Msh
The Msh color space is not registered in Color by default
Properties
Name: msh
White Point: D65 / 2˚
Coordinates:
| Name | Range* |
|---|---|
m |
[0, 179.95] |
s |
[0, 1.6] |
h |
[0, 6.283] |
* Space is not bound to the range and is only used as a reference to define percentage inputs/outputs in relation to the Display P3 color space.
Figure 1. The sRGB gamut represented within the Msh color space.
The Msh color space is a polar transform of the CIELab color space developed by Kenneth Moreland. The space aims to help provide better color map for 3D scientific visualizations, specifically divergent color maps, by reducing Mach bands.
Hue Units
While most polar spaces represent hue in degrees, the Msh paper actually defines hues in units of radians. When using
Msh, it is important to be aware of this quirk. When serializing in CSS, you can specify the degree form via
color(--msh 80 1.08 40deg), but the channel is stored in radians by default:
color(--msh 80 1.08 0.69813rad).
Channel Aliases
| Channels | Aliases |
|---|---|
m |
magnitude |
s |
saturation |
h |
hue |
Input/Output
The Msh space is not currently supported in the CSS spec, the parsed input and string output formats use
the color() function format using the custom name --msh:
color(--msh m s h / a) // Color function
When manually creating a color via raw data or specifying a color space as a parameter in a function, the color space name is always used:
Color("msh", [0, 0, 0], 1)
The string representation of the color object and the default string output use the
color(--msh m s h / a) form.
>>> Color("msh", [117.32, 1.0998, 0.69813])
color(--msh 117.32 1.0998 0.69813rad / 1)
>>> Color("msh", [111.45, 0.83341, 1.2765]).to_string()
'color(--msh 111.45 0.83341 1.2765rad)'
Registering
from coloraide import Color as Base
from coloraide.spaces.msh import Msh
class Color(Base): ...
Color.register(Msh())
Creating Divergent Color Maps
The "Diverging Color Maps for Scientific Visualization (Expanded)" paper by Kenneth Moreland outlines an approach to creating better divergent color maps utilizing Msh. It takes two end colors and will inject white between the colors if neither of the sides is unsaturated. It then adjusts the unsaturated color's hue to ensure a smooth transition by adding some "spin" in the radial direction to avoid things like a purple shift in blue.
>>> import math
>>> def prepare_msh_divergent_interpolation(c1, c2):
... """Optimize colors for interpolation."""
...
... hue_cutoff = math.pi / 3
...
... def rad_diff(r1, r2):
... """Get the radian difference."""
...
... diff = abs(r1 - r2)
... return min(diff, math.tau - diff)
...
... def adjust_hue(msh_sat, m_unsat):
... """Adjust hue."""
...
... m_sat, s_sat, h_sat = msh_sat
...
... if m_sat >= m_unsat:
... return h_sat
... else:
... h_spin = s_sat * math.sqrt(m_unsat ** 2 - m_sat ** 2) / (m_sat * math.sin(s_sat))
... if h_sat > -hue_cutoff:
... return h_sat + h_spin
... else:
... return h_sat - h_spin
...
... # Normalize values and and remove NaNs.
... c1 = Color(c1).convert('msh', norm=False).normalize(nans=False)
... c2 = Color(c2).convert('msh', norm=False).normalize(nans=False)
...
... # Msh interpolation logic expects values above 180 degrees (or PI) to be negative.
... if c1['h'] > math.pi:
... c1['h'] -= math.tau
... if c2['h'] > math.pi:
... c2['h'] -= math.tau
...
... # Insert white between saturated colors
... colors = [c1]
... if (c1['s'] > 0.05) and (c2['s'] > 0.05) and (rad_diff(c1['h'], c2['h']) > hue_cutoff):
... mid = max(c1['m'], c2['m'], 88.0)
... colors.append(Color('msh', [mid, 0.0, 0.0]))
... colors.append(c2)
...
... # Adjust hue of unsaturated colors.
... if (colors[1]['s'] < 0.05) and (colors[0]['s'] > 0.05):
... colors[1]['h'] = adjust_hue(colors[0].coords(), colors[1]['m'])
... elif (colors[-2]['s'] < 0.05) and (colors[-1]['s'] > 0.05):
... colors[-2]['h'] = adjust_hue(colors[-1].coords(), colors[-2]['m'])
...
... # If white was inserted, adjust hues of unsaturated color on the right side.
... if len(colors) > 2:
... colors[1] = stop(colors[1], 0.5)
... colors[-2] = stop(colors[-2], 0.5)
...
... return colors
...
>>> Color.interpolate(
... prepare_msh_divergent_interpolation(
... Color('srgb', [0.230, 0.299, 0.754]),
... Color('srgb', [0.706, 0.016, 0.150])
... ),
... space='msh',
... out_space='srgb'
... )
<coloraide.interpolate.linear.InterpolatorLinear object at 0x7f396c946450>
>>> Color.interpolate(
... prepare_msh_divergent_interpolation(
... Color('srgb', [0.436, 0.308, 0.631]),
... Color('srgb', [0.759, 0.334, 0.046])
... ),
... space='msh',
... out_space='srgb'
... )
<coloraide.interpolate.linear.InterpolatorLinear object at 0x7f396c946e50>
>>> Color.interpolate(
... prepare_msh_divergent_interpolation(
... Color('srgb', [0.085, 0.532, 0.201]),
... Color('srgb', [0.436, 0.308, 0.631])
... ),
... space='msh',
... out_space='srgb'
... )
<coloraide.interpolate.linear.InterpolatorLinear object at 0x7f396c946450>
>>> Color.interpolate(
... prepare_msh_divergent_interpolation(
... Color('srgb', [0.217, 0.525, 0.910]),
... Color('srgb', [0.677, 0.492, 0.093])
... ),
... space='msh',
... out_space='srgb'
... )
<coloraide.interpolate.linear.InterpolatorLinear object at 0x7f396c946e50>
>>> Color.interpolate(
... prepare_msh_divergent_interpolation(
... Color('srgb', [0.085, 0.532, 0.201]),
... Color('srgb', [0.758, 0.214, 0.233])
... ),
... space='msh',
... out_space='srgb'
... )
<coloraide.interpolate.linear.InterpolatorLinear object at 0x7f396c946450>