How can I convert into new coordinates over a loop?

I am working with a set of vectors for a calculation: the vectors are obtained in spherical polar coordinates and I then need to convert them all so that they are in Cartesian coordinates.

Basically, I have a matrix where I store the positions of a set of N vectors in spherical polar coordinates. So the first row is composed of the theta component of each of the vectors, the second row is the phi component, and the third is the radial coordinate and I would then like to form a new matrix which is the same but now the first row is the x component, the second row is the y component, and the third row is the z component. However, when I try to create this new matrix, MATLAB just says that the dimensionality of the matrices doesn't work, for example:

r(1,1:10)= sin(alpha)*cos(phi);

where alpha and phi have been specified as the row vectors formed from the first and second rows of the original matrix.

The example above is if I were to try to create the first row of the new matrix for 10 vectors in the original spherical polar coordinates. I have looked it up and the advice is that I should basically make MATLAB to do it by looping over the combinations which are needed but I am unsure how to do this, could someone advise?

Answer 1

[Star Strider]

This task might be easier with the sph2cart (link) function.

[Tom]

Yes, that looks a lot easier, thanks for letting me know about this.

[Star Strider]

My pleasure.

If my Answer helps you solve your problem, please Accept it!

[Tom]

Hang on, I think your answer would work in theory but it assumes that you have already created the array explicitly using that construction. In my case I just follow a formula and it spits out some numerical values into an array which are in spherical coordinates ie. I just happen to know they are in spherical coordinates but they are only values. I just need some loop which converts each of the entries using the usual formulae and makes a new matrix where the entries are now in Cartesian coordinates.

[Star Strider]

If your vectors are in the format that sph2cart expects, you should be able to use it without modification. The arguments can be ‘a scalar, vector, matrix, or multidimensional array.’

I do not understand the problem you are having with it.

Answer 2

[Tom]

I will show you what I am intending, basically I have a piece of code which creates a 3 x N array depending on the values I choose for N_alpha and N_phi, let's say it's a 3 x 4 array, so I have four position vectors with the first row corresponding to the theta component of each vector, the second row is the phi component of the vector and the third row is for the radial component of the vector.

[i, j] = ndgrid(1:N_alpha, 1:N_phi);

alpha = (i-1)*2*pi/N_alpha;

phi = (j)*pi/(N_phi+1);

r = 1;

b = [alpha(:).'; phi(:).'; r * ones(1,numel(alpha))];

I would then like a new array B which is the same but with everything converted to Cartesian coordinates, if I try

B=sph2cart(alpha,phi,r);

it creates a 2 x 2 array which is smaller than the matrix I started with. If I do sph2cart(b) it says that the dimensions don't agree.

[Star Strider]

What are representative values for ‘N_alpha’ and ‘N_phi’?

[Tom]

For example, 2 for both of them. Doesn't really matter as long as they are both the same.

[Star Strider]

I am still not certain what you want.

Try this:

b = [alpha(:).'; phi(:).'; r * ones(1,numel(alpha))];

[x,y,z]=sph2cart(b(1,:),b(2,:),b(3,:));

figure
plot3(x, y, z)
grid on
% axis equal

[Tom]

That also creates a smaller matrix. Basically, let's say I have a position vector for a point in spherical coordinates and I want to convert it to a vector for that same point in Cartesian coordinates. I essentially have an matrix formed from several such vectors in spherical coordinates and I want to convert them all to Cartesian coordinates.

[Star Strider]

The output is the same size as the input, in this example 3 (1x4) vectors. If you want longer output vectors, you need to provide longer input vectors.

Example —

[theta,phi] = ndgrid(0:0.15:2*pi);
r = 2*ones(size(theta));

[x,y,z,] = sph2cart(theta,phi,r);

figure
scatter3(x(:), y(:), z(:), '.')
grid on
axis equal

[Tom]

The output seems to be smaller, so if I feed in a 3x4 vector I get 2x2 back, so something must be going wrong. Basically I have a point which has a column vector in spherical coordinates on a sphere, then I take several such vectors for different points and slot them next to each other to make a matrix. I just want to take the position vectors in that matrix and change them so they are in Cartesian coordinates, there must be a simple way of doing this as I cannot get the function to work.

[Star Strider]

‘Basically I have a point which has a column vector in spherical coordinates on a sphere, then I take several such vectors for different points and slot them next to each other to make a matrix.’

Apparently, I still do not understand the problem you are having.

If your data vectors are gridded (have regularly-repeating patterns in the x- and y-coordinates), you can make them into a matrix using the reshape function first, then sph2cart.

If you simply have vectors in spherical coordinates that you want to change to Cartesian coordinates, you can do that easily enough with sph2cart.

You can then plot them using any function you wish. I use scatter3 in my example. Any other 3-D plotting function will work.