how to interpolate x and y coordinates of contour?

Hi,

I have been trying to interpolate the x and y coordinates obtained from contour matrix. The way i extract x and y coordinates from contour matrix is as show below.

In the for loop for every iteration I can obtain x and y values from the contour matrix K. I want to interpolate these (x and y coordinate ) values with a resolution of 1800 'res'. I wrote detailed explanation of what im doing beside every line. Basically when I plot 'contour(isq,isd,Psi_abs,v)' it gives me 6 concentric ellipses which are not very smooth, my intention is to make these concentric ellipses more smooth by giving a resolution res=1800 ( with a hope that generated ellipses have more x and y coordinates such that they are very smooth thatn before). But after using the above given code i'm getting weird plots as i attached image.

what i'm expecting is more smooth concentric ellipses. Also in the code Im not including level-verices column and the last columns of K matrix (controur matrix) (since it contains same values as in second column of K matrix). But still its producing the plots as shown above. Is there any way then to interpolate the x and y coordinates.

• Can anyone plz provide me brief or detailed way to do this? The code what I wrote may also be a incorrect, please provide me any sugesstions.

Answer 1

[Bjorn Gustavsson]

You extract the contours wrong, at least if you have multiple contours at the same level v(i). It is simpler if you plot all the contours at once:

[K,c] = contour(idq,isd,Psi_abs,v);

Then you have to extract them segment-by-segment. The format for K is:

K = [level1, x1_1,x1_2,.. ,x1_n1,level2, x2_1,x2_2,..,x2_n2,level3
       n1,y1_1,y1_2,..,y1_n1, n2, y2_1,y2_2,..,y2_n2, n3]

So you'll have to extract your contour-segments something like this:

iC = 1;
idxC = 1;
while iC < size(K,2)
  nP = K(2,iC); % number of points in current contour
  xC{idxC} = K(1,iC+(1:nP)); % x coordinates of current contour
  yC{idxC} = K(2,iC+(1:nP)); % y coordinates of current contour
  iC = iC+nP+1;    % Start-point of next contour
  idxC = idxC + 1; % next contourline index
  % plot(xC{idxC-1},yC{idxC-1},'b.-') %% If you want to look at the separate
  % pause                             %% segments as they are separated.
end

That would give you a pair of cell-arrays with the x and y coordinates for the contour-segments, that you then can reinterploate and doodle with as you see fit, perhaps the Interparc contribution is of interest to you...

HTH

[manoj saladi]

Hi bjorn,

Now I managed to extract all the contours into Xc and Yc. So, you mean now I have to use interparc function to interpolate each dataset in Xc, Yc.

Regards,

Manoj.

[Bjorn Gustavsson]

Well, that is a function you might get good results from, other ideas might be to use NURBS or other types of spline-interpolation like you tried, but I've not tested any of them, I just thought interparc would be a suitable tool to try.

HTH

[manoj saladi]

Hi,

I successfully interpolated the ellipses. But I have an other question

explanation: I have a an mxn matrix and I want to interpolate this matrix with the x and y coordinates which I obtained from interparc function using interp2 function. The syntax might look like this

A=interp2(x, y, mxn_matrix, interparc_xcoordinates, interparc_ycoordinates)

But as the x and y coordinates obtained from interparc are not monotonic ( since they are coordinate values of ellipses and may not be strictly unique as well). So, in this case is using interp2 possible?

I haven't tried it yet, but want to know before I use interp2

Regards,

Manoj

[Bjorn Gustavsson]

Well if you have the x, y and mxn_matrix that interp2 accepts you can call interp2 with just about anything for xi and yi, and if they are both row or column vectors you will get the interpolated values for those points.

HTH

[manoj saladi]

Hi,

I did interpolation using interp2 function and its working very fine. But it takes too much of time to simulate when I increase 'v' in the contour.

syntax:[K,c] = contour(idq,isd,Psi_abs,v);

I know the reason , its because im storing all the values into a cell every time. When I did this for v= 1000; it may take nearly 10 min. I there any way to not to store the values of contours but get the result finally?

Thank you.

Answer 2

[darova]

Look for interp2 then build countour

[manoj saladi]

Hi,

How would I know query points before using Contour? Can you plz explain a bit more detail?

Thank you.

[darova]

You have some data (isq; isd; Psi_abs). Its your XYZ. Why can you interpolate it?

clc, clear
x = -3:3;                    % your isq
y = -3:3;                    % your isd

[X, Y] = meshgrid(x,y);
Z = -X.^2 -3*Y.^2;           % your Psi_abs

subplot(221)
contour(x, y, Z)             
subplot(223)
surf(x, y, Z)
title('initial data');

[Xq, Yq] = meshgrid(-3:0.3:3);        % creating mesh with more points
Zq = interp2(X,Y,Z, Xq,Yq,'cubic');   % interpolating 

subplot(222)
contour(Xq, Yq, Zq)
subplot(224)
surf(Xq, Yq, Zq)
title('interpolated data');

[manoj saladi]

Hi,

Thank you very much for your explanation . I tried using this code, but I got to know that I'm not extracting contour values correctly in every iteration, so I have to interpolate it first.

Best Regards,

Manoj.

Answer 3

[manoj saladi]

I will try it today