python - Project a circle onto a square? -


i have numpy array contains circle.

array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],        [ 0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.],        [ 0.,  0.,  1.,  1.,  1.,  1.,  1.,  0.,  0.],        [ 0.,  0.,  1.,  1.,  1.,  1.,  1.,  0.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  0.,  1.,  1.,  1.,  1.,  1.,  0.,  0.],        [ 0.,  0.,  1.,  1.,  1.,  1.,  1.,  0.,  0.],        [ 0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.],        [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])

this represent gray scale image (ei. it's bigger, , values aren't 1.). centered in array. how can project circle (stretch somehow?) becomes square without being cropped?

so looks this:

array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])

what i'm looking python implementation of conformal transformations, seen in image conformal transformation

you can use maximum , minimum indices of none-zero elements in row , column scope of 1's fill array indices based on scope :

>>> a=np.array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.], ...        [ 0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.], ...        [ 0.,  0.,  1.,  1.,  1.,  1.,  1.,  0.,  0.], ...        [ 0.,  0.,  1.,  1.,  1.,  1.,  1.,  0.,  0.], ...        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.], ...        [ 0.,  0.,  1.,  1.,  1.,  1.,  1.,  0.,  0.], ...        [ 0.,  0.,  1.,  1.,  1.,  1.,  1.,  0.,  0.], ...        [ 0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.], ...        [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]]) >>>  >>> (min_row,max_row),(min_col,max_col)=map(lambda x :(np.min(x),np.max(x)),np.nonzero(a)) >>> a[min_row:max_row+1,min_col:max_col+1]=1 >>> array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  0.],        [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])

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