How can I convert vector fields from Cartesian to polar coordinate system in MATLAB 7.10 (R2010a)?

I have a vector (velocity) field and would like to convert it from Cartesian to polar coordinate system. I am looking for a MATLAB function that directly does the conversion.

Answer 1

[MathWorks Support Team]

To convert a vector field from Cartesian to polar coordinate system, there is no MATLAB function that directly does the conversion. However, the command CART2POL can be used to convert a single set of Cartesian co-ordinates to the corresponding polar co-ordinates. As a workaround, this function can be applied manually. The following MATLAB code provides an example:

[X,Y] = meshgrid(-2:.2:2);

U = X.*exp(-X.^2 - Y.^2);

V = X.*exp(+X.^2 + Y.^2);

THETA = cart2pol(X,Y);

Ur = U .* cos(THETA) + V.* sin(THETA);

Uth = V .* cos(THETA) - U.* sin(THETA);

The above code computes radial (Ur) and azimuthal (Uth) velocity vectors from the Cartesian velocity (U and V).