accessibility cones for each face on a polyhedral object and the set of directions from which they are accessed [11].

The parting line can be generated upon the determination of the parting direction. Wong et al. proposed an algorithm which adopts an uneven slicing on the molding to locate the parting line and parting surface [12]. Weinstein et al. presented a methodology using the multi-objective function criteria [13]. Several mold design factors, including draw depth and the number of undercuts, are considered. The draw direction range and the parting line location are then identified. Furthermore, Fu et al. proposed an approach to generating the parting line [14]. By collecting all the external edge-loops in the surfaces molded by the main core and cavity, the maximum external-loop in the core-molded surfaces is extracted as the potential parting lines. Based on different flatness criteria, Majhi et al. presented an algorithm to compute an undercut-free parting line for a convex polyhedron [15]. Surface moldability under different parting line locations is compared and the best parting line is determined according to this criterion. To create the parting surfaces, Ravi first proposed an approach by using the nine criteria to form nine factors [16]. These factors are considered and synthesized to identify the best parting surface. In addition, Hui and Tan developed a methodology to define the optimal parting surface [17]. When this optimal parting  surface is identified and located, the number of side core should be minimized. By tackling the limitations of the approaches for processing conventional parting surface generation, Li proposed an approach for patching up the parting surface segments which cannot be generated by extruding the parting lines to the external boundaries of the core or cavity block based on surface subpision [18,19]. The parting surfaces with more complex parting lines can be generated by using the subpision and extrusion algorithms. Ahn et al. presented an algorithm focusing on the separating condition of the molding piece and mold [20]. The issue of the optimal parting direction and parting direction selection are discussed and addressed. Recently, a parting line algorithm for the use of complex meshes has been presented by Li et al. [21]. A smooth parting line consisting of a large amount of triangles, approximately vertical to the parting direction are computed in this algorithm.

In addition, more attention has also been paid to side core generation. By employing Euler operations, Shin et al. first presented a method to generate the side core after identification of all the interference surfaces from the main mold [22]. The calculation of the normal vectors at the sample points is made for interference surface determination. In Dhaliwal’s feature-based approach for dealing with multi-piece molds [23], the desired gross mold for molding is generated and decomposed into sub- components to ensure the accessibility of the molding. This algorithm is further developed by Huang [24]. In his work, the molding is extracted and projected onto a unit sphere. After partition and reorientation for mold accessibility, the suitable multi-piece molds are generated and separated by the partition plane. Based on EAFEG, Ye developed a new method for automatic side core design [25]. In his research, the undercut features are recognized through searching the cut-sets of subgraph, Boolean operations are then used for side core generation. Based on the global accessibility analysis result, Priyadarshi and Gupta developed an algorithm  to  find  and  locate  the  parting  line and parting direction [26]. A region based method focusing on automatic design of the mold was established by Chen and Rosen [27]. The smallest number of partitions of surface is found by minimizing the number of mold piece. Later, they proposed another approach to generating two-piece and multi-piece molds by investigating glue operations and relations with the parting surface [28]. Furthermore, Banerjee et al. proposed an approach to  recognizing  undercut  features  by  computing  the candidate