Matlab equivalent of Maple densityplot - matlab

Question

I would like to create a density plot of this function:
In Maple, one could use the densityplot function to achieve this (code at the end), which gives:
However, I am not sure what to use for plotting a similar figure in MATLAB.
Here is my current MATLAB code:
x = [0:10:100];
y = [-50:10:50];
s = [10, 0];
i = [50,25];
for ii = 1 : length(x)
sir(ii) = -10 * 9.8 * log10((power((x(ii) - s(1)),2) + power((y(ii) - s(2)),2)) / (power((x(ii) - i(1)),2) + power((y(ii) - i(2)),2)));
end
Could someone suggest an equivalent in MATLAB?
For the density plot in Maple, I used
densityplot(sir(x,y), x=0..100, y=-50..50, axes=boxed, style=patchnogrid, scaletorange=-5..50, colorscheme = [black, "green", "white"])

Answer 1

You can use surf (a 3D surface plot) to achieve this, but you will need a finer grid than steps of 10 for it to look good!
Also you will need meshgrid to get all combinations of the x and y coordinates.
Please see the comments for further details.
% Set up grid points
x = 0:0.1:100;
y = -50:0.1:50;
[x,y] = meshgrid(x,y);
% Set up parameters i, s and g
i = [50 25]; s = [10 0]; g = 9.8;
% Work out density
% - no need for loop if we use element-wise operations ./ and .^
% - power(z,2) replaced by z.^2 (same function, more concise)
% - You forgot the sqare roots in your question's code, included using .^(1/2)
% - line continuation with "...", could remove and have on one line
sir = -10*g*log10( ((x-s(1)).^2 + (y-s(2)).^2).^(1/2) ./ ...
((x-i(1)).^2 + (y-i(2)).^2).^(1/2) );
% Plot, and set to a view from above
surf(x,y,sir,'edgecolor','none','facecolor','interp');
view(2);
% Change the colour scheme
colormap('bone')
Result:
Matching your example
You used the Maple command scaletorange=-5..50. This limits the scale between -5 and 50 (docs), so since sir is our scale variable, we should limit it the same. In MATLAB:
% Restrict sir to the range [-5,50]
sir = min(max(sir,-5),50);
% Of course we now have to replot
surf(x,y,sir,'edgecolor','none','facecolor','interp');
view(2);
Now, if you wanted the black/green colours, you can use a custom colormap, this would also smooth out the banding caused by the 'bone' colormap only having 64 colours.
% Define the three colours to interpolate between, and n interpolation points
black = [0 0 0]; green = [0 1 0]; white = [1 1 1];
n = 1000;
% Do colour interpolation, equivalent to Maple's 'colorscheme = [black, "green", "white"]'
% We need an nx3 matrix of colours (columns R,G,B), which we get using interp1
colormap(interp1(1:3, [black; green; white], linspace(1,3,n)));
With g=3.5 (not sure what you used), we get an almost identical plot