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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