Linear plot to contour plot

Hello, I'm creating a temperature profile of a cylinder, and got a range of temperatures to different radiuses, like shown in the picture below. Kelvin on the y-axis and radius [m] on the x-axis.

So i did this with the plot(r,T) command, r-vector having the radius and T-vector my corresponding temperatures. Now, i want to make this into a contour plot, so i can see it like circle, to show it like a real cross-cut of my cylinder. (I know it might not be up to much practical use, but i want to learn how to do it)

I've tried to read about contourplots, meshgrids and so on, but just can't seem to figure out a way to do this. Could anyone explain me how to transform a line plot into a contour plot with circular level curves.

Answer 1

[Asger]

OK, I found a solution, a bit inspired by José-Luis' answer, but i was not satisfied with the way he did it, as i didn't get any indepth knowledge of contourplots, which is what i will need to use in my further work with a more complex model. If anyone is interested here is my solution.

As a background story i got some different temperatures in a few layers, T1,T2,T3, and also different temperature gradients dT1,dT2 through each layer depending on their thermal conductivity.

Now i make a meshgrid for x and y coordinates, calculate the corresponding radius in each array-element. I have 2 for loops that goes through each r(m,n) and calculates the temperature. Basicly it's temperature, T, as a function of the radius, r.

% Make the coordinatesystem that fits with the radius.
[x_coor,y_coor] = meshgrid(-r3:0.001:r3,r3:-0.001:-r3);
r = sqrt(x_coor.^2+y_coor.^2); % Corresponding radius

% Get ready for the loop
m = 1;
n = 1;
T_matrix = zeros(size(r));
dT2 = (T2-T1)/(r2-r1);
dT3 = (T3-T2)/(r3-r2);

for m = 1:length(r)
     for n = 1:length(r)
         if r(m,n) <= r1 % layer 1
             T_matrix(m,n) = T1;
         elseif r(m,n) < r2 % layer 2
             T_matrix(m,n) = T1 + (r(m,n)-r1)*dT2;
         elseif r(m,n) <= r3 % layer 3
             T_matrix(m,n) = T2 + (r(m,n)-r2)*dT3;
         else % if none of these layers, it must be outside
             T_matrix(m,n) = Te; % environmental temperature
         end
     end
end

% Draw the contour
contourf(x_coor,y_coor,T_matrix,80,... % 80 colours
                        'edgecolor','none'); % no edge

% Draw the cable boundaries
hold all
phi = 0:0.01:2*pi; x_circ = r1*cos(phi); y_circ = r1*sin(phi);
plot(x_circ,y_circ,'Color','black','LineWidth',2)

phi = 0:0.01:2*pi; x_circ = r2*cos(phi); y_circ = r2*sin(phi);
plot(x_circ,y_circ,'Color','black','LineWidth',2)

phi = 0:0.01:2*pi; x_circ = r3*cos(phi); y_circ = r3*sin(phi);
plot(x_circ,y_circ,'Color','black','LineWidth',2)

And this gives me a contourplot that looks like this: http://i.imgur.com/oZIq5.png

Thanks for the help.

Answer 2

[Jürgen]

Hi,

to make a contour plot you need two dimensions, since you only have r the radius it won't work

You need the (x,y) coordinates of the cilinder or (r,angle) is you want to use polar coord. Then you could try a polar plot

once you have the coord in two dimensions use meshgrid en contour

regardsJ

[Asger]

Yes, i think i can transfer my radius into (x,y)-coordinates by polarcoordinates, but how do i get my temperature T (which will be the height z of the contour plot) to follow into the right element in the array?

Answer 3

[José-Luis]

I don't think a polar plot would do the trick, you could use patches:

 data_length = 10;
  %The values you want to plot:
  your_vals = rand(data_length,1);
  x = (0:data_length - 1)'; %Coordinates, gotta start somewhere
  y = 0.*x;

coord_mat = [x y];

numColors = 64; %How many colors you want
color_array = autumn(numColors); %Colormap, could be something else

%Getting color index:
minVal = min(your_vals);
maxVal = max(your_vals);
your_idx = (your_vals - minVal) ./ (maxVal - minVal); %Linearly mapping the colormap
your_idx = round((numColors - 1) * your_idx + 1); 

R = @(x)[cos(x) -sin(x); sin(x) cos(x)]; %Rotation matrix
numVals = 0;
newVec = [];

%Rotating your data, do less intervals if you want less patches
for ii = 0:pi/20:2*pi
    newVec = [newVec;coord_mat*R(ii)];
    numVals = numVals + 1;
end

 %Cushioning so as not to get out of bounds
  newVec = [newVec repmat(color_array(your_idx,:),numVals,1)];
  newVec = [newVec ; newVec(1:data_length,:)];
  numVals = numVals + 1;

%Patching
 for ii = 1:numVals-1
     for jj =  1:data_length-1
         idx_vec = [(ii-1)*data_length + jj;...
             (ii-1)*data_length + jj + 1;...
             ii*data_length + jj + 1;...
             ii*data_length + jj;...
             ];
         p = patch('Faces',idx_vec','Vertices',newVec(:,[1 2]));
         set(p,'FaceColor','interp',...
                'FaceVertexCData',newVec(:, [3 4 5]),...
                'EdgeColor','none')
         hold on;
     end

   end

You could probably simplify the loop...

Or reduce the number of patches, e.g. patching circle sections