I thought I’d share some of the easier things I had to do as part of the first year of my course. One of those tasks was to generate a 3D plot of a function and then also plot 2D cross sections at different values.

We start off with a mathematical function that describes, what we will call, our hill. This function represents the ‘height’ of our hill, h if you will, at the different points in x and y.

So, in our MATLAB script we first of all generate a grid of points using x values from -1.5 to 3.5 and y values from -2 to 2. The follow code achieves this.

`x = linspace(-1.5,3.5,50); % 50 values of x`

y = linspace(-2,2,25); % 25 values of x

[xg yg] = meshgrid(x,y); % generate points

And next we generate the height values of our hill, using the grid we have just created with x -> xg and y ->yg.

`h = exp(-(xg.^2)-(yg.^2)) + 0.5.*exp(-((xg-2).^2)-(yg.^2)); % calculate height values`

With our hight values in the array h, all we need to do now is plot them. Firstly, to create the 3D plot we just plot x,y and h using the **surf()** function.

`figure(1); % create new figure window`

surf(x,y,h); % surface plot

title('3D Hill Plot'); % title and axis labels

xlabel('x');

ylabel('y');

zlabel('height');

Now, to look at several slices through the hill at different values of y, we need to select the different values of y from its array and plot them on the same graph.

`figure(2);`

plot(x,h([1,10,20],:)); % plot 1st, 10th and 20th values of y

title('2D Hill Plot'); % title and axis labels

xlabel('x');

ylabel('height');

legend('y = -1.5','y = -0.4','y = 1.2',0); % legend not overlapping any of the plot

Putting it all together you get a 3D plot of the function and the cross sections in two windows. Job done.