CODEWITHSUNDEEP
mathnumpygeometrycoordinatespolar-coordinates
Eugene B
Eugene B

Reputation: 1013

Smart way to convert polars to Cartesian coordinates with numpy

I have an array of Cartesian coordinates produced from polars in a usual way:

for k in range(0, Phi_term):
    for j in range(0, R_term):
        X[k,j] = R[j]*np.cos(phi[k]);
        Y[k,j] = R[j]*np.sin(phi[k]);

The problem is that the zeroth element of such an array corresponds to the origin of the polar circle. I would like to have an array of the same elements but starting in the top right corner. For example, elements in the current array distribute in the following way (for the upper half):

11 10 9 6 7 8
14 13 12 3 4 5
17 16 15 0 1 2

(imagine it's a circle). What I want to get is the grid starting with the zeroth element:

0 1 2 3 4 5
6 7 8 9 10 11
12 13 14 15 16 17

though preserving the values, i.e. the value of the 11th element of the initial array is now the value of the 0th element of the new array.

Is there any smart way to perform such a transformation in numpy?

Upvotes: 0

Views: 933

Answers (1)

Phil H
Phil H

Reputation: 20141

def quasiCartesianOrder(arr, R_term, Phi_term):
       # deal with odd phi count by starting from top of top spike.
       rhsOddOffset = 0
       if Phi_term % 2 == 1:
          rhsOddOffset = R_term
          for r in xrange(0, R_term):
             yield (Phi_term + 1)/2 * R_term - r - 1

       # 'rectangular' section, starting down 11 o'clock and up 1 o'clock.
       phiBaseLeft = Phi_term / 2 + rhsOddOffset/R_term
       phiBaseRight = Phi_term / 2
       for phiLine in xrange(0, Phi_term / 2):
          # down 11
          base = (phiBaseLeft + phiLine) * R_term - 1
          for idx in xrange(base + R_term, base, -1):
             yield idx

          # up 1
          base = (phiBaseRight - phiLine ) * R_term
          for idx in xrange(base - R_term, base):
             yield idx

Behaviour:

        11
        10
        9
14 13 12 6 7 8
17 16 15 3 4 5
20 19 18 0 1 2

Becomes

        0
        1
        2
 3 4  5  6  7  8
 9 10 11 12 13 14
15 16 17 18 19 20

Result

11 10 9 14 13 12 6 7 8 17 16 15 3 4 5 20 19 18 0 1 2

The style is a generator, so that you can iterate. If you just want the indices themselves, call list with the returned generator, and you should be able to use that with numpy's index arrays stuff.

Upvotes: 1

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