Fig. 13.    Possible parting directions for one surfaces set and the pocket.

corresponding parting direction, the fragment f t is rearranged to the same mold piece region as the fragment f e.

As shown in Fig. 14, the fragment f e is obscured by other surfaces when viewed from infinity along direction −d3 . Thus, it is an exact fragment that only belongs to the mold piece associated with parting direction d5 . Conversely, f t is a tentative fragment that is visible in both directions −d3 and −d5 ; hence, it can belong to either mold pieces associated with d3 or d5 . However, the mold piece containing f e will pass through f t if it is withdrawn along direction d5 . Therefore, f t is rearranged into the same region as f e. To check whether a tentative fragment f t is passed  through  by the mold piece of the exact fragment f e, we create extrusion surfaces from edges of f e along the parting direction. If the interior

its accessibility to the surfaces of each set Si  must be analyzed. If

of f t

intersects with the extrusion surfaces, f t

e

is considered to be

all surfaces of Si are accessible by the APD, the surfaces of Si are grouped with the surfaces of the undercut feature to create a new surface set associated with the APD. This process ensures that the

passed through by the mold piece of f   .

Criterion 2.  When a tentative fragment f t

e

is adjacent to  several

number of mold pieces is reduced to a minimum.

exact  fragments f

of several mold-piece regions, the   tentative

4.4. Formation of regions for mold pieces

fragment is rearranged into the mold-piece region having the most

exact fragments adjacent to f t .

As shown in Fig. 15, fragments f e  and f e  are exact  fragments

1 2

The regions for mold pieces are determined using all visible-

moldable surfaces of each set Si associated with direction di. These

of the mold-piece region associated with parting direction d5 . Fragment  f t e

regions are groups of adjacent surfaces connected together to form f e

1    is  a  tentative  fragment  adjacent  to  both  f1     and

a united region. In the proposed algorithm, a region of  a mold piece is called ‘mold-piece region’, and is denoted by Ri. Inpidual

2 . Moreover, there are no exact fragments of other mold-piece regions adjacent to f t . Thus, f t  is rearranged into the same mold-

1 1

piece region as f e and f e.

1 2

visible-moldable surfaces and surface regions pided from dual

moldable surfaces or pided from partially obscured surfaces are generally called ‘fragments’. In reality, a fragment of surface sets Si may either belong to exactly one mold-piece region associated with one parting direction di (in which case it is an ‘exact fragment’,

Criterion 3. A tentative fragment f t is rearranged into the mold- piece region associated with the parting direction along which the withdraw distance of f t   is minimal.

t

denoted by f e), or to several mold-piece regions associated  with

The withdraw distance of a tentative fragment f

is measured by

t

several parting directions (in which case it is a ‘tentative fragment’, denoted by f t ). Rearrangement of tentative fragments in surface sets Si into appropriate regions is the most important process in the formation of mold-piece regions. Three criteria are proposed for this work.