| OCR Text |
Show 22 tables and the additional points required by the Bezier representation. 2.6.6 One idea that did not work As mentioned previously, the leaf bounding boxes contain starting values for the Newton iteration. During the implementation the following idea was tested : Since there is a reasonable chance that the next ray to strike the surface will strike at a point near where the previous ray struck, the parametric values ( u, v) from the previous intersection should be cached, and used as the starting guess for the next ray to intersect that particular leaf node. This did result in a significant speed up. The number of r\ewton iterations required was reduced to one or two (instead of two to four) and the overall time was reduced significantly. The technique , however, produced inaccurate results. This was due to the way it caused the starting values for the surface parameters to 'crawl' within the bounding box. For example, consider a single surface fragment within a bounding box as it is struck by the starting ray from the eye (see Figure 2.5 ). Since the ray tracer works in scanline order (bottom to top , left to right) the starting guesses for the fragmen t start at the left and mo\'e right. until the rays no longer intersect the bounding New guess fails on next scanline ~ Figure 2 .. ) . ·Crawling' of starti ~g guess \'alues within a bounding box. |
