Multi-criteria geometric optimization problems in Layered Manufacturing
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Multi-criteria geometric optimization problems in Layered Manufacturing
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1997
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Abstract
In Layered Manufacturing, the choice of the build direction for the model influences several
design criteria, including the number of layers, the volume and contact-area of the support
structures, and the surface finish. These, in turn, impact the throughput and cost of the
process. In this paper, efficient geometric algorithms are given to reconcile two or more of
these criteria simultaneously, under three formulations of multi-criteria optimization: Finding a
build direction which (i) optimizes the criteria sequentially, (ii) optimizes their weighted sum, or
(iii) allows the criteria to meet designer-prescribed thresholds. While the algorithms involving
"support volume" or "contact area" apply only to convex models, the solutions for "surface
finish" and "number of layers" are applicable to any polyhedral model. Some of the latter
algorithms have also been implemented and tested on real-world models obtained from industry.
The geometric techniques used include construction and searching of certain arrangements on
the unit-sphere, 3-dimensional convex hulls, Voronoi diagrams, point location, and hierarchical
representations. Additionally, solutions are also provided, for the first time, for the constrained
versions of two fundamental geometric problems, namely polyhedron width and largest empty
disk on the unit-sphere.
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Majhi, Jayanth; Janardan, Ravi; Smid, Michiel; Schwerdt, Jorg. (1997). Multi-criteria geometric optimization problems in Layered Manufacturing. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/215340.
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