Foreword

ISO/PDTS 10303-1095 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.

Introduction

A mesh is a division of a continuous region into a finite number of cells, each of which has 1, 2 ,3 or higher dimension. The cells can be connected so that a point on one cell boundary is also on the boundary of one or more other cells.

NOTE - From a mesh, it is possible to derive a mathematical space that is a product of:

• an integer tuple space which identifies the cells; and

  For an unstructured mesh, this is usually an integer interval, such as [1, n]. For a structure mesh, this can be an integer pair (i, j) or an integer triple (i, j, k) according to the dimension of the mesh.

• a real tuple space which identifies a point within a cell.

  This can be a single real (x), a real pair (x,h) or a real triple (x,h,z) according to the dimension of the cell.

There is a mapping from each point within the meshed region to this mathematical space. The mapping is not a function, because some points in the meshed region map to more than one value within the mathematical space.

A mesh can be specified for a continuum of positions within a product, a continuum of states within an activity, or a 4D continum of positions for states. A variation of a property with respect to position within a product,or state within an activity, or both, can be described by a mathematical function defined with respect to a mesh.

A mesh is a class that indicates the nature of the sub-divisions within a continuous region.

Industrial automation systems and integration —
Product data representation and exchange —
Part 1095: Application module: Mesh

1 Scope

This application module defines the basic topological concepts of:

• vertex - a 0 dimension topological object;
• region - a continuum of 1 or higher dimension; and
• mesh - a region that is subdivided into cells.

The following are within the scope of this application module:

• the relationship between a topological object and a physical space that has the topology;
• the relationship between two regions that indicates one overlaps the other;
• the relationship between one mesh and another that indicates one is part of the other;
• a Cartesian product of an n dimensional mesh and a 1 dimensional mesh to define an n+1 dimensional mesh.

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

• the nature of a physical object that has the topology;

  NOTE - Physical space is defined in the product feature space module and the activity or state space module.

• the interpolation functions that are used within a cell of the mesh to describe a property distribution with respect to a mesh;

  NOTE - A mathematical function with respect to a mesh is defined in the mesh function module.

• a finite element model that uses the mesh;
• an unstructured or structured definition of the mesh.

  NOTE - A structured mesh is defined in the structured mesh module. An unstructured mesh is defined in the unstructured mesh module.