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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.

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