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    1. It should be possible to have high-level objects ready to
    use while mould designers think on the level of realworld
    objects.
    2. The representation of assemblies should encapsulate operational
    functions to automate routine processes such as
    pocketing and interference checks.
    To meet these requirements, a feature-based and object-oriented
    hierarchical model is proposed to represent injection moulds.
    An assembly may be pided into subassemblies, which in turn
    consists of subassemblies and/or inpidual components. Thus,
    a hierarchical model is most appropriate for representing the
    structural relations between components. A hierarchy implies
    a definite assembly sequence. In addition, a hierarchical model
    can provide an explicit representation of the dependency of
    the position of one part on another.
    Feature-based design [10] allows designers to work at a
    somewhat higher level of abstraction than that possible with
    the direct use of solid modellers. Geometric features are
    instanced, sized, and located quickly by the user by specifying
    a minimum set of parameters, while the feature modeller works
    out the details. Also, it is easy to make design changes because
    of the associativities between geometric entities maintained in
    the data structure of feature modellers. Without features,
    designers have to be concerned with all the details of geometric
    construction procedures required by solid modellers, and design
    changes have to be strictly specified for every entity affected
    by the change. Moreover, the feature-based representation will
    provide high-level assembly objects for designers to use. For
    example, while mould designers think on the level of a realworld
    object, e.g. a counterbore hole, a feature object of a
    counterbore hole will be ready in the computer for use.
    Object-oriented modelling [11,12] is a new way of thinking
    about problems using models organised around real-world concepts.
    The fundamental entity is the object, which combines
    both data structures and behaviour in a single entity. Objectoriented
    models are useful for understanding problems and
    designing programs and databases. In addition, the objectoriented
        representation of assemblies makes it easy for a
    “child” object to inherit information from its “parent”.
    Figure 2 shows the feature-based and object-oriented hierarchical
    representation of an injection mould. The representation
    is a hierarchical structure at multiple levels of abstraction,
    from low-level geometric entities (form feature) to high-level
    subassemblies. The items enclosed in the boxes represent
    “assembly objects” (SUBFAs, PARTs and FFs); the solid lines
    represent “part-of” relation; and the dashed lines represent
    other relationships. Subassembly (SUBFA) consists of parts
    (PARTs). A part can be thought of as an “assembly” of form
    features (FFs). The representation combines the strengths of a
    feature-based geometric model with those of object-oriented
    models. It not only contains the “part-of” relations between
    the parent object and the child object, but also includes a
    richer set of structural relations and a group of operational
    functions for assembly objects. In Section 3.1, there is further
    discussion on the definition of an assembly object, and detailed
    relations between assembly objects are presented in Section 3.2.
      3.1 Definition of Assembly Objects
    In our work, an assembly object, O, is defined as a unique,
    identifiable entity in the following form:
    O = (Oid, A, M, R) (1)
    Where:
    Oid is a unique identifier of an assembly object (O).
    A is a set of three-tuples, (t, a, v). Each a is called an
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