How can i plot pressure in polar coordinate with only values in one direction, and then transforming the system into cartesian.

• I have values of pressure in one direction (r=0:20:10,000, theta=0)

so i have data of pressure in 1 direction only, since this are poin source i can assure that the distribution in all direction are the same. so i would like to kind of sweep these value to all direction, the ilustration is given as following

• how to change the system into cartesian so the p that assigned to the exact same location still hold

what i have done so far :

%step 1 : preparing the meshgrid (sample only \pi step)
dr=0:20:10000;
dt=0:pi/2:2*pi;
[theta,rho] = meshgrid(dt,dr);

%step 2 : read pressure
p_init=readtxt(fname,SR,SC,ER,EC); %just some files containing pressure data from 0 to 10,000 with stepsize of 20
p(:,1)=p_init;  %   i am assign the same value to these 3 
p(:,2)=p(:,1);  %   "sample" direction that later on will be used as 
p(:,3)=p(:,1);  %   the base for interp2

%step 3 : interp2 those pressure into 1\deg angle-step (query angle)
dt_new=0:pi/180:2*pi;
[thetaq,rhoq] = meshgrid(dt_new,dr);    
pq=interp2(theta,rho,p,thetaq,rhoq);    %query pressure value at the query angle

%step 4 : transform from polar to cartesian using pol2cart
[xq,yq,pq]=pol2cart(thetaq,rhoq,pq);
localpressure=pq;

Answer 1

[Ayush Modi]

Hi Mahardika,

I understand you would like to interpolate the pressure values to a grid. You can achieve this using interp1 function. interp1 function is suitable for this purpose because, pressure data is a set of one-dimensional data points. Here is an example to demonstrate how you can acheive this:

% Create a Cartesian grid
[X, Y] = meshgrid(-10000:20:10000, -10000:20:10000); % Adjust the range and step size as needed

% Calculate the radial distance for each point on the Cartesian grid
R = sqrt(X.^2 + Y.^2);

% Interpolate the pressure values at each radial distance in R
% P is the pressure data
% r is the radial distance vector
PCartesian = interp1(r, P, R, 'linear', 'extrap');

Note - The grid size and spacing can be changed as per the requirement.

Please refer to the following MathWorks documentation for more information on the interp1 function:

https://www.mathworks.com/help/matlab/ref/interp1.html

Hope this helps!