Interpolate Data associated to cartesian meshgrid to all direction (like polar interpolation)

so i have data of pressure in 1 direction only, since this is just a point 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

i know how to do this if i use polar coordinate as the meshgrid and then uses pol2chart to convert to cartesian coordinate, but for my particular purpose i need the meshgrid is in cartesian and i dont know how to do this.

hope someone can helps

Answer 1

[Stephen23]

Interpolating in 1D to:

• give the shape formed by rotation around X=Y=0
• correctly return NaN for values outside the data domain.

R = 0:20:10000;
P = 5000./R.^0.15;
plot(R,P)

[Xq,Yq] = meshgrid(-10000:20:10000);
Rq = sqrt(Xq.^2+Yq.^2);
Pq = interp1(R,P,Rq(:));
Pq = reshape(Pq,size(Rq));
surf(Xq,Yq,Pq,'EdgeColor','none')

[Mahardika Firjatullah]

Thank you so much you are awesome

how you be able to do that in a short time, while i spend all day to figure this out and still failed.