Changeset 282 for trunk


Ignore:
Timestamp:
09/16/05 18:22:17 (19 years ago)
Author:
bittner
Message:
 
Location:
trunk/VUT/doc/SciReport
Files:
2 added
2 edited

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  • trunk/VUT/doc/SciReport/mutual.tex

    r277 r282  
    401401If the subdivision does not terminate till reaching a predefined 
    402402subdivision depth, we conservatively classify the tested regions as 
    403 mutually visible. 
     403mutually visible. The conservative verifier is illustrated at 
     404Figure~\ref{fig:conservative_sampling}. 
     405 
     406\begin{figure}[htb] 
     407\centerline{ 
     408\includegraphics[width=0.7\textwidth,draft=\DRAFTFIGS]{figs/conservative_sampling}} 
     409\caption{An example of the conservative visibility verification. The figure shows two 
     410  tested regions (the view cell and the object) and several 
     411  occluders. For sake of clarity we only show samples which are 
     412  boundaries of shafts on one path of the line space subdivision tree. 
     413  The subdivision terminates at the yellow shaft since a single strong 
     414  occluder has been found. } 
     415\label{fig:conservative_sampling} 
     416\end{figure} 
    404417 
    405418 
     
    409422conservative one. However it will behave differently in the finer 
    410423subdivision of the ray shafts. The idea is to use the above algorithm 
    411 as far as the shafts get small enough that we can guarantee that even 
    412 if the shaft is not blocked by the scene objects, a pixel error 
    413 induced due to omission of objects potential visible behind the shaft 
    414 is bellow a given threshold. 
     424as far as the shafts get small enough that we can neglect objects 
     425which can be seen through such a shaft. Even if not all rays inside 
     426the shaft are not blocked by scene objects, a pixel error induced due 
     427to omission of objects potential visible behind the shaft will be 
     428bellow a given threshold. 
    415429 
    416430For the computation of the maximal error due to the current shaft we 
    417431assume that one tested region is a view cell, whereas the other is an 
    418432object bounding box or cell of the spatial hierarchy. The threshold is 
    419 computed as follows: We first triangulate the farthest intersection 
    420 points in the shaft as seen from the view cell side of the shaft. Then 
    421 for each computed triangle we calculate a point in the view cell which 
    422 maximizes the projected area of the triangle. The conservative 
    423 estimate of the maximal error is then given by a sum of the computed 
    424 projected areas. 
     433computed as follows: We calculate a point in the view cell which 
     434maximizes the projected area of the object with respect to the shaft 
     435(see Figure~\ref{fig:approximate_sampling}). The conservative estimate 
     436of the maximal error is then given by the computed projected area. If 
     437this error is below a specified threshold we terminate the subdivision 
     438of the current shaft. 
     439 
     440\begin{figure}[htb] 
     441\centerline{ 
     442\includegraphics[width=0.7\textwidth,draft=\DRAFTFIGS]{figs/approximate_sampling}} 
     443\caption{An example of the approximate error bound visibility verification. The figure shows two 
     444  tested regions (the view cell and the object) and two 
     445  occluders. The maximal error inside the yellow shaft corresponds to the angle $\alpha$. 
     446} 
     447\label{fig:approximate_sampling} 
     448\end{figure} 
    425449 
    426450%Option: - if there is sufficient number of samples from 1 + 2 and some 
  • trunk/VUT/doc/SciReport/sampling.tex

    r279 r282  
    490490are planar planes whereas the EEE are in general quadratic surfaces. 
    491491 
    492  To account for these event we explicitly place samples passing by the 
    493 object edges which are directed to edges and/or vertices of other 
    494 objects. 
     492 To account for these events we explicitly place samples passing by 
     493the object edges which are directed to edges and/or vertices of other 
     494objects. In this way we perform stochastic sampling at boundaries of 
     495the visibility complex~\cite{Durand:1996:VCN}. 
    495496 
    496497The first strategy starts similarly to the above described sampling 
     
    499500connectivity information we select a random silhouette edge from this 
    500501object and cast a sample which is tangent to that object at the 
    501 selected edge . 
     502selected edge. 
    502503 
    503504The second strategy works as follows: we randomly pickup two objects 
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