Code: Select all
and the wind is not given a negative value, as direction is dealt with separately.
\begin{figure}
\begin{center}
\includegraphics[scale = 1]{Edge.png}
\caption{Movement through Weighted Graph}
\end{center}
\end{figure}
\paragraph{}
All preceding values are included in the summation of the shortest path to any node. As in the diagram above, the shortest path to the next edge $ V $ is the distance from the source to the current node $ C $, and the next node $ V $, plus the weight, or cost, to travel to that edge $ w2 $. This process is completed for all the reachable nodes in the map.
\section{Reachable Sections of the Course}
\paragraph{}
The use of the weighted graph with the information of wind included allows for an optimal path to be completed. Taking real time values for the wind, a section of the Irish sea from Co. Antrim to Scotland for the \date{9 January 2011}\cite{grib}. This set of data was chosen as the wind directions and strengths changed on a large enough scale to test the robustness of the programmed algorithm . Due to physical limitations some of the nodes were not reachable on the course, so were not included in the calculations.
Code: Select all
As in the diagram above, the shortest path to the next edge $ V $ is the distance from the source to the current node $ C $, and the next node $ V $, plus the
both images called above, appear here in the pdf
weight, or cost, to travel to that edge $ w2 $. This process is completed for all the reachable nodes in the map.