How does BOG work?BOG is based on a gridsearch optimization technique. The process of gem design optimization can be likened to mountain climbing (see figure below). Imagine a world in which one grid direction (i.e. eastwest) corresponds to the current pavillion angle, and the other (northsouth) corresponds to the current crown angle. The altitude at any point is a measure of how good the gem is with that particular combination of pavillion and crown angles. BOG calculates a merit function to determine this altitude (gem quality). Finding the best gem then becomes a problem of finding the highest peak within the area defined by an acceptable range of pavillion and crown angles  essentially within the edges of the world below. How do we go about finding the highest peak? Finding the maxima (and minima) of surfaces is a very important problem in all areas of science and engineering, and there are a large number of peakfinding algorithms. BOG uses the simplest and most robust of these, a socalled grid search. Imagine you are a mountaineer dropped down somewhere on the world below with the task of finding the peak. To do a grid search, you would begin by taking a step in one direction, say east. If the terrain goes up, you take another step. If the very first step is downhill, you reverse direction and start looking the other way. Having selected a search direction, you carry on taking steps until the ground stops getting higher. At this point, things go downhill to both the east and west. The obvious strategy is to begin exploring northsouth in the same way. When that is no longer productive, you switch back to searching eastwest. And so on. The grid search algorithm within BOG has a few additional bells and whistles. For example, before switching to the other grid direction, it uses the altitude of the last three steps to make a more accurate estimate of the highest point before setting off at right angles. It also continuously adjusts the size of the steps, based on how long it took to exhaust a certain grid direction.



Documentation maintained by Tom Herbst. Last modified 17Sep2002