dipy/viz/colormap.py
def boys2rgb(v):
    """ boys 2 rgb cool colormap

    Maps a given field of undirected lines (line field) to rgb colors using
    Boy's Surface immersion of the real projective plane.

    Boy's Surface is one of the three possible surfaces obtained by gluing a
    Mobius strip to the edge of a disk. The other two are the crosscap and
    Roman surface, Steiner surfaces that are homeomorphic to the real
    projective plane (Pinkall 1986). The Boy's surface is the only 3D
    immersion of the projective plane without singularities.

    Visit http://hci.stanford.edu/~cagatay//rp2coloring/index.html for
    further details. Cagatay Demiralp, 9/7/2008.

    Code was initially in matlab and was rewritten in Python for dipy by
    the Dipy Team. Thank you Cagatay for putting this online.

    Parameters
    ------------

    v : array, shape (N, 3) of unit vectors (e.g., principal eigenvectors of
       tensor data) representing one of the two directions of the
       undirected lines in a line field.

    Returns
    ---------

    c : array, shape (N, 3) matrix of rgb colors corresponding to the vectors
           given in V.

    Examples
    ----------

    >>> from dipy.viz import colormap
    >>> v=np.array([[1,0,0],[0,1,0],[0,0,1]])
    >>> c=colormap.boys2rgb(v)

    """

    if v.ndim == 1:
        x = v[0]
        y = v[1]
        z = v[2]

    if v.ndim == 2:
        x = v[:, 0]
        y = v[:, 1]
        z = v[:, 2]

    x2 = x**2
    y2 = y**2
    z2 = z**2

    x3 = x*x2
    y3 = y*y2
    z3 = z*z2

    z4 = z*z2

    xy = x*y
    xz = x*z
    yz = y*z

    hh1 = .5 * (3 * z2 - 1)/1.58
    hh2 = 3 * xz/2.745
    hh3 = 3 * yz/2.745
    hh4 = 1.5 * (x2 - y2)/2.745
    hh5 = 6 * xy/5.5
    hh6 = (1/1.176) * .125 * (35 * z4 - 30 * z2 + 3)
    hh7 = 2.5 * x * (7 * z3 - 3*z)/3.737
    hh8 = 2.5 * y * (7 * z3 - 3*z)/3.737
    hh9 = ((x2 - y2) * 7.5 * (7 * z2 - 1))/15.85
    hh10 = ((2 * xy) * (7.5 * (7 * z2 - 1)))/15.85
    hh11 = 105 * (4 * x3 * z - 3 * xz * (1 - z2))/59.32
    hh12 = 105 * (-4 * y3 * z + 3 * yz * (1 - z2))/59.32

    s0 = -23.0
    s1 = 227.9
    s2 = 251.0
    s3 = 125.0

    ss23 = ss(2.71, s0)
    cc23 = cc(2.71, s0)

    ss45 = ss(2.12, s1)
    cc45 = cc(2.12, s1)

    ss67 = ss(.972, s2)
    cc67 = cc(.972, s2)

    ss89 = ss(.868, s3)
    cc89 = cc(.868, s3)

    X = 0.0

    X = X + hh2 * cc23
    X = X + hh3 * ss23
    X = X + hh5 * cc45
    X = X + hh4 * ss45

    X = X + hh7 * cc67
    X = X + hh8 * ss67
    X = X + hh10 * cc89
    X = X + hh9 * ss89

    Y = 0.0
    Y = Y + hh2 * -ss23
    Y = Y + hh3 * cc23
    Y = Y + hh5 * -ss45
    Y = Y + hh4 * cc45
    Y = Y + hh7 * -ss67
    Y = Y + hh8 * cc67
    Y = Y + hh10 * -ss89
    Y = Y + hh9 * cc89

    Z = 0.0
    Z = Z + hh1 * -2.8
    Z = Z + hh6 * -0.5
    Z = Z + hh11 * 0.3
    Z = Z + hh12 * -2.5

