In this paper we will show how to model nonoverlap as well as uniform and nonuniform boundary-distance constraints between poly-Bézier shapes using an analytical computational-geometry library. We then use this capability to develop, implement and analyze analytical-optimization solutions to minimum-area rectangular-boundary packing-problems as well as minimum-area one- and two-dimensional puzzle-piece packing-problems. In the process, we will demonstrate the ease and efficiency with which analytical-optimization solutions to complex packing-problems can be formulated, implemented, solved, and analyzed using these models.
MonarchIP P.O. Box 202767 Austin, Texas 78720 December 2021