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are still designing moulds 9 manually, which is timeconsuming and errorprone. The development of a ComputerAided Injection Mould Design System (CAIMDS) has bee the focus of research in both industry and academia. 2. Definition and classification of undercut features In a moulding, concave regions such as local recesses, slots, pockets and holes are potential undercut features。 while convex regions such as cylinders, bosses, cones and spheres can also be undercut features. If the main core and cavity and their inserts cannot mould the undercut features, sidecores or sidecavities or other local tools are required to be incorporated in the mould structure. In Fig. 1, there are three undercut features A, B, C in the moulded part. If the parting direction is selected as shown in the figure, then undercut feature A can be moulded in by the main core, but undercut features B and C cannot be moulded in by the main core, cavity and inserts, and would need sidecores and sidecavities for moulding. Consequently, they are the real undercuts. It is noted that whether A, B or C would bee the real undercut is dependent on the particular parting direction. 3. Undercut feature parameters Undercut feature parameters are undercut feature volume and undercut feature direction. The undercut feature volume can be determined based on the geometric entities of the undercut feature, while the undercut directions can be determined by the visibility map (Vmap) of the undercut feature surfaces. The Vmap of a surface is a notion to describe the surface visibility and is formed by the points on the unit sphere from which the surface is pletely visible from infinity [9]. The surface Vmap is a twin notion of Gauss map, which is introduced by Gauss through mapping the surface normal of a given 10 point in a surface onto a unit sphere to describe the surface property [10]. 5. Inside external undercut features If the edgeloops of the target surface are more than two, there are more than one IEU in the target surface consisting of edgeloop related adjacent surfaces. Fig. 15 shows that IEUs, edgeloops, and edgeloop related adjacent surfaces. In Fig. 15, (a) shows two IEUs, one is a convex and the other is concave IEU, (b) is the edgeloops of undercut features with target surface, and (c) shows the edgeloop related surfaces of which the IEUs are posed. The main procedures to identify the The main procedures to identify the IEU are as follows: (a) Determine the internal and external edgeloops of thetarget surface. (b) Identify the convexity and concavity of internal edgeloops. (c) Extract the edgelooprelated surfaces. If the edgeloop is concave, the mon second adjacent surface of the edgelooprelated surfaces needs to be extracted. The mon second adjacent surfaces are shown in Fig. 15(c). 11 6. Internal undercut features Fig. 16 shows the internal undercut features. There are also two types of internal undercuts, namely inside internal undercut (IIU) and outside internal undercut (OIU). The definitions and criteria of IIU and OIU are similar to those of IEU and OEU. The following rule is used to determine if the undercut feature is an internal or external undercut feature. If the undercut feature is an IU, the rays in the undercut direction and its opposite direction will have more than on。
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