| 674 |
|
works as follows: |
| 675 |
|
\begin{enumerate} |
| 676 |
|
\item Each processor computes the convex hull for its own atomic sites |
| 677 |
< |
(dashed lines in Fig. \ref{fig:parallel}). |
| 677 |
> |
(left panel in Fig. \ref{fig:parallel}). |
| 678 |
|
\item The Hull vertices from each processor are passed out to all of |
| 679 |
|
the processors, and each processor assembles a complete list of hull |
| 680 |
|
sites (this is much smaller than the original number of points in |
| 681 |
|
the point cloud). |
| 682 |
< |
\item Each processor computes the global convex hull (solid line in |
| 682 |
> |
\item Each processor computes the global convex hull (right panel in |
| 683 |
|
Fig. \ref{fig:parallel}) using only those points that are the union |
| 684 |
|
of sites gathered from all of the subset hulls. Delaunay |
| 685 |
|
triangulation is then done to obtain the facets of the global hull. |
| 686 |
|
\end{enumerate} |
| 687 |
|
|
| 688 |
|
\begin{figure} |
| 689 |
< |
\begin{centering} |
| 690 |
< |
\includegraphics[width=3in]{parallel} |
| 689 |
> |
\includegraphics[width=\linewidth]{parallel} |
| 690 |
|
\caption{When the sites are distributed among many nodes for parallel |
| 691 |
|
computation, the processors first compute the convex hulls for their |
| 692 |
< |
own sites (dashed lines in upper panel). The positions of the sites |
| 693 |
< |
that make up the convex hulls are then communicated to all |
| 694 |
< |
processors. The convex hull of the system (solid line in lower |
| 696 |
< |
panel) is the convex hull of the points on the hulls for all |
| 697 |
< |
processors. } |
| 698 |
< |
\end{centering} |
| 692 |
> |
own sites (dashed lines in left panel). The positions of the sites |
| 693 |
> |
that make up the subset hulls are then communicated to all |
| 694 |
> |
processors (middle panel). The convex hull of the system (solid line in right panel) is the convex hull of the points on the union of the subset hulls.} |
| 695 |
|
\label{fig:parallel} |
| 696 |
|
\end{figure} |
| 697 |
|
|
