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    recognition of undercut features, determination of parting
    direction, parting lines and surfaces, generation of side
    core and cavity, etc. Different from the volume-based
    approach mentioned above, undercut features are recog-
    nized based on the geometric and topological entities of
    the B-rep model [5, 6]. A surface in which there are
    features attached to is called target surface and according
    to the edge convexity and loop type on the target surface
    different types of undercut features are further identified.
    The withdrawal direction of the undercut features is
    based on V-Map computation. In their work [17, 18]
    the visibility computation of some elementary surfaces
    such as plane or cylinder/cone can get satisfactory result,
    butthewaytheydealwithfreeformsurfacemaylack
    accuracy. Furthermore, Ye et al. [7, 8] proposed a hybrid
    method for recognition of undercut features from molded
    parts with planar, quadric, and freeform surfaces based on
    the extended attributed face-edge graphs. But this method
    is based on a known parting direction and both cavity and
    core faces of the molded part have been identified. Such
    assumptions are usually unreasonable to the procedure of
    the injection mold design. In the above two methods the
    geometric and topological entities of the B-rep model are
    directly used for feature recognition. It is assumed that
    faces are pided across regions of sharp curvature by
    edges. If a single freeform face describes an entire part or
    region with protrusions and depressions without being
    pided along regions of major curvature changes, these
    methods may fail to recognize the DP feature on it.
    Recently, Chakraborty and Reddy [19]proposeda
    method to determine the best pair of parting directions of
    the molded part by considering three major factors. To
    handle the part with freeform surface the part model should
    be tessellated in advance. Non-convex regions which form
    the probable undercut regions are computed facet by facet.
    Then non-convex facets are grouped into regions by their
    connectivity. The accuracy of the solution depends on the
    density of the mesh while the computation complexity is
    increased with the number of the facets.
    It can be summarized from the literature review that
    most works have difficulty in recognizing undercuts from
    solid model with freeform surfaces especially the surfaces
    having DPs without being pided along regions of major
    curvature changes. To solve this problem in this paper the
    curvature region representation (CR-rep) is first constructed
    on the basis of curvature properties of the entities in B-rep
    model. During this process a global curvature analysis
    approach is used to segment freeform surface into mean-
    ingful regions. Then both isolated and interacting DP
    feature with freeform surfaces can be identified from the
    CR-rep. Among the recognized DP feature the depressions
    and the concave transitions between protrusions are
    potential undercuts (PUs). Geometric reasoning and V-
    Map computation of freeform surfaces are employed to
    derive the possible withdrawal directions of the potential
    undercut. Special types of intersecting undercuts which can
    be split and resides in both halves of the die are also
    checked by computing the visibility of undercuts regions
    along a pair of opposite direction. Finally, the identified
    potential undercuts with their possible withdrawal direc-
    tions can allow for optimal parting direction search and set
    the base to moldability analysis during the design stage.
    2 Curvature region representation of parts
    with freeform surfaces
    Boundary representation (B-rep) is the most popular
    scheme used to represent a 3D solid object. But the
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