Integrated generic resource: Mathematical representation ISO 10303-51:2005(E)
© ISO

Cover page
Table of contents
Copyright
Foreword
Introduction
1 Scope
2 Normative references
3 Terms, definitions and abbreviations

4 Mathematical context
   4.1 Introduction
   4.2 Fundamental concepts and assumptions
   4.3 Mathematical context type definitions
   4.4 Mathematical context entity definitions
5 Mathematical description of distribution
   5.1 Introduction
   5.2 Fundamental concepts and assumptions
   5.3 Mathematical description of distribution type definition
   5.4 Mathematical description of distribution entity definitions

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

4 Mathematical context schema

The following Express declaration begins the mathematical_context_schema and identifies the necessary external references.

EXPRESS specification:

*)
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.

4.1 Introduction

The mathematical_context_schema specifies a mapping between a physical set or space and a mathematical space.

The physical set can be:

The mapping defines an identification scheme for members of the physical set. A member of the physical set is identified by a mathematical value within the mathematical space.

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

4.2 Fundamental concepts and assumptions

A mapping between a physical set and a mathematical space is called a parameterisation if the physical set is:

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.

4.3 mathematical_context_schema type definitions

4.3.1 space_context_select   EXPRESS-G

The space_context_select type is an extensible list of alternate data types. It provides a mechanism to refer to instances of the data types included in the space_context_select type or in its extensions.

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;
(*

4.3.2 value_context_select   EXPRESS-G

The value_context_select type is an extensible list of alternate data types. It provides a mechanism to refer to instances of the data types included in the value_context_select type or in its extensions.

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;
(*

4.4 mathematical_context_schema entity definitions

4.4.1 compound_maths_space_context   EXPRESS-G

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.

4.4.2 defined_maths_space_context   EXPRESS-G

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;
(*

4.4.3 explicitly_enumerated_maths_space_context   EXPRESS-G

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.

4.4.4 maths_space_context   EXPRESS-G

A maths_space_context is a 1-1 mapping between a physical space and a maths_space that indicates a meaning for the maths_space.

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.

4.4.5 maths_value_context   EXPRESS-G

A maths_value_context is an association between a physical value and a maths_space. A meaning assigned to a maths_value by such an association can be deduced from a maths_space_context that has the maths_value_context as a member.

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.

4.4.6 membership_of_maths_space_context   EXPRESS-G

A membership_of_maths_space_context is an association between a maths_value_context and a maths_space_context that indicates the maths_value_context is a member of the maths_space_context.

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.

4.4.7 normalized_maths_space_context   EXPRESS-G

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.

4.4.8 representation_context_defined_maths_space_context   EXPRESS-G

A representation_context_defined_maths_space_context is a type of defined_maths_space_context that specifies a coordinate system. It is defined by reference to a representation_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.

4.4.9 unit_defined_maths_space_context   EXPRESS-G

A unit_defined_maths_space_context is a type of defined_maths_space_context that is defined by a single unit of measure.

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
(*


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