maths_function);
REFERENCE FROM
process_property_schema
--
ISO 10303-49
(action_property,
resource_property);
REFERENCE FROM
product_property_definition_schema
--
ISO 10303-41
(property_definition,
general_property_relationship);
REFERENCE FROM
support_resource_schema
--
ISO 10303-41
(identifier,
label,
text);
(*
NOTE 1 The schemas referenced above are specified in the following part of ISO 10303:
mathematical_context_schema ISO 10303-51 mathematical_functions_schema ISO 10303-50 process_property_schema ISO 10303-49 product_property_definition_schema ISO 10303-41 support_resource_schema ISO 10303-41
NOTE 2 See Annex D for a graphical representation of this schema.
The mathematical_description_of_distribution_schema specifies a mapping between a property distribution and a mathematical function. The mapping gives semantics to the mathematical function, so that the mathematical function describes or identifies the property distribution.
A property distribution can be with respect to:
EXAMPLE 1 The variation of power output with respect to:
is a property distribution.
EXAMPLE 2 The variation of temperature with respect to:
is a property distribution.
A property distribution D:X->P, where:
The description or identification depends upon:
NOTE The list of entity data types will be extended in application resources that use the constructs of this resource.
EXPRESS specification:
*)
TYPE
property_distribution_select
=
EXTENSIBLE
SELECT
(action_property,
general_property_relationship,
property_definition,
resource_property);
END_TYPE;
(*
EXPRESS specification:
*)
ENTITY maths_space_context_relationship;
id : identifier;
name : label;
description :
OPTIONAL
text;
relating_context : maths_space_context;
related_context : maths_space_context;
END_ENTITY;
(*
Attribute definitions:
id: the identifier for the maths_space_context_relationship.
name: the label by which the maths_space_context_relationship is known.
description: the text that characterizes the maths_space_context_relationship. The value of this attribute need not be specified.
relating_context: the instance of maths_space_context that has a relationship with the related_context.
related_context: the instance of maths_space_context that has a relationship with the relating_context.
A maths_space_context_relationship_description is a specification that a maths_function defines the relationship between two instances of maths_space_context.
Let:
the relating maths_space_context be A:P->S1 ;
the related maths_space_context be B:P->S2;
P be a physical space;
S1 and S2 be two instances of maths_space;
the description of the relationship between the instances of maths_space_context be T:S1->S2 (a maths_function).
An instance of maths_space_context_relationship_description specifies that:
B(p) = T(A(p)) for each p in P.
EXPRESS specification:
*)
ENTITY maths_space_context_relationship_description;
id : identifier;
name : label;
description :
OPTIONAL
text;
described_relationship : maths_space_context_relationship;
describing_relationship : maths_function;
END_ENTITY;
(*
Attribute definitions:
id: the identifier for the maths_space_context_relationship_description.
name: the label by which the maths_space_context_relationship_description is known.
description: the text that characterizes the maths_space_context_relationship_description. The value of this attribute need not be specified.
described_relationship: the maths_space_context_relationship_description that is described by the description.
describing_relationship: the maths_space_context_relationship that is described by the description.
A normalized_property_distribution_description is a specification of how a maths_function describes a property distribution with respect to a reference property distribution.
Let:
An instance of normalized_property_distribution_description specifies that:
D(p) = F(A(p)).D0(p) for each p in P.
EXPRESS specification:
*)
ENTITY normalized_property_distribution_description;
id : identifier;
name : label;
description :
OPTIONAL
text;
abstract_function : maths_function;
domain_context : maths_space_context;
normalization_basis : property_distribution_select;
physical_function : property_distribution_select;
END_ENTITY;
(*
Attribute definitions:
id: the identifier for the normalized_property_distribution_description.
name: the label by which the normalized_property_distribution_description is referenced.
description: the text that characterizes the normalized_property_distribution_description. The value of this attribute need not be specified.
abstract_function: the maths_function that describes the physical_function.
domain_context: the maths_space_context that is used to interpret the domain of the abstract_function.
normalization_basis: the reference property distribution that is the basis for the description of the physical_function.
NOTE The physical_function equals the normalization_basis wherever the abstract_function evaluates to 1.
physical_function: the property distribution that is described by the physical_function.
A property_distribution_description is a specificiation of how a maths_function describes a property distribution. Let:
D(p) = U-1(F(A(p))) for each p in P.
NOTE U-1 is well defined because U is a 1-1 mapping.
EXPRESS specification:
*)
ENTITY property_distribution_description;
id : identifier;
name : label;
description :
OPTIONAL
text;
abstract_function : maths_function;
domain_context : maths_space_context;
physical_function : property_distribution_select;
range_context : maths_space_context;
END_ENTITY;
(*
Attribute definitions:
id: the identifier for the property_distribution_description.
name: the label by which the property_distribution_description is known.
description: the text that characterizes the property_distribution_description. The value of this attribute need not be specified.
abstract_function: the maths_function that describes the physical_function.
domain_context: the maths_space_context that is used to interpret the domain of the abstract_function.
physical_function: the property distribution that is described by the abstract_function.
range_context: the maths_space_context that is used to interpret the range of the abstract_function.
*)
END_SCHEMA; -- mathematical_description_of_distribution_schema
(*
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