MATLAB: Creating an Array for Different Radial Positions

MATLAB

I am basically looking to take a point in spherical polar coordinates such that theta = 0, phi = pi/2 and r = 1, then extend outwards at the same angles but increasing the radius by 0.2 each time until a radius of 10 is reached.

Corresponding to each of these points on a radial line, I then need a 3 x 46 array such that each 3 x 1 vector in the array corresponds to the position of each of the consecutive radial points in Cartesian coordinates, what would be the easiest way of doing this? Please let me know if this is not clear.

Best Answer

theta = 0;
phi   = pi/2;
r = 1 : 0.2 : 10;
theta = repmat(theta,size(r));
phi   = repmat(phi,  size(r));
[x,y,z] = sph2cart(theta,phi,r);
xyz = [x; y; z];

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MATLAB: Loop not working properly

What you are observing seems correct to me.

theta is 0, and phi is constant. This means that even as r increases

y is zero (because theta is 0)
x and z increase in proportion to each other

(You can see this is true in the xyz array, if you place a breakpoint and look at the values).

Therefore, the normal vector always points in the same direction -- and is constant because it is also normalized.

All seems well.

Side note:

You can take the calculation

normal=(p(1:3,II)/(norm(p(1:3,II))))';

outside of the IJ loop, because its value doesn't depend on IJ. Just calculate it once for ever II loop.

MATLAB: Creating a Matrix from Distances between Vectors

This can be achieved easily without a loop:

%demo data
m = 46
n = 100
A = rand(3,m)
B = rand(3,n)
distance = sqrt(sum((permute(A, [2, 3, 1]) - permute(B, [3, 2, 1])).^2, 3));

The result is a mxn matrix. It basically moves the (X, Y, Z) of each point into the 3rd dimension for both matrix, and move the 2nd dimension of the 1st matrix into the 1st. So points in A are along the rows, and points in B are along the column (and coordinates across the 3rd for both). We now have compatible array sizes, so can create a 3D matrix of (Xa-Xb, Ya-Yb, Za-Zb) for all the points. Square that, sum across (X, Y, Z) so it reduces to a 2D matrix, and take the square root for the distance.

Or, if you have the stats toolbox, you can use pdist2.

edit: Note that if you want to store the vectors between the points as suggested by Jon instead of the distance (norm of the vectors), then it's simply:

vectors = permute(A, [2, 3, 1]) - permute(B, [3, 2, 1])

vectors(p1, p2, :) is the vector between point A(:, p1) and point B(:, p2).

Best Answer

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MATLAB: Loop not working properly

MATLAB: Creating a Matrix from Distances between Vectors

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