Introduction

ISO 10303 is an International Standard for the computer-interpretable representation of product information and for the exchange of product data. The objective is to provide a neutral mechanism capable of describing products throughout their life cycle. This mechanism is suitable not only for neutral file exchange, but also as a basis for implementing and sharing product databases, and as a basis for retention and archiving.

This part of ISO 10303 specifies an application module to record a mathematical space. A mathematical space is a set of mathematical values that can be either finite or infinite. A mathematical space can be used as follows:

• to identify a set of property values;

  EXAMPLE    The set of property values that is the set of temperatures between 20 degrees Celsius and 30 degrees Celsius is identified by the set of real values between 20.0 and 30.0 with respect to the Celsius scale.

  EXAMPLE    The set of properties that is the set of spatial positions within the metal of beam 'XB_001' is defined by the set of real triples within 'my subset of the space of real triples' with respect to metres and a my coordinate system.

  'My subset of the space of real triples' is defined as the image of a function from:

  • the unit cube which is a parameter space for beam 'XB_001'; to
  • the space of real triples which are Cartesian coordinates for space.

• to identify a set of features within a physical object;

  EXAMPLE    The set of points within beam 'XB_001' is identified by the set of real triples within the unit cube with opposite corners (0, 0, 0) and (1, 1, 1). This unit cube is a parameter space for 'XB_001'.

An infinite set of mathematical values cannot (clearly) be explicitly enumerated. Instead an infinite set is defined implicitly as follows:

• as the image or graph of a mathematical function; or

• by parameterisation.

  EXAMPLE    The set of real values within a unit cube can be defined by specifying the mathematical values that lie at the corners of the cube.

Clause 1 defines the scope of the application module and summarizes the functionality and data covered. Clause 3 lists the words defined in this part of ISO 10303 and gives pointers to words defined elsewhere. The information requirements of the application are specified in Clause 4 using terminology appropriate to the application. A graphical representation of the information requirements, referred to as the application reference model, is given in Annex C. Resource constructs are interpreted to meet the information requirements. This interpretation produces the module interpreted model (MIM). This interpretation, given in 5.1, shows the correspondence between the information requirements and the MIM. The short listing of the MIM specifies the interface to the resources and is given in 5.2. A graphical representation of the short listing of the MIM is given in Annex D.

In ISO 10303, the same English language words can be used to refer to an object in the real world or concept, and as the name of an EXPRESS data type that represents this object or concept.

The following typographical convention is used to distinguish between these. If a word or phrase occurs in the same typeface as narrative text, the referent is the object or concept. If the word or phrase occurs in a bold typeface or as a hyperlink, the referent is the EXPRESS data type.

The name of an EXPRESS data type can be used to refer to the data type itself, or to an instance of the data type. The distinction between these uses is normally clear from the context. If there is a likelihood of ambiguity, either the phrase "entity data type" or "instance(s) of" is included in the text.

Double quotation marks " " denote quoted text. Single quotation marks ' ' denote particular text string values.

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