Visualization of Data in polar coordinates
 

Hi,

Can anyone help in converting a polar grid (r- and theta-) to X and Y for the purpose of plotting (The gird is unevenly spaced in r- and of course, evenly spaced in theta-)? MATLAB can do it using griddata() but cannot compute values close to the origin. MATLAB returns NaN (Not a Number) value for points near the origin.

Is there any visualization software (free, Unix based) that can read in 2D matrices with rows representing the r- direction and columns the theta- direction (and each element filled with value representing the function at that value of r- and theta-)?

Many Thanks

--Sujit

Re: Visualization of Data in polar coordinates
 

Are you asking for simply:

x = r*cos(theta)

y = r*sin(theta)

or am I missing something?

Re: Visualization of Data in polar coordinates
 

Yes exactly, but its a little more complicated. Here's how:

I have a 2D (say N by N) matrix with where each element corresponds to the value of a function at certain r and certain theta.

By doing x = r*cos(theta) and y = r*sin(theta) I get a set of (N*N) x's and (N*N) y's because for each x there are N r's and N theta's. So now I have a N*N matrix for the x-coordinates and another N*N matrix for the y-coordinates. Clearly, values of x- and y- are unevenly spaced.

The question is .. how do I interpolate my data which is evaluated at these various N*N x's and y's to an evenly spaced grid? MATLAB needs an evenly spaced 2D grid to plot countours or surfaces.

I hope you understand the problem.

Thanks for your interest -- Sujit

Re: Visualization of Data in polar coordinates
 

Matlab does not require evenly spaced data. You can simply calculated the x and y coordinates and use them directly in contour function.

Re: Visualization of Data in polar coordinates
 

Hi, thanks for your help. Indeed MATLAB can take in 2D matrices for X and Y that don't need to be evenly spaced.

I have another question: Would you know how to visualize 3D contour data? Plot surfaces of constant function value? I wrote something like this: but it dies (returns NaN) at the origin. Could someone show me a better way to do it?

Many Thanks,

--Sujit

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear

start = cputime;

nz = 128;

nt = 128;

nx = 128;

zlen = 4.33121852439964;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%load r and theta collocation points.

load rData.dat;

load thetaData.dat;

ti = -4:.1:4;

[XI,YI] = meshgrid(ti,ti);

%clear ti;

for i=1:nz

for j=1:nt*2

x(i,j) = rData(i)*cos(thetaData(j));

y(i,j) = rData(i)*sin(thetaData(j));

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%load up the 3D matrix for vorticity

%It is actually a 2D ascii file

load omegaZ_3D_001;

rawData = omegaZ_3D_001;

clear omegaZ_3D_001;

%rearrange the 2D ascii data into the 3D matrix it

%represents.

for i=0:nx-1

temp = rawData((nz+1)*i+1:(nz+1)*(i+1),1:2*(nt+1));

data(:,:,i+1) = temp(:,:);

end

clear temp, rawData; <font color = red> %convert vorticity from r- theta- to x- y-

%This is where griddata() returns NaN at the origin.

for k=1:nx

temp = data(1:nz,1:2*nt,k);

output(:,:,k) = griddata(x,y,temp,XI,YI, 'cubic');

now = cputime-start

end </font> clear temp

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Various ways to visualize.

%surf(XI,YI,output(:,:,64)), hold; grid on; view([30 65])

%shading flat; shading interp;

z = 0:zlen/nx:zlen;

z = (z(1:nx))';

x = (XI(1,:))';

y = YI(:,1);

%output = smooth3(output);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%this produces contour lines in various slices

%this is probably the best!

%h = contourslice(x,y,z,output,[0],[0],[1:0.1:12]);

%axis([-3,3,-3,3,0,13]); daspect([1,1,1])

%camva(24); camproj perspective;

%campos([-20,-6,25])

%set(gcf,'Color',[.5,.5,.5],'Renderer','zbuffer')

%set(gca,'Color','black','XColor','white','YColor' ,'whi te','ZColor','white')

%box on

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%use this for solid and multicolored tubes

%note: for a good view 'output' must have positive vorticity

%if everything is red, make output = -output

p1 = patch(isosurface(x,y,z,output),'FaceColor','blue', 'Edge Color','none');

p2 = patch(isocaps(x,y,z,output),'FaceColor','interp',' EdgeC olor','none');

isonormals(x,y,z,output,p1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%if you want a hollow tube use this one:

%p = patch(isosurface(x,y,z,output));

%isonormals(x,y,z,output,p)

%set(p,'FaceColor','red','EdgeColor','none');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

view(3); axis vis3d;

axis([-4 4 -4 4 0 zlen])

camlight left; camlight; lighting phong;

timeItTook = cputime - start