Polygonal object dilation and packing in vector space for die-cutting machine tools

Packing polygonal objects to be cut in fiber or leather densely for efficient use of material is important to automatic die-cutting machine tools. Prior to computing a tight pack of objects in a given area of material, proper gaps among packed objects should be firstly reserved to prevent over-cutting on the edges of neighboring objects by a die. To maintain object gaps for packing, we propose a new computational approach of polygonal object dilation in vector space to dilate polygonal objects to preset scales accurately. The proposed approach is new and novel in that it can be applied to expand both convex and concave polygonal objects by a constant distance to original object boundaries, and derives similar results to image object dilations but with higher computational accuracies in vector space. Such a property, which is not held by vector object enlargement, fits the need of deriving required object gaps for packing. Combining the proposed object dilation method with practical object packing heuristics, accurate and dense object packing results with proper object gap reservations can thus be obtained for various die shapes.