    # Scale and normalize to fit in the rgb space.
    w_x = 4.1925
    trl_x = -2.0425

    w_y = 4.0217
    trl_y = -1.8541

    w_z = 4.0694
    trl_z = -2.1899

    if v.ndim == 2:
        N = len(x)
        C = np.zeros((N, 3))
        C[:, 0] = 0.9 * np.abs(((X-trl_x)/w_x)) + 0.05
        C[:, 1] = 0.9 * np.abs(((Y-trl_y)/w_y)) + 0.05
        C[:, 2] = 0.9 * np.abs(((Z-trl_z)/w_z)) + 0.05

    if v.ndim == 1:
        C = np.zeros((3,))
        C[0] = 0.9 * np.abs(((X-trl_x)/w_x)) + 0.05
        C[1] = 0.9 * np.abs(((Y-trl_y)/w_y)) + 0.05
        C[2] = 0.9 * np.abs(((Z-trl_z)/w_z)) + 0.05

    return C
 boys 2 rgb cool colormap

    Maps a given field of undirected lines (line field) to rgb colors using
    Boy's Surface immersion of the real projective plane.

    Boy's Surface is one of the three possible surfaces obtained by gluing a
    Mobius strip to the edge of a disk. The other two are the crosscap and
    Roman surface, Steiner surfaces that are homeomorphic to the real
    projective plane (Pinkall 1986). The Boy's surface is the only 3D
    immersion of the projective plane without singularities.

    Visit http://hci.stanford.edu/~cagatay//rp2coloring/index.html for
    further details. Cagatay Demiralp, 9/7/2008.

    Code was initially in matlab and was rewritten in Python for dipy by
    the Dipy Team. Thank you Cagatay for putting this online.

    Parameters
    ------------

    v : array, shape (N, 3) of unit vectors (e.g., principal eigenvectors of
       tensor data) representing one of the two directions of the
       undirected lines in a line field.

    Returns
    ---------

    c : array, shape (N, 3) matrix of rgb colors corresponding to the vectors
           given in V.

    Examples
    ----------

    >>> from dipy.viz import colormap
    >>> v=np.array([[1,0,0],[0,1,0],[0,0,1]])
    >>> c=colormap.boys2rgb(v)

    
boys 2 rgb cool colormap
Maps a given field of undirected lines (line field) to rgb colors using
Boy's Surface immersion of the real projective plane.

Boy's Surface is one of the three possible surfaces obtained by gluing a
Mobius strip to the edge of a disk. The other two are the crosscap and
Roman surface, Steiner surfaces that are homeomorphic to the real
projective plane (Pinkall 1986). The Boy's surface is the only 3D
immersion of the projective plane without singularities.



Code was initially in matlab and was rewritten in Python for dipy by
the Dipy Team. Thank you Cagatay for putting this online.

Parameters

v : array, shape (N, 3) of unit vectors  representing one of the two directions of the
undirected lines in a line field.

Returns

c : array, shape (N, 3) matrix of rgb colors corresponding to the vectors
given in V.

