Creating a 2D-array with radial and angular components

I have a function which contains a radial and an angular part, which I need to enter into a matrix (for evaluating measured data).

My first approach was to create a matrix with the appropriate cartesian coordinates x,y and a second matrix () with the corresponding angle with respect to a certain point which defines the centre. From this, I calculated for every point in the matrix the radial function and then multiplied it with the angular part. Computationally, this is quite a brutal way, but it works.

: The radial function contains binomial coefficients which blow up the computational time.

: I want to calculate the radial function once (say, for the angle ) and then "project" it onto the whole circle depending on the angle α, as in complex multiplication: , where .

: The accuracy of the radial plot is lower.

I attached an examplary calculation with a linear radial function, including the code.

Is there a more elegant way for this kind of problem? For instance, a function designed for projection onto a unit circle? Unfortunately, my research did not yield anything suitable :(

Thank you for your answers in advance!

[Sergej Poplavski]

Forgot the code... :-/

Answer 1

[darova]

Create polar coordinates (radius and angle) using meshgrid. Convert data into cartesian system and calculate

[R,T] = meshgrid(0:5,0:20:360);     % radius and angle
[X1,Y1] = pol2cart(T*pi/180,R);     % X and Y
[X2,Y2] = meshgrid(-5:5);           % cartesian X Y
Z1 = X1+Y1.^2;
Z2 = X2+Y2.^2;
surf(X1,Y1,Z1)
surface(X2,Y2,Z2,'facecolor','none')
axis vis3d