Changeset 284 for trunk

Timestamp:

09/16/05 18:42:21 (19 years ago)

Author:

bittner

Message:

 

Location:

trunk/VUT/doc/SciReport

Files:

• figs/approximate_sampling2.fig (added)
• mutual.tex (modified) (1 diff)

trunk/VUT/doc/SciReport/mutual.tex

@@ -431 +431 @@
 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 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.
+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 (see
+Figure~\ref{fig:approximate_sampling}).  The conservative estimate of
+the maximal error is then given by a sum of the computed projected
+areas. If this error is below a specified threshold we terminate the
+subdivision of the current shaft.
+
+%We calculate a point in the view cell which
+%maximizes the projected area of the object with respect to the shaft
+%. The conservative estimate
+%of the maximal error is then given by the computed projected area. 
 
 \begin{figure}[htb]
 \centerline{
-\includegraphics[width=0.7\textwidth,draft=\DRAFTFIGS]{figs/approximate_sampling}}
+\includegraphics[width=0.7\textwidth,draft=\DRAFTFIGS]{figs/approximate_sampling2}}
 \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 $\alpha$.
+  occluders. Due to the 2D nature of the example the triangulation is depicted as
+  the red line segment. The maximal error for the possible viewpoints in the shaft
+  corresponds to the angle $\alpha$.
 }
 \label{fig:approximate_sampling}