Foreword

ISO/PDTS 10303-1096 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 inter-preted 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.

Introduction

A property can vary with respect to position within a product, state within an activity, or both. In many cases a mathematical description of the property variation is obtained by an analysis or test method that:

• divides the product up into a mesh of connected regions; and
• divides the activity up into a sequence (a 1 dimensional mesh) of connected steps.

A mesh function is a convenient mathematical function that:

• has its control values defined within respect to the mesh; and
• carries out interpolation or extrapolation for each cell independently.

EXAMPLE - The positions within 'widget type XYZ' are divided into a mesh of connected hexahedral cells. The variation of temperature within 'widget type XYZ' for the state 'widget type XYZ running' is described by a mesh function that is defined by control values at the corners of the cells.

The mesh function interpolates within each cell independently. The control values that are relevant to each cell are determined by the topology of the mesh.

EXAMPLE - The positions within 'widget type XYZ' are divided into a mesh of connected hexahedral cells. The times within 'widget type XYZ start up' are divided into a seqence of steps.

The 4D space of positions within 'widget type XYZ' for times within activity 'widget type XYZ start up' is divided into a mesh of 4D hyperbrick cells. This mesh is the Cartesian product of:

• the spatial mesh of points within 'widget type XYZ'; and
• the temporal mesh of times within 'widget type XYZ start-up'.

The variation of temperature with respect to space and time is described by a mesh function that has control values at the corners of the 4D hyperbrick cells.

Industrial automation systems and integration —
Product data representation and exchange —
Part 1096: Application module: Mesh function

1 Scope

The mesh function application module is concerned with mathematical functions that:

• have their control values defined within respect to a mesh; and
• carry out interpolation or extrapolation for each cell of the mesh independently.

The following are within the scope of this application module:

• the specification of the mesh for a mesh function;

• the specification of the control values for a mesh function;

• the specificiation of the interpolation or extrapolation method used by the function within each cell of the mesh.

The following are not within the scope of this application module:

• the definition of a property variation that is described by a mesh function;

  NOTE - The relationship between a mathematical function and a property distribution which it describes is defined in the distribution mapping module.

• the definition of a mesh;

  NOTE - A mesh is defined in the mesh module.

• the definition of control values.

  NOTE - A table or array of control values is defined in the tabular function module.