Download Geometry. Cliffs Quick Review by Edward Kohn PDF
By Edward Kohn
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Of course, we have to answer also a (vertical line segment/horizontal line segment) stabbing query. This is done by a simple rotation of 90 degrees. A subset of horizontal line segments of S is stabbed by the line passing through the vertical line segment s. 10. If s is given by (x, yl) and (x, yu), the corresponding box is represented by [−∞, x] × [yl, yu]. 10: A rectangular range query by an infinite box grounded in s will answer the windowing query in the third case. Now, we have a stabbing query and a range query, and we adapt an interval tree accordingly.
Note that a convex cell (which is possibly unbounded) is associated with each node of the BSP. 1, the convex region of one of the leaves has been highlighted as an example. With BSPs, we have much more freedom to place the splitting planes than with kd-trees. However, this also makes that decision much harder (as almost always in life). If our input is a set of polygons, then a very common approach is to choose one of the polygons from the input set and use this as the splitting plane. 2). 2: Left: an auto-partition.
1. Rendering without a Z-Buffer BSP trees were introduced to computer graphics in [Fuchs et al. 80]. At the time, hidden-surface removal was still a major obstacle to interactive computer graphics, because a Z-buffer was just too costly in terms of memory. [1] A simple algorithm to render a set of polygons with correct hidden-surface removal, and without a Z-buffer, is the painter’s algorithm: render the scene from back to front as seen from the current viewpoint. Front polygons will just over-write the contents of the frame buffer, thus effectively hiding the polygons in the back.