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@endolith endolith/bipolar.py
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WIP: bipolar colormap with bezier curve
#!/usr/bin/env python
"""
Copyright 2012 endolith at gmail com
Copyright 2009 Ged Ridgway at gmail com
Translation and modification of
http://www.mathworks.com/matlabcentral/fileexchange/26026-bipolar-colormap
Based on Manja Lehmann's hand-crafted colormap for cortical visualisation
"""
from __future__ import division
from matplotlib import cm
import numpy as np
# rename to hotcold
def bipolar(lutsize=1024, neutral=0.333, weight=1, interp=[]):
"""
Bipolar hot/cold colormap, with neutral central color.
This colormap is meant for visualizing diverging data; positive
and negative deviations from a central value. It is similar to a
blackbody colormap for positive values, but with a complementary
"cold" colormap for negative values.
Parameters
----------
lutsize : int
The number of elements in the colormap lookup table. (Default is 256.)
neutral : float
The gray value for the neutral middle of the colormap. (Default is
1/3.)
The colormap goes from cyan-blue-neutral-red-yellow if neutral
is < 0.5, and from blue-cyan-neutral-yellow-red if neutral > 0.5.
For shaded 3D surfaces, an `n` near 0.5 is better, because it
minimizes luminance changes that would otherwise obscure shading cues
for determining 3D structure.
For 2D heat maps, an `n` near the 0 or 1 extremes is better, for
maximizing luminance change and showing details of the data.
weight : float
The weight of the Bezier curve at the red and blue points. 1 is a
normal Bezier curve. Greater than one gets closer to pure colors and
banding, less than one does the opposite
interp : str or int, optional
Specifies the type of interpolation.
('linear', 'nearest', 'zero', 'slinear', 'quadratic, 'cubic')
or as an integer specifying the order of the spline interpolator
to use. Default is 'linear'. See `scipy.interpolate.interp1d`.
Returns
-------
out : matplotlib.colors.LinearSegmentedColormap
The resulting colormap object
Notes
-----
If neutral is exactly 0.5, then a map which yields a linear increase in
intensity when converted to grayscale is produced. This colormap should
also be reasonably good
for colorblind viewers, as it avoids green and is predominantly based on
the purple-yellow pairing which is easily discriminated by the two common
types of colorblindness. [2]_
Examples
--------
>>> from mpl_toolkits.mplot3d import axes3d
>>> from matplotlib import cm
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> from bipolar import bipolar
>>> fig = plt.figure()
>>> ax = fig.gca(projection='3d')
>>> X, Y, Z = axes3d.get_test_data(0.05)
>>> ax.plot_surface(X, Y, Z, rstride=1, cstride=1, linewidth=0.1,
>>> cmap=bipolar(),
>>> vmax=abs(Z).max(), vmin=-abs(Z).max())
>>> fig.colorbar()
>>> plt.show()
>>> set_cmap(bipolar(201))
>>> waitforbuttonpress()
>>> set_cmap(bipolar(201, 0.1)) # dark gray as neutral
>>> waitforbuttonpress()
>>> set_cmap(bipolar(201, 0.9)) # light gray as neutral
>>> waitforbuttonpress()
>>> set_cmap(bipolar(201, 0.5)) # grayscale-friendly colormap
References
----------
