In the manufacturing industry, finding an orientation for a mould that eliminates surface defects and ensures a complete fill after the termination of the gravity casting process is an important and difficult problem which has not previously been investigated formally. The paper initiates the study of the gravity casting process from a geometric perspective and presents an optimal θ(n log n) time algorithm that solves this problem in 2D given an object of size n. The paper also characterizes the object shapes (modelled as simple polygons) that can be 1-filled and relate fillability to well known classes of polygons. For certain classes of objects, an optimal direction of fillability can be determined in linear time.

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Keywords algorithms, computational geometry, gravity casting
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Journal CAD Computer Aided Design
Bose, P, & Toussaint, G. (Godfried). (1995). Geometric and computational aspects of gravity casting. CAD Computer Aided Design, 27(6), 455–464. doi:10.1016/0010-4485(95)00018-M