Examples


boys 2 rgb cool colormap Maps a given field of undirected lines ( line field ) to rgb colors using Boy ' s Surface immersion of the real projective plane . Boy ' s Surface is one of the three possible surfaces obtained by gluing a Mobius strip to the edge of a disk . The other two are the crosscap and Roman surface Steiner surfaces that are homeomorphic to the real projective plane ( Pinkall 1986 ) . The Boy ' s surface is the only 3D immersion of the projective plane without singularities . Code was initially in matlab and was rewritten in Python for dipy by the Dipy Team . Thank you Cagatay for putting this online . Parameters v : array shape ( N 3 ) of unit vectors representing one of the two directions of the undirected lines in a line field . Returns c : array shape ( N 3 ) matrix of rgb colors corresponding to the vectors given in V . Examples
def boys2rgb(v):
    if v.ndim == 1:
        x = v[0]
        y = v[1]
        z = v[2]
    if v.ndim == 2:
        x = v[:, 0]
        y = v[:, 1]
        z = v[:, 2]
    x2 = x**2
    y2 = y**2
    z2 = z**2
    x3 = x*x2
    y3 = y*y2
    z3 = z*z2
    z4 = z*z2
    xy = x*y
    xz = x*z
    yz = y*z
    hh1 = .5 * (3 * z2 - 1)/1.58
    hh2 = 3 * xz/2.745
    hh3 = 3 * yz/2.745
    hh4 = 1.5 * (x2 - y2)/2.745
    hh5 = 6 * xy/5.5
    hh6 = (1/1.176) * .125 * (35 * z4 - 30 * z2 + 3)
    hh7 = 2.5 * x * (7 * z3 - 3*z)/3.737
    hh8 = 2.5 * y * (7 * z3 - 3*z)/3.737
    hh9 = ((x2 - y2) * 7.5 * (7 * z2 - 1))/15.85
    hh10 = ((2 * xy) * (7.5 * (7 * z2 - 1)))/15.85
    hh11 = 105 * (4 * x3 * z - 3 * xz * (1 - z2))/59.32
    hh12 = 105 * (-4 * y3 * z + 3 * yz * (1 - z2))/59.32
    s0 = -23.0
    s1 = 227.9
    s2 = 251.0
    s3 = 125.0
    ss23 = ss(2.71, s0)
    cc23 = cc(2.71, s0)
    ss45 = ss(2.12, s1)
    cc45 = cc(2.12, s1)
    ss67 = ss(.972, s2)
    cc67 = cc(.972, s2)
    ss89 = ss(.868, s3)
    cc89 = cc(.868, s3)
    X = 0.0
    X = X + hh2 * cc23
    X = X + hh3 * ss23
    X = X + hh5 * cc45
    X = X + hh4 * ss45
    X = X + hh7 * cc67
    X = X + hh8 * ss67
    X = X + hh10 * cc89
    X = X + hh9 * ss89
    Y = 0.0
    Y = Y + hh2 * -ss23
    Y = Y + hh3 * cc23
    Y = Y + hh5 * -ss45
    Y = Y + hh4 * cc45
    Y = Y + hh7 * -ss67
    Y = Y + hh8 * cc67
    Y = Y + hh10 * -ss89
    Y = Y + hh9 * cc89
    Z = 0.0
    Z = Z + hh1 * -2.8
    Z = Z + hh6 * -0.5
    Z = Z + hh11 * 0.3
    Z = Z + hh12 * -2.5
    w_x = 4.1925
    trl_x = -2.0425
    w_y = 4.0217
    trl_y = -1.8541
    w_z = 4.0694
    trl_z = -2.1899
    if v.ndim == 2:
        N = len(x)
        C = np.zeros((N, 3))
        C[:, 0] = 0.9 * np.abs(((X-trl_x)/w_x)) + 0.05
        C[:, 1] = 0.9 * np.abs(((Y-trl_y)/w_y)) + 0.05
        C[:, 2] = 0.9 * np.abs(((Z-trl_z)/w_z)) + 0.05
    if v.ndim == 1:
        C = np.zeros((3,))
        C[0] = 0.9 * np.abs(((X-trl_x)/w_x)) + 0.05
        C[1] = 0.9 * np.abs(((Y-trl_y)/w_y)) + 0.05
        C[2] = 0.9 * np.abs(((Z-trl_z)/w_z)) + 0.05
    return C
