Table of Contents

Foreword
Introduction
1 Scope
2 Normative references
3 Terms, definitions, abbreviated terms and symbols
  3.1 Terms defined in ISO 15926-1
  3.2 Terms defined in ISO 10303-42
  3.3 Other terms and definitions
  3.4 Abbreviated terms
  3.5 Symbols
4 Geometric and topological reference data
  4.1 Introduction to geometric and topological reference data
      4.1.1 Data for each item
      4.1.2 Interface with ISO 15926-2
      4.1.3 Organization of the reference data
  4.2 Some mathematical basics
      4.2.1 General
      4.2.2 Classes of structure
      4.2.3 Members of structure
      4.2.4 Classes of mapping
      4.2.5 Structures of basic mathematical objects
      4.2.6 Relationships between basic mathematical objects
      4.2.7 Properties of basic mathematical objects
  4.3 Topology
      4.3.1 General
      4.3.2 Classes of topological object
      4.3.3 Structures of topological objects
      4.3.4 Relationships with topological objects
      4.3.5 Properties of topological objects
  4.4 Geometry basics
      4.4.1 General
      4.4.2 Derived concepts
      4.4.3 Primary identified concepts
      4.4.4 Coordinate system
      4.4.5 Direction
      4.4.6 Transformation
      4.4.7 Founding
      4.4.8 Structures of basic geometric objects
      4.4.9 Relationships between basic geometric objects
      4.4.10 Basic geometric properties
      4.4.11 Physical space and time
  4.5 Curve
      4.5.1 General
      4.5.2 Derived concepts
      4.5.3 Classes_of_curve
      4.5.4 Curve parameterization
      4.5.5 Relationships with curves
      4.5.6 Structures of curves
      4.5.7 Curve properties
  4.6 Surface
      4.6.1 General
      4.6.2 Derived concepts
      4.6.3 Classes_of_surface
      4.6.4 Surface parameterization
      4.6.5 Relationships with surfaces
      4.6.6 Structures of surfaces
      4.6.7 Surface properties
  4.7 Solid
      4.7.1 General
      4.7.2 Derived concepts
      4.7.3 Classes_of_solid
      4.7.4 Solid parameterization
      4.7.5 Relationships with solids
      4.7.6 Solid properties
  4.8 Mesh topology
      4.8.1 General
      4.8.2 Mesh and its subclasses
      4.8.3 Canonically parameterized topological primitive
             and its subclasses
      4.8.4 Mesh derived parameterization
      4.8.5 Relationships with meshes
      4.8.6 Structures of meshes
      4.8.7 Mesh properties
  4.9 Mesh function
      4.9.1 General
      4.9.2 Functions over mesh derived domains
5 Implementation with ISO 15926-2
  5.1 Structure and mapping in ISO 15926-2
  5.2 Physical space
  5.3 Coordinate system
  5.4 Physical object and space
Annex A (normative) Information object registration
Annex B (normative) Document URN
Annex C (normative) Reference data relationships
  C.1 Spreadsheet files
  C.2 Spreadsheet formats
Annex D (informative) Reference data as EXPRESS and OWL
Annex E (informative) CAD examples
  E.1 Boundary representation solid: Half cylinder with void
  E.2 Boundary representation solid: Circular flat washer
  E.3 Boundary representation solid: Circular domed washer
Annex F (informative) Approaches to meshes and distributions
  F.1 General
  F.2 A mesh of space with matter at rest
  F.3 A mesh of matter at rest
  F.4 Manifold of temporal parts
  F.5 A mesh of space which deforms
  F.6 Physical function and representation function
  F.7 Table of control values
Annex G (informative) Mesh and distribution examples
  G.1 General
  G.2 Geometry of the example
  G.3 Mesh of space - CAD topology - Linear spatial interpolation
  G.4 Mesh of space - FEA topology - Linear spatial interpolation
  G.5 Mesh of matter - FEA topology - Linear spatial interpolation
  G.6 Interpolation of quantity or number
  G.7 Thickness variation
  G.8 Mesh of space - Linear thickness interpolation
  G.9 Mesh of matter - Linear thickness interpolation
  Bibliography
Index

Abstract

Describes geometric and topological concepts, enabling the recording of geometric and topological data using ISO 15926-2 and in a way consistent with first order logic.

General Product Information

Published
Document Type	Standard
Status	Current
Publisher	International Organization for Standardization
Pages
ISBN
Committee	TC 184