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Show 72 can be divided into a two phase operation to conserve list storage space. Firt the patches ere sorted on their maximum Y Bezier control point. As long as the scan plane is above this Y value no part of the patch can be visible. When the scan plane drops below the Y value of the top patch in this "standby" list the patch becomes active. Bivariate optimization is performed to find the ctual local maxima of the patch and these are put in a Y sorted "active peak" list. Then new iteration points- are created by pulling elements off the top of this list. defined as rational bicubic functions. This limits the The actual local maxima of a patch are found by choosing an initial guess at the u,v and applying the non-linear optimization process of Chapter 4. Because there may be several local maxima per patch, several initial guesses must be tried and any duplicate maxima must be eliminated. The patches used in this thesis were all total number of local maxima to five. The maximum finding process uses, as its initial guesses, the four corner points of the patch and the center point. This has worked well in practice and, for those objects encountered so far, has not missed any local maxima. Unfortunately, without some higher order knowledge of the form of the functions used, there is no known method for guaranteeing that all the local maxima have been found. |
