JonLeonard-FrontToBackBSP - p olygons F ront-to-Back in Sk...

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[ polygons in Sk, j I Front-to-Back Display of BSP Trees Dan Gordon and Shuhong Chen Texas A&M University Combining polygon scan-conversion with a dynamic screen data structure led to a front-to-back approach for displaying BSP trees. This technique improves significantly over the back-to-front method. W c developed a technique to display binary space partitioning (BSP) trees that is faster than the usual back-to-front display method. Our tech- nique-a front-to-back approach-provides significant speed-up in the dis- play time of polygonal scents that depend on BSP trees. especially in cases where the number of polygons is large. BSP trees ’ arc one of the most useful data structures for polygonal scenes. The structure of BSP trees embodies the geometrical priorities of a set of polygons in 3D space. Independent of any viewpoint, this structure (once constructed) enables fast display with hidden surface removal. It proves especially useful in applications with a fixed environment where we need to generate many images from different viewpoints-in flight simulators, for example. Once we have determined a viewpoint. we can display the scene by tra- versing the BSP tree in back-to-tront order and scan-converting each poly- gon. Since polygons closer to the viewpoint will be displayed later than further ones, they will overwrite the further ones. producing correct hidden surface removal.
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rlgure 1. lnvuonment split by plane ofpk. In voxel and octree environments, researchers have had some success with display algorithms that traverse the scene in front- to-back order (instead of back-to-front).2 ’3 In principle, we can convert any back-to-front display method to a front-to-back one by a simple additional check: Before a pixel is set, it is checked to verify that it had not already been set. However, this simple modification has no advantage. Success lies in the use of certain data structures to represent the image during process- ing. These structures enable the algorithms to eliminate from consideration large chunks of pixels that have already been set. [ Polygons in Sk,i I [ Polygons in S;,,] 1 Polygon Pk 1 / \ [ Polygon Pjl [ Polygons in S\] Figure 3. BSP tree after the second split of polygons. 80 In our method for displaying BSP trees in front-to-back order, we use the data structure introduced elsewhere ’ for front-to-back display of voxel-based objects. This data struc- ture combines with polygon scan-conversion for efficient dis- play of polygonal scenes. In principle, any priority-based algorithm (for example, the depth-sort algorithm4, ‘ ) that scan- converts polygons one at a time can be modified in this manner. Back-to-front display A BSP tree, which is a data structure for polygonal objects, enables easy traversal in any order relative to an observer. ’ Suppose the 3D environment is defined by a set of polygons P = bl,P2, . . ., p,). We choose an arbitrary polygon Pk from this set to serve as the root of the tree. The plane defined by pk partitions the rest of the three-space into two half-spaces, as shown in Figure 1. Let Sk and Sk ’ denote the two half-spaces,
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JonLeonard-FrontToBackBSP - p olygons F ront-to-Back in Sk...

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