Geometric and Computational Aspects of Injection Molding

In the manufacturing industry, finding an orientation for a mold that eliminates surface defects and insures a complete fill after the injection process is an important and difficult problem which has not previously been investigated formally. To date, only heuristic solutions have been proposed. We initiate the study of the geometrical and computational aspects of the injection molding process and present a linear time algorithm that solves this problem in two dimensions. We also characterize the object shapes (modeled as simple polygons) that can be 1-filled and relate fillability to known classes of polygons.