2.1. Related works

Automated processes for mold design have been developed in many publications. Most work focuses on traditional two-piece molds, including the determination of parting direction, undercuts, parting curves, and parting surfaces.  Fu  et  al.  [1] introduced an algorithm related to the determination, classification, and recognition of feature parameters for detecting undercuts. Ismail et al. [2] proposed a method to recognize cylindrical-based features based on an edge-boundary classification technique. Kharderkar et al. [3] described an algorithm to identify and display undercut features by implementing the Gauss map. Building upon these related techniques, Fu et al. [4] proposed an algorithm that determined the optimal parting direction in injection-molded parts by the number of undercut features and their corresponding volumes. Furthermore, Chen et al. [5] posed a method in which three possible parting directions were defined by surface normal vectors of a bounding box. Feasible parting directions were then estimated based on the dexel model and fuzzy decision-making.

In order to determine parting curves and parting surfaces, Fu et al. [6] described a technique employing the maximum ex- ternal edge loops between the core- and cavity-molded surface groups. Chakraborty et al. [7] presented a method to determine the parting curve and parting surface for a two-piece permanent mold based on a combination of the surface area of the undercut, the flatness of the parting surface, and the draw depth. In addi- tion, Wong et al. [8] proposed an uneven slicing approach to find- ing the feasible parting curves of a CAD model. The optimal parting curve was evaluated based on the criteria described by Ravi and Srinivasan [9]. Furthermore, Paramio et al. [10] evaluated the de- moldability of injection-molded parts through the slicing of their CAD models, which could then be used to identify feasible parting curves. For the generation of parting surfaces, Li et al. [11,12] posed an approach by evaluating the extrudability of parting curves; a subpision technique was employed to generate parting surface regions for the portions of the parting curves that were not extrud- able.

Side cores or pins can be generated along with the recognition of undercuts. Banerjee et al. [13] used the retraction space of each undercut surface to identify the shapes of the side cores. The undercut surfaces were grouped into undercut regions according to a discrete set of feasible and non-dominated retractions, after which the geometry of inpidual side cores could be obtained. Fu [14] used the concepts of surface  visibility, demoldability, and moldability to identify the surfaces molded by side cores. Furthermore, Ran and Fu [15] described an algorithm for automatic design of internal pins after identifying the inner undercuts and extracting the related surfaces.

The development of CAD research for mold design has also been connected to manufacturability and manufacturing costs. Bidkar et al. [16] presented a feature recognition method based on the el- emental cubes to assess the critical manufacturability information

of injection-molded parts. Denkena et al. [17] introduced a method in which a CAD-based application of the calculation tool ‘visual form calculator’ was used to generate and analyze CAD models of mold cavities in order to compute tool accessibility and manufac- turing costs.

In the area of multi-piece molding, few articles have been pub- lished. Dhaliwal et al. [18] presented a feature-based approach to automatic design of multi-piece sacrificial molds. In their ap- proach, the desired gross mold shape is decomposed into simpler shapes for manufacturability and assemblability purposes. By the same rationale, Huang et al. [19] described an algorithm for gen- erating multi-piece sacrificial molds with an accessibility driven spatial partitioning scheme. Chen and Rosen [20,21] introduced a region-based method for partitioning parting surfaces into regions and combining them into mold pieces. The basic elements in their approach are concave regions and convex surfaces. A reverse glue operation is then proposed to automate the construction of multi- piece molds based on the generation of parting surfaces. In addi- tion, Priyadarshi et al. [22] described a geometric algorithm for automatic design of multi-piece permanent molds. The mold pieces are constructed based on the results of a global accessibility analysis of the part.