Determination of Pull Directions for a Freeform Surface Using Cascade Filters of Visibility Maps

Determination of pull directions for a freeform surface is a challenging problem because the number of normal vectors is unlimited for such type of surfaces. Consequently, researchers generally convert a freeform surface into planar faces to limit the number of normal vectors. This paper presents an approach using cascade filters of visibility maps to determine feasible pull directions for freeform surfaces such that the required accuracy is retained. Pull direction candidates are first generated using a modified regular placement method. Normal vectors are then extracted by a sampling box, and the number of normal vectors is optimized through a numerical approach. Significant normal vectors are then selected by a modified Barycentric method. A cascade filter of the visibility map is built using these vectors and used for the selection of feasible pull directions. A minimum number of sliders and cavities in molding are finally achieved using a clustering algorithm based on maximum intersections of visibility maps. A real-life part is created using commercial CAD software for performance evaluation of the proposed algorithm.