Finding All Undercut-Free Parting Directions for Extrusions

For molding and casting processes, geometries that have undercut-free parting directions (UFPDs) are preferred for manufacturing. Identifying all UFPDs for arbitrary geometries at interactive speeds remains an open problem, however; for polyhedral parts with

n

vertices, existing algorithms take at least

O

(

n

4

) time. In this paper, we introduce a new algorithm to calculate all the UFPDs for extrusions, an important class of geometry for manufacturing in its own right and a basic geometric building block in solid modeling systems. The algorithm is based on analyzing the 2D generator profile for the extrusion, building on our previous results for 2D undercut analysis of polygons. The running time is

O

(

n

2

log

n

) to find the exact set of UFPDs or

O

(

n

) to find a slightly conservative superset of the UFPDs, where

n

is the geometric complexity of the 2D generator profile. Using this approach, the set of possible UFPDs for a part containing multiple extruded features can be reduced based upon an analysis of each such feature, efficiently identifying many parts that have no UFPDs and reducing the search time for complete algorithms that find all UFPDs.