how to INTERPOLATE starting from three circles

Through the information of 3 distances and 3 wind speeds I was able to create circles as shown in the figure where each point that makes up the circles is characterized by X=latitude, Y=longitude of the point and Z is the probability of obtaining the speed of a given wind at that distance from the center.

Now what I would like to do is create the same graph but INTERPOLATING on the entire grid: in each point of the grid starting from values ​​of X=3 known distances and Y= 3 known speeds and entering a distance from the point of interest (xi), I would like calculate the angle at that point with respect to the source (as I did for the three circles), then with this distance from the source I thought I would enter the graph by interpolating and see what is the speed it takes to get to that point at that distance.

I had read about the function yi = interp1q (X, Y, xi): for example I thought that to calculate the probability of the speed, I know how far I am (like 100km), I use interp1q, I calculate what minimum speed (yi) I need to reach the distance (100km) and consequently calculate the probability of having a speed higher than the minimum speed I found.

I tried to use this function but it fails. Can anyone help me?

Answer 1

[Image Analyst]

See how they use sin and cos in the third example in the FAQ:

https://matlab.fandom.com/wiki/FAQ#How_do_I_create_a_circle.3F

Basically put that code into a double loop over your Xs and Ys. Here's a start:

angles = linspace(0, 360, 1000);
for k = 1 : length(X)
    xCenter = X(k);
    for k2 = 1 : length(Y)
        yCenter = Y(k2);
        xCircle = xCenter + radius * cosd(angles)
        yCircle = yCenter + radius * sind(angles)
        plot(xCircle, yCircle, '-', 'LineWidth', 3);
        hold on;
    end
end

Write back if you still can't figure it out.

[ELISABETTA BILLOTTA]

Hi .. I still don't understand how to do it :( this is the result that comes out .. i dont think it is right

[Image Analyst]

If you want markers only, and not lines connecting them, use * instead of -:

plot(xCircle, yCircle, '*', 'MarkerSize', 7);

You can adjust the number of markers by adjusting the number of angles. For example if you wanted 12 markers

angles = linspace(0, 360, 13); % One more than 12 because 0 and 360 are on top of each other.