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Designing 2D Colormaps

Usual 1d colormaps can be represented as a path in a 3d colorspace. If the colorspace is uniform, even movement along the path generates a smoothly varying colormap.

This is an example of a 1d colormap that winds through 3d colorspace 1d_colormap

For 2d colormaps, we need to put a surface instead of a path into colorspace. Optimal colorsurfaces need to make a few compromises to use the maximum extend of the colorspace while at the same time remaining as smooth as possible.

Especially at convergent points around black (zero lightness) and white (max lightness), the topology of the color surfaces has to be as even as possible such that the lightness doesn't increase differently in different directions. This ensures that maximum and minimums in displayed functions remain round and don't become star-shaped or shifted towards darker colors like blue and red. At 0.5, the color surfaces can vary a in lightness to make use of strongy saturated colors.

Newwheel2d is a 2d colormap that goes from black to white with maximum saturated colors around 0.5. newwheel2d

Wheel2d is similar to Newwheel but saturates the colors a bit more wheel2d

Darkwheel2d is a 2d colormap that goes from black to light and saturated colors. Exclusion of white allows for better coverage of the saturated corners of the Gamut cube. darkwheel2d

Brightwheel2d the equivalent of Darkwheel starting from white instead of black. I have chosen slightly harder transitions between the six colors in this colormap. brightwheel2d

Smoothwheel2d is the equivalent of wheel2d with even lightness and even angular variations. The colors are smoother and less saturated but lightness is much easier to identify because we don't need to adapt lightness to the hue value smoothwheel2d

comparison with:

complex sine poles and zeros function