3D graphics eBook - Course Materials Repository
3D graphics eBook - Course Materials Repository
3D graphics eBook - Course Materials Repository
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Potentially visible set 112<br />
• Can't be used for completely dynamic scenes.<br />
• The visible set for a region can in some cases be much larger than for a point.<br />
Primary Problem<br />
The primary problem in PVS computation then becomes: For a set of polyhedral regions, for each region compute<br />
the set of polygons that can be visible from anywhere inside the region.<br />
[1] [2]<br />
There are various classifications of PVS algorithms with respect to the type of visibility set they compute.<br />
Conservative algorithms<br />
These overestimate visibility consistently, such that no triangle that is visible may be omitted. The net result is that<br />
no image error is possible, however, it is possible to greatly over-estimate visibility, leading to inefficient rendering<br />
(due to the rendering of invisible geometry). The focus on conservative algorithm research is maximizing occluder<br />
fusion in order to reduce this overestimation. The list of publications on this type of algorithm is extensive - good<br />
surveys on this topic include Cohen-Or et al. [2] and Durand. [3]<br />
Aggressive algorithms<br />
These underestimate visibility consistently, such that no redundant (invisible) polygons exist in the PVS set,<br />
although it may be possible to miss a polygon that is actually visible leading to image errors. The focus on<br />
[4] [5]<br />
aggressive algorithm research is to reduce the potential error.<br />
Approximate algorithms<br />
These can result in both redundancy and image error. [6]<br />
Exact algorithms<br />
These provide optimal visibility sets, where there is no image error and no redundancy. They are, however, complex<br />
to implement and typically run a lot slower than other PVS based visibility algorithms. Teller computed exact<br />
visibility for a scene subdivided into cells and portals [7] (see also portal rendering).<br />
The first general tractable <strong>3D</strong> solutions were presented in 2002 by Nirenstein et al. [1] and Bittner [8] . Haumont et<br />
al. [9] improve on the performance of these techniques significantly. Bittner et al. [10] solve the problem for 2.5D<br />
urban scenes. Although not quite related to PVS computation, the work on the <strong>3D</strong> Visibility Complex and <strong>3D</strong><br />
Visibility Skeleton by Durand [3] provides an excellent theoretical background on analytic visibility.<br />
Visibility in <strong>3D</strong> is inherently a 4-Dimensional problem. To tackle this, solutions are often performed using Plücker<br />
(see Julius Plücker) coordinates, which effectively linearize the problem in a 5D projective space. Ultimately, these<br />
problems are solved with higher dimensional constructive solid geometry.