Got basic timeseries with linestack working. I've also got some code snippets for interpolating to display heatmap with non-uniformly sampled timeseries data. I should be able to have this fully working with time series very soon :D

Got heatmap to display timeseries working. It should also work with non-uniformly sampled data by interpolating, need to test.

Also need to implementing switching between heatmap and line representations, need to delete the graphic when switching.

So timeseries can be represented with arrays of one of the following shapes (let's ignore x-axis values for now).

If we have:

l: number of timeseries
p: number of datapoints in a timeseries

We can have the following shapes:

p: only y-values
p, 2: yz vals
l, p: l-timeseries with y values
l, p 2: l-timeseries with yz values

Extended to n-dimensional arrays (for example, trajectories projected onto principal components?). If each non-timeseries dim is $d_1, d_2, ... d_n$, then the above becomes:

I don't think we can auto-detect if l is present or not and the user should specify, something like:

multi_timeseries: bool = True

Scatters can be similar to some cases of nd-lines 🤔 , but x values would be directly specified and the current index is parametric (example with time indicating position in a low dim space). This would actually be true for lines as well if representing trajectories.

So for nd-line maybe we have two versions, parametric (y and z are not functions of x, but x, y, z are a function of some other dim) and non-parametric (simple timeseries lines where y and z are functions of x).

I made a more generalist NDPositions which can map data that is:

[s1, s2, ... sn, l, p, 2 | 3]

where:
s1, s2, .... sn are slider dims
l is number of lines or number of scatters, this dimension is optional and the user must specify whether or not it exists
2 | 3 is the last dim, indicating xy or xyz positions.

It can map arrays of these dims to a line, line collection, line stack, scatter, or list of scatters (similar to multi-line).

I think this is a much more elegant way to deal with things, and NDTimeSeries is not necessary. The user can provide a slider mapping (to map from reference units to array index) for the p dimension which is the same as the "x-axis" for time series data!

Example if we have data that is [n_timepoints, 2], and the x-positions here (in the last dim) are in seconds. The NDWidget reference units for the slider can also be in seconds, and we can provide a mapping function that goes from the slider reference units to the n_timepoints index.

I think we can also use this for heatmaps and interpolation. Use the reference units to determine a uniform x-range for the current display window, and we can interpolate using [n_timepoints, 2] data.

EDIT: I think that the NDPositions will also work for PolygonGraphic ! Can think about meshes in general later.

For positions graphics, I should actually do [n_datapoints, n_lines, 2 | 3] so everything before the last 1 or 2 dims is always sliders.