Reprojecting polar to cartesian grid
Question: I have a polar (r,theta) grid (which means that each cell is an annulus
section) containing values of some physical quantity (e.g. temperature), and I
would like to re-grid (or re-project) these values onto a cartesian grid. Are
there any Python packages that can do this?

I am not interested in converting the coordinates of the centers of the cells
from polar to cartesian - this is very easy. Instead, I'm looking for a
package that can actually re-grid the data properly.

Thanks for any suggestions!


Answer: Thanks for your answers - after thinking a bit more about this I came up with
the following code:

    
    
    import numpy as np
    
    import matplotlib
    matplotlib.use('Agg')
    import matplotlib.pyplot as mpl
    
    from scipy.interpolate import interp1d
    from scipy.ndimage import map_coordinates
    
    
    def polar2cartesian(r, t, grid, x, y, order=3):
    
        X, Y = np.meshgrid(x, y)
    
        new_r = np.sqrt(X*X+Y*Y)
        new_t = np.arctan2(X, Y)
    
        ir = interp1d(r, np.arange(len(r)), bounds_error=False)
        it = interp1d(t, np.arange(len(t)))
    
        new_ir = ir(new_r.ravel())
        new_it = it(new_t.ravel())
    
        new_ir[new_r.ravel() > r.max()] = len(r)-1
        new_ir[new_r.ravel() < r.min()] = 0
    
        return map_coordinates(grid, np.array([new_ir, new_it]),
                                order=order).reshape(new_r.shape)
    
    # Define original polar grid
    
    nr = 10
    nt = 10
    
    r = np.linspace(1, 100, nr)
    t = np.linspace(0., np.pi, nt)
    z = np.random.random((nr, nt))
    
    # Define new cartesian grid
    
    nx = 100
    ny = 200
    
    x = np.linspace(0., 100., nx)
    y = np.linspace(-100., 100., ny)
    
    # Interpolate polar grid to cartesian grid (nearest neighbor)
    
    fig = mpl.figure()
    ax = fig.add_subplot(111)
    ax.imshow(polar2cartesian(r, t, z, x, y, order=0), interpolation='nearest')
    fig.savefig('test1.png')
    
    # Interpolate polar grid to cartesian grid (cubic spline)
    
    fig = mpl.figure()
    ax = fig.add_subplot(111)
    ax.imshow(polar2cartesian(r, t, z, x, y, order=3), interpolation='nearest')
    fig.savefig('test2.png')
    

Which is not strictly re-gridding, but works fine for what I need. Just
posting the code in case it is useful to anyone else. Feel free to suggest
improvements!

