Consider the topography of a terrain stored in the file terrain.mat. Download the

f

ile from CANVAS and load it into MATLAB. The files contain the spatial coordinates of

the terrain in vectors x and y and the altitude in a $2-$dimensional matrix altitude. The

coordinates and the altitude are given in the unit of meters.

$($a$-$ d$)$ How many peaks $($i$.$e$.,$ local maxima$)$ are there on the terrain? Put the answer in

p$5$a$.$ Include the peaks on the boundary of the terrain. Find the x and y coordinates and

the altitude of the peaks and put the answers in p$5$b$,$ p$5$c and p$5$d$,$ respectively.

$($e$-$ h$)$ How many troughs $($i$.$e$.,$ local minima$)$ are there on the terrain? Put the answer

in p$5$e$.$ Include the troughs on the boundary of the terrain. Find the x and y coordinates

and the altitude of the troughs and put the answers in p$5$f$,$ p$5$g and p$5$h$,$ respectively.

$($i$,$ j$)$ Make figure $1$ to include the following items:

$$ Use function surf to plot the terrain. Use shading interp to make the surface plot

smooth. Set view$(3)$ to put the plot in three$-$dimensional view.

$$ Use red filled circles to identify the peaks.

$$ Use green filled circles to identify the troughs.

$$ Extra credit $(5$ points$)$: An eagle initially standing at the tallest peak takes a direct

dive $($i$.$e$,$ three$-$dimensional straight line$)$ toward a prey which stands on the terrain at

x $=-800$ m and y $=-600$ m$.$ Use magenta filled circles to mark the projection of the

dive path on the terrain.

Set p$5$i $=$ 'See figure $1\text{'}.$ Be sure to label the axes with correct units, provide a title and

include a legend box. If you attempt the extra credit, set p$5$j $=$ 'See projection of dive

path'