Switching an array of Vectors from Cartesian to Spherical Coordinates

I have a 3 x 46 array called V which I am viewing as an array of 46 column vectors in Cartesian components, I am attempting to switch the components to spherical, so that I have an array of 46 column vectors in spherical polar coordinates r, theta, phi using the cart2sph function but I cannot seem to get the syntax right?

Do I need to separate out the rows first

X=V(1,:);
Y=V(2,:);
Z=V(3,:);

or can the function be applied directly to the array to make a conversion?

Answer 1

[dpb]

The documentation syntax is pretty clear--

"[azimuth,elevation,r] = cart2sph(x,y,z) transforms corresponding elements of the Cartesian coordinate arrays x, y, and z to spherical coordinates azimuth, elevation, and r."

Yes, you must supply three separate x,y,z coordinate arrays to cart2sph because it can operate on either scalar, vector or array inputs and so the three coordinates have to be separated.

If you have the array, you don't need to create explicit temporaries, just pass the references...

[az,el,r]=cart2sph(V(1,:),V(2,:),V(3,:));

[Tom]

I already tried

cart2sph(X,Y,Z)

and I got a 1x46 array when I am looking for a 3x46 array which is just the same vectors as before but they are switched to spherical polar rather than Cartesian coordinates.

[Bruno Luong]

" because it can operate on either scalar, vector or array inputs and so the three coordinates have to be separated."

This is not a good reason for user not to able to pass n x 3 array like many other functions (delaunay, convexhull...). It's just not thoughfully designed initially.

[dpb]

Well, it is what it is... :)

Altho, yes, it could have been different. But, there hasn't seemed to be any overall coherent interface design regimen established by TMW to try to create such consistency, unfortunately, and with the plethora of new toolboxes and data classes and the transitioning to named parameter/object-oriented interfaces from the classic procedural ones, it's only getting worse with time.

[dpb]

"I already tried cart2sph(X,Y,Z) and I got a 1x46 array when I am looking for a 3x46 array..."

Because you didn't provide anything except the default ans location for Matlab to return the three variables [az,el,r] so all you got back was az; el and r weren't returned because that syntax didn't ask for them.

Answer 2

[David Hill]

[ax,el,r]=cart2sph(V(:,1),V(:,2),V(:,3));
V=[ax,el,r];

I believe the above should work for you.

[Tom]

Hi David, this doesn't work unfortunately, it creates a 3 x 3 matrix.

[David Hill]

It is working for me.

[Bruno Luong]

Tom has xyz data ranged in 3-rows not 3-columns

[David Hill]

Sorry, just change V to V'. I thought it was a 46x3 array.

Answer 3

[Bruno Luong]

OK since nobody care to give you the complete commands I'll

[az,el,r] = cart2sph(V(1,:),V(2,:),V(3,:));
S = [az; el; r]; % <- here is your 3 x 46 array of spherical coordinates

[Tom]

Is this right? This can't be right surely, as my first vector in Cartesian is -1.6x10^-04, the second one is -3.33x10^-16 and the third one is 1.0000, but the first entry in the matrix is -3.14, however this should correspond to the radial component of the first vector, which is going to be 1.000 again, surely?

[Tom]

Would it be perhaps be easier to just have a loop which takes each vector in the array and manually makes a row formed of the radial components of each vector, as this is what needs to be fed into the graph.

[Bruno Luong]

Waoh; you coudn't figure out where is the radial component from

S = [az; el; r]

It's a third row if you pay attention.

[dpb]

To repeat my first comment--

The documentation syntax is pretty clear--

"[azimuth,elevation,r] = cart2sph(x,y,z) transforms corresponding elements of the Cartesian coordinate arrays x, y, and z to spherical coordinates azimuth, elevation, and r."

Nothing says you can't build an output array in whatever form/order you want it, but as Bruno says, "pay attention" to the documentation--it 'splains it all explicitly and even gives examples.

What might be "easier" is all dependent upon what you are actually going to do with the result which we only have in some general use of the word plot but no specific type nor code to know anything about the specific syntax needed to do so.

The above syntax directly from cart2sph has already built such a set of row vectors; if you want to use them. There's no need to necessarily build an array again at all excepting that is the form you asked for in the original question so folks were simply trying to oblige.