Support sequential (✅), divergent, and cyclic colormaps

[mfisher87]

Use case

Eventually users will want to use colormaps to display data with multiple critical values. Sequential colormaps have two critical values: the minimum and the maximum. For example, viridis transitions from low-lightness to high-lightness. Currently we only support sequential colormaps (plus rainbow/jet, which is kind of a special case with implicit critical values that actually distort the perception of the underlying data).

A divergent colormap has a critical value in the center, many times that's 0, and the extremes diverge from that value, e.g. "balance":

Cyclical colormaps are... cyclical! They begin and end with the same value (e.g. 0 degrees is the same direction as 360 degrees), e.g. "phase":

Preferred solution

Prioritize divergent colormaps, as that's a much more common use case than cyclical.

Support a new "type" attribute for colormaps so our code can tell the difference for the purpose of displaying tick marks on legends (#880) -- divergent colormaps need a tick mark at the critical value (usually in the center), and sequential ones don't.

Enable users to set a minimum and maximum value for the colormap to interpolate across, this way divergent colormaps can be calibrated with 0 (or whatever the critical value is) in the middle (#137).

Think about the "mode" field for divergent colormaps. Quantiles, for example, can pull the distribution towards one side and misalign the critical value. Not sure off the top of my head what the best solution for this is.

For legends, display the critical values in the legend. For sequential colormaps, we only need to display the minimum and maximum. For divergent, we need to display the central critical value too. For cyclical... 🤷

[nakul-py]

@mfisher87, which colors do you want we should support from Divergent, Cyclic, Sequential, Sequential 2, and there are other colormaps also as we also have some of these in cmocean cplormaps.

[nakul-py]

I think we have do do this?

• Add a type attribute to colormaps.
  Extend colormap metadata to include type: 'sequential' | 'divergent' | 'cyclic'.
• Handle divergent colormaps first
  Divergent colormaps need a critical value. Ensure interpolation splits at that value: [min -> critical] and [critical -> max].
• Add UI fields so users can see:
  Sequential -> min & max.
  Divergent -> min, max, and critical (default 0).
  Cyclic -> min & max
• Implement basic support (min & max, wrap-around interpolation).
  Legends can show ticks.
  Divergent -> ticks: [min, critical, max].

(confusing in will sequential and cyclical also needs ticks and about quantile mode)

[mfisher87]

This looks correct, thanks Nakul for fleshing it out!

For this ticket, let's not add any new sequential colormaps, we've got lots of those. Let's start with only divergent in the first PR, and I have no huge preference about which ones we add. cmocean's "balance" is cool :)

Divergent -> min, max, and critical (default 0).

I don't think we should add a UI field to set the critical value, because the critical value is baked into the colormap (at the center in most cases) and the user can't change it without skewing the colormap. Perhaps we can display the critical value? We'd need an additional attribute of colormaps for "critical values". For example oxy has critical values at 0.2 and 0.8.

(confusing in will sequential and cyclical also needs ticks and about quantile mode)

Let's punt on quantiles for now, it needs some more design thought. 🤔 Sequential should definitely have min/max ticks. cyclical ticks is a harder question -- let's punt on that as well. The min/max have the same color! Not sure how to handle that yet.