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http://sinews.siam.org/current-issue-content/october-2008/semi-infinite-optimization-meets-industry-a-deterministic-approach-to-gemstone-cutting/
It is pretty heavy, but interesting for some - here is the intro
by Karl-Heinz Küfer, Oliver Stein, and Anton Winterfeld
It is pretty heavy, but interesting for some - here is the intro
by Karl-Heinz Küfer, Oliver Stein, and Anton Winterfeld
For five centuries artisans have been cutting faceted gemstones, creating jewels that sparkle with internally reflected light, showing off the “fire†of the stones. Working with stones that are transparent or translucent, a cutter makes the most of the color of a stone through careful choice of the angles between facets, depending on the refractive index of the material. At the same time, gem producers have their own goal: to use as much of the volume of the rough stones as possible. By applying modern methods of semi-infinite optimization to this problem, we were able to improve the volume yield significantly while guaranteeing optimal optical properties of the faceted gemstones.