Fig. 2.   Surface classification.

Outline, Outer edges and Outer edge loop

As shown in Fig. 3, when a parting direction Pd is given, the edges of the molding can be projected onto a plane perpendicular to Pd. The largest edge-loop is formed, as shown in Fig. 3(b). Extrusion of the largest edge-loop of the molding in Pd direction will intersect with the molding itself, as shown in Fig. 3(c). The

outline is thus defined as the intersection of the extruded surfaces with the molding. So does −Pd in Fig. 3(d). Partially visible edges are those edges which are invisible from −Pd or Pd and visible from

the opposite direction. The outer edges are defined as the edges that lie in the intersection of Outline 1 and Outline 2 along the pair of parting direction. This intersection will exclude any partially visible edges from the set of outer edges. The outer edge loop is the

largest loop in Pd and −Pd, as shown in Fig. 3(e) to (f).

Visibility

For the normal vector at any arbitrary point on the target surface and a series of parallel rays from infinity to the target surface, the surface is considered completely visible if the multiplication of the normal vector and the ray vector is smaller than zero. The surface will be considered as partially visible if the above result is smaller than zero and there is at least one point on the surface whose normal vector multiplying the ray vector is equal to zero [30].

Based on this definition, the principle for judging the visibility of a geometrical entity is to check if the target entity is ‘‘blocked’’ by other geometrical entities from the view of observer. The method to determine the visibility of an entity is to cast a ray from the observation point of the viewer to the target geometrical   entity. If the ray passes through any other entities before it reaches the

target geometrical entity, the visibility of the target geometrical entity will be defined as invisible. In Fig. 4, Point A is defined as an observation point and Point B is a vertex of Facet 2. The half-infinite ray from Point A to Point B is intersected by Facet 1. Therefore, Facet 2 is considered to be invisible from Point A, as it is obscured by Facet 1.

2.2. Internal pin design  framework

Fig. 5 shows a general procedure for internal pin design. The solid model of a molding and the parting directions are first given. The dimensions of the main mold blocks (core and cavity blocks) also need to be input. Upon the classification of the outer edges, all the surfaces of the model are categorized into three categories. The ID and the visibility of the geometrical entities are then determined and the core and cavity are generated based on the relationship of these entities. The detection of the deep inner undercut is conducted to find out if there is any inaccessible region in the main mold blocks. If yes, a molding redesign suggestion will be provided. Finally, the design of the internal pins is conducted.

2.3. Problem statement

2.3.1. Internal pin generation

For the given 3D solid model of a molding and the parting directions, the objective of this research is to generate the internal pins for molding of inner undercuts. It is thus necessary to identify all the undercuts and generate the main core and cavity. On the other hand, the molding needs to be withdrawn from these components without obscuring or being obscured.

(a) 3D model of the molding piece.

(b) The largest projection boundary.