ISO/WD 10303-107 was prepared by Technical Committee ISO/TC 184, Industrial automation systems and integration, Subcommittee SC4, Industrial data.
This International Standard is organized as a series of parts, each published separately. The parts of ISO 10303 fall into one of the following series: description methods, integrated resources, application interpreted constructs, application modules, application protocols, abstract test suites, implementation methods, and conformance testing. The series are described in ISO 10303-1. A complete list of parts of ISO 10303 is available from the Internet:
http://www.nist.gov/sc4/editing/step/titles/.
Annexes A and B form an integral part of this part of ISO 10303. Annexes, C, D, E, aand F are for information only.
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.
The maths space application module defines a mathematical space.
The following are within the scope of this application module:
The following are not within the scope of this application module:
the relationship between a mathematical space and a property space that it identifies;
Information about the coordinate systems and units of measure that can be used to interpret a mathematical value within a mathematical space as a description of a property value within a property space is not within the scope of this application module.
an individual mathematical value;
relationships between mathematical values;
Expressions are not within the scope of this application module.
relationships between mathematical spaces.
Functions are not within the scope of this application module.
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