.. [1] Lehmann Manja, Crutch SJ, Ridgway GR et al. "Cortical thickness
and voxel-based morphometry in posterior cortical atrophy and typical
Alzheimer's disease", Neurobiology of Aging, 2009,
doi:10.1016/j.neurobiolaging.2009.08.017
.. [2] Brewer, Cynthia A., "Guidelines for Selecting Colors for
Diverging Schemes on Maps", The Cartographic Journal, Volume 33,
Number 2, December 1996, pp. 79-86(8)
http://www.ingentaconnect.com/content/maney/caj/1996/00000033/00000002/art00002
"""
n = neutral
if n < 0.5:
if not interp:
interp = 'linear' # seems to work well with dark neutral colors
# cyan-blue-dark-red-yellow
data = (
(0, 1, 1), # cyan
(0, 0, 1), # blue
(n, n, n), # dark neutral
(1, 0, 0), # red
(1, 1, 0), # yellow
)
elif n >= 0.5:
if not interp:
interp = 'cubic' # seems to work better with bright neutral colors
# blue-cyan-light-yellow-red
# produces bright yellow or cyan rings otherwise
data = (
(0, 0, 1), # blue
(0, 1, 1), # cyan
(n, n, n), # light neutral
(1, 1, 0), # yellow
(1, 0, 0), # red
)
else:
raise ValueError('n must be 0.0 < n < 1.0')
t = np.linspace(0, 1, lutsize/2)
# t = t**(3)
# Super ugly Bezier curve
# Do 2, one for each half, from nnn to 100 and from 001 to nnn
x1 = data[2][0]
y1 = data[2][1]
z1 = data[2][2]
xc = data[1][0]
yc = data[1][1]
zc = data[1][2]
x2 = data[0][0]
y2 = data[0][1]
z2 = data[0][2]
w = weight
r1 = (((1 - t)**2*x1 + 2*(1 - t)*t*w*xc + t**2*x2) /
((1 - t)**2 + 2*(1 - t)*t*w + t**2))
g1 = (((1 - t)**2*y1 + 2*(1 - t)*t*w*yc + t**2*y2) /
((1 - t)**2 + 2*(1 - t)*t*w + t**2))
b1 = (((1 - t)**2*z1 + 2*(1 - t)*t*w*zc + t**2*z2) /
((1 - t)**2 + 2*(1 - t)*t*w + t**2))
x1 = data[2][0]
y1 = data[2][1]
z1 = data[2][2]
xc = data[3][0]
yc = data[3][1]
zc = data[3][2]
x2 = data[4][0]
y2 = data[4][1]
z2 = data[4][2]
r2 = (((1 - t)**2*x1 + 2*(1 - t)*t*w*xc + t**2*x2) /
((1 - t)**2 + 2*(1 - t)*t*w + t**2))
g2 = (((1 - t)**2*y1 + 2*(1 - t)*t*w*yc + t**2*y2) /
((1 - t)**2 + 2*(1 - t)*t*w + t**2))
b2 = (((1 - t)**2*z1 + 2*(1 - t)*t*w*zc + t**2*z2) /
((1 - t)**2 + 2*(1 - t)*t*w + t**2))
rgb1 = np.dstack((r1, g1, b1))[0]
rgb2 = np.dstack((r2, g2, b2))[0]
ynew = np.concatenate((rgb1[1:][::-1], rgb2))
return cm.colors.LinearSegmentedColormap.from_list('bipolar', ynew,
lutsize)
if __name__ == "__main__":
import matplotlib.pyplot as plt
def relative_luminance(RGB):
R, G, B = RGB
Y = 0.2126 * R + 0.7152 * G + 0.0722 * B
return Y
dx, dy = 0.01, 0.01
def func3(x, y):
# Sinusoid clearly shows edges, bands, or halos in the colormap
return np.sin(x) + np.sin(y)
x = np.arange(-4.0, 4.0001, dx)
y = np.arange(-4.0, 4.0001, dy)
X, Y = np.meshgrid(x, y)
Z = func3(X, Y)
plt.figure()
im = plt.imshow(Z, vmax=abs(Z).max(), vmin=-abs(Z).max(),
origin='lower',
extent=[-3, 3, -3, 3],
cmap=bipolar(neutral=0, lutsize=1024), # my favorite
)
plt.colorbar()
plt.show()
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endolith commented Dec 19, 2014

if I ever clean this up I will delete it and put it here: https://gist.github.com/endolith/2879736

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endolith commented Mar 3, 2016

Example:
my favorite

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