def boys2rgb ( v ) : if v . ndim == 1 : x = v [ 0 ] y = v [ 1 ] z = v [ 2 ] if v . ndim == 2 : x = v [ : , 0 ] y = v [ : , 1 ] z = v [ : , 2 ] x2 = x ** 2 y2 = y ** 2 z2 = z ** 2 x3 = x * x2 y3 = y * y2 z3 = z * z2 z4 = z * z2 xy = x * y xz = x * z yz = y * z hh1 = .5 * ( 3 * z2 - 1 ) / 1.58 hh2 = 3 * xz / 2.745 hh3 = 3 * yz / 2.745 hh4 = 1.5 * ( x2 - y2 ) / 2.745 hh5 = 6 * xy / 5.5 hh6 = ( 1 / 1.176 ) * .125 * ( 35 * z4 - 30 * z2 + 3 ) hh7 = 2.5 * x * ( 7 * z3 - 3 * z ) / 3.737 hh8 = 2.5 * y * ( 7 * z3 - 3 * z ) / 3.737 hh9 = ( ( x2 - y2 ) * 7.5 * ( 7 * z2 - 1 ) ) / 15.85 hh10 = ( ( 2 * xy ) * ( 7.5 * ( 7 * z2 - 1 ) ) ) / 15.85 hh11 = 105 * ( 4 * x3 * z - 3 * xz * ( 1 - z2 ) ) / 59.32 hh12 = 105 * ( - 4 * y3 * z + 3 * yz * ( 1 - z2 ) ) / 59.32 s0 = - 23.0 s1 = 227.9 s2 = 251.0 s3 = 125.0 ss23 = ss ( 2.71 , s0 ) cc23 = cc ( 2.71 , s0 ) ss45 = ss ( 2.12 , s1 ) cc45 = cc ( 2.12 , s1 ) ss67 = ss ( .972 , s2 ) cc67 = cc ( .972 , s2 ) ss89 = ss ( .868 , s3 ) cc89 = cc ( .868 , s3 ) X = 0.0 X = X + hh2 * cc23 X = X + hh3 * ss23 X = X + hh5 * cc45 X = X + hh4 * ss45 X = X + hh7 * cc67 X = X + hh8 * ss67 X = X + hh10 * cc89 X = X + hh9 * ss89 Y = 0.0 Y = Y + hh2 * - ss23 Y = Y + hh3 * cc23 Y = Y + hh5 * - ss45 Y = Y + hh4 * cc45 Y = Y + hh7 * - ss67 Y = Y + hh8 * cc67 Y = Y + hh10 * - ss89 Y = Y + hh9 * cc89 Z = 0.0 Z = Z + hh1 * - 2.8 Z = Z + hh6 * - 0.5 Z = Z + hh11 * 0.3 Z = Z + hh12 * - 2.5 w_x = 4.1925 trl_x = - 2.0425 w_y = 4.0217 trl_y = - 1.8541 w_z = 4.0694 trl_z = - 2.1899 if v . ndim == 2 : N = len ( x ) C = np . zeros ( ( N , 3 ) ) C [ : , 0 ] = 0.9 * np . abs ( ( ( X - trl_x ) / w_x ) ) + 0.05 C [ : , 1 ] = 0.9 * np . abs ( ( ( Y - trl_y ) / w_y ) ) + 0.05 C [ : , 2 ] = 0.9 * np . abs ( ( ( Z - trl_z ) / w_z ) ) + 0.05 if v . ndim == 1 : C = np . zeros ( ( 3 , ) ) C [ 0 ] = 0.9 * np . abs ( ( ( X - trl_x ) / w_x ) ) + 0.05 C [ 1 ] = 0.9 * np . abs ( ( ( Y - trl_y ) / w_y ) ) + 0.05 C [ 2 ] = 0.9 * np . abs ( ( ( Z - trl_z ) / w_z ) ) + 0.05 return C
boys 2 rgb cool colormap
Maps a given field of undirected lines (line field) to rgb colors using
Boy's Surface immersion of the real projective plane.
boys 2 rgb cool colormap Maps a given field of undirected lines ( line field ) to rgb colors using Boy ' s Surface immersion of the real projective plane .
""" boys 2 rgb cool colormap

    Maps a given field of undirected lines (line field) to rgb colors using
    Boy's Surface immersion of the real projective plane.

    Boy's Surface is one of the three possible surfaces obtained by gluing a
    Mobius strip to the edge of a disk. The other two are the crosscap and
    Roman surface, Steiner surfaces that are homeomorphic to the real
    projective plane (Pinkall 1986). The Boy's surface is the only 3D
    immersion of the projective plane without singularities.

    Visit http://hci.stanford.edu/~cagatay//rp2coloring/index.html for
    further details. Cagatay Demiralp, 9/7/2008.

    Code was initially in matlab and was rewritten in Python for dipy by
    the Dipy Team. Thank you Cagatay for putting this online.

    Parameters
    ------------

    v : array, shape (N, 3) of unit vectors (e.g., principal eigenvectors of
       tensor data) representing one of the two directions of the
       undirected lines in a line field.

    Returns
    ---------

    c : array, shape (N, 3) matrix of rgb colors corresponding to the vectors
           given in V.

    Examples
    ----------

    >>> from dipy.viz import colormap
    >>> v=np.array([[1,0,0],[0,1,0],[0,0,1]])
    >>> c=colormap.boys2rgb(v)

    """ # Scale and normalize to fit in the rgb space.
v