Integrated generic resource: Mathematical representation | ISO 10303-51:2005(E) © ISO |
INTERNATIONAL STANDARD | ISO 10303-51:2005(E) |
This part of ISO 10303 specifies the integrated resource constructs for Mathematical representation. The following are within the scope of this part of ISO 10303:
the use of a mathematical values to identify or describe a product, feature, state, activity or property;
the use of a mathematical space as an identification scheme for a set or space of products, features, states, activities, or properties;
the use of a mathematical function to describe a property variation within a set or space of products, features, states or activities;
EXAMPLE 1 The set of points within a widget of type XYZ is parameterised by the unit cube within real triple space that has corners (0, 0, 0), (1, 0, 0), (0, 1, 0), (1, 1, 0), (0, 0, 1), (1, 0, 1), (0, 1, 1), (1, 1, 1).
A widget of type XYZ has a simple shape which makes this mapping possible. A more complex widget could be divided into parts, such that each part can map on to a unit cube or some other simple mathematical space.
the identification scheme or parameterisation for a set of features within the body of a product;
EXAMPLE 2 The volume of geometric space within 'my duct' is a product which is has air flowing through it. There is a set of planes within this volume, such that each is approximately normal to the direction of flow. Each of these planes can be regarded as a feature of the volume.
There are properties for each of the planes in the volume, such as average pressure, average velocity and average temperature. Hence there is a variation of average pressure (say) with respect to the set of planes.
the identification scheme or parameterisation for states within a state space or within an activity;
EXAMPLE 3 The set of states within the start up sequence for a 'my duct' is parameterised by the unit real interval [0.0, 1.0].
the identification scheme or parameterisation for a set of features within the body of a product, or for a set of states within a state space or activity;
EXAMPLE 4 A parameterisation of a one dimensional set of planes within a duct is defined by example 2. A parameterisation of a one dimensional set of states during a start up sequence is defined by example 3.
There is a two dimensional set of states for planes within the duct during the start up sequence. This two dimensional space is parameterised by the unit square with corners (0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0).
the identification or description of values within a physical quantity space, with respect to a unit or measure, coordinate system and encoding method;
EXAMPLE 5 The Kelvin scale is an identification or description of each temperature value by a real value.
The temperature value that is the triple point of water is identified or described by the real value 273.16, with respect to the Kelvin scale.
the description of a property distribution by a mathematical function;
NOTE 1 The description of a property distribution relies upon:
the description of the relationship between two parameterisations by a mathematical function;
EXAMPLE 6 The top surface of part XYZ_123 is parameterised by the unit square with corners (0,0), (1,0), (0,1) and 1,1). This parameterisation is used for a B-spline description of the surface shape. The top surface of part XYZ_123 is also parameterised by 'my finite element mesh'. This parameterisation is used to describe the variation of pressure over the surface. There is a mathematical function over the finite element mesh that gives the point in the unit square corresponding to each point in the mesh.
the description of the relationship between two scales by a mathematical function.
EXAMPLE 7 Celsius and Fahrenheit are two different temperature scales. The two scales are related by the mathematical function that is:
f(x): 100/180(x-32)
The following are outside the scope of this part of ISO 10303:
the definition of the domain and range of a property distribution;
NOTE 2 The definition of the domain and range for a property distribution specify what it is. This part of ISO 10303 is solely concerned with its numeric representation.
the definition of a mathematical function.
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