Changeset 282 for trunk/VUT/doc

Timestamp:

09/16/05 18:22:17 (19 years ago)

Author:

bittner

Message:

 

Location:

trunk/VUT/doc/SciReport

Files:

• figs/approximate_sampling.fig (added)
• figs/conservative_sampling.fig (added)
• mutual.tex (modified) (2 diffs)
• sampling.tex (modified) (2 diffs)

trunk/VUT/doc/SciReport/mutual.tex

@@ -401 +401 @@
 If the subdivision does not terminate till reaching a predefined
 subdivision depth, we conservatively classify the tested regions as
-mutually visible.
+mutually visible. The conservative verifier is illustrated at
+Figure~\ref{fig:conservative_sampling}.
+
+\begin{figure}[htb]
+\centerline{
+\includegraphics[width=0.7\textwidth,draft=\DRAFTFIGS]{figs/conservative_sampling}}
+\caption{An example of the conservative visibility verification. The figure shows two
+  tested regions (the view cell and the object) and several
+  occluders. For sake of clarity we only show samples which are
+  boundaries of shafts on one path of the line space subdivision tree.
+  The subdivision terminates at the yellow shaft since a single strong
+  occluder has been found. }
+\label{fig:conservative_sampling}
+\end{figure}
 
 
@@ -409 +422 @@
 conservative one. However it will behave differently in the finer
 subdivision of the ray shafts. The idea is to use the above algorithm
-as far as the shafts get small enough that we can guarantee that even
-if the shaft is not blocked by the scene objects, a pixel error
-induced due to omission of objects potential visible behind the shaft
-is bellow a given threshold.
+as far as the shafts get small enough that we can neglect objects
+which can be seen through such a shaft. Even if not all rays inside
+the shaft are not blocked by scene objects, a pixel error induced due
+to omission of objects potential visible behind the shaft will be
+bellow a given threshold.
 
 For the computation of the maximal error due to the current shaft we
 assume that one tested region is a view cell, whereas the other is an
 object bounding box or cell of the spatial hierarchy. The threshold is
-computed as follows: We first triangulate the farthest intersection
-points in the shaft as seen from the view cell side of the shaft. Then
-for each computed triangle we calculate a point in the view cell which
-maximizes the projected area of the triangle. The conservative
-estimate of the maximal error is then given by a sum of the computed
-projected areas.
+computed as follows: We calculate a point in the view cell which
+maximizes the projected area of the object with respect to the shaft
+(see Figure~\ref{fig:approximate_sampling}). The conservative estimate
+of the maximal error is then given by the computed projected area. If
+this error is below a specified threshold we terminate the subdivision
+of the current shaft.
+
+\begin{figure}[htb]
+\centerline{
+\includegraphics[width=0.7\textwidth,draft=\DRAFTFIGS]{figs/approximate_sampling}}
+\caption{An example of the approximate error bound visibility verification. The figure shows two
+  tested regions (the view cell and the object) and two
+  occluders. The maximal error inside the yellow shaft corresponds to the angle $\alpha$.
+}
+\label{fig:approximate_sampling}
+\end{figure}
 
 %Option: - if there is sufficient number of samples from 1 + 2 and some

trunk/VUT/doc/SciReport/sampling.tex

@@ -490 +490 @@
 are planar planes whereas the EEE are in general quadratic surfaces.
 
- To account for these event we explicitly place samples passing by the
-object edges which are directed to edges and/or vertices of other
-objects.
+ To account for these events we explicitly place samples passing by
+the object edges which are directed to edges and/or vertices of other
+objects. In this way we perform stochastic sampling at boundaries of
+the visibility complex~\cite{Durand:1996:VCN}.
 
 The first strategy starts similarly to the above described sampling
@@ -499 +500 @@
 connectivity information we select a random silhouette edge from this
 object and cast a sample which is tangent to that object at the
-selected edge .
+selected edge.
 
 The second strategy works as follows: we randomly pickup two objects