id,node_id,number,title,user,state,locked,assignee,milestone,comments,created_at,updated_at,closed_at,author_association,active_lock_reason,draft,pull_request,body,reactions,performed_via_github_app,state_reason,repo,type
1812188730,I_kwDOAMm_X85sA846,8004,Rotation Functional Index example,35968931,open,0,,,2,2023-07-19T15:23:20Z,2023-08-24T13:26:56Z,,MEMBER,,,,"### Is your feature request related to a problem?

I'm trying to think of an example that would demonstrate the ""functional index"" pattern discussed in https://github.com/pydata/xarray/issues/3620.

I think a 2D rotation is the simplest example of an analytically-expressible, non-trivial, domain-agnostic case where you might want to back a set of multiple coordinates with a single functional index. It's also nice because there is additional information that must be passed and stored (the angle of the rotation), but that part is very simple, and domain-agnostic. I'm proposing we make this example work and put it in the custom index docs.

I had a go at making that example ([notebook here](https://gist.github.com/TomNicholas/daa15f71e38f07259c6c2e251d0fb38e)) @benbovy, but I'm confused about a couple of things:

1) How do I implement `.sel` in such a way that it supports indexing with slices (i.e. to crop my image)
2) How can I make this lazy?
3) Should the implementation be a ""MetaIndex"" (i.e. wrapping some pandas indexes)?

### Describe the solution you'd like

_No response_

### Describe alternatives you've considered

_No response_

### Additional context

This example is inspired by @jni's use case in napari, where (IIUC) they want to do a lazy functional affine transformation from pixel to physical coordinates, where the simplest example of such a transform might be a linear shear (caused by the imaging focal plane being at an angle to the physical sample).","{""url"": ""https://api.github.com/repos/pydata/xarray/issues/8004/reactions"", ""total_count"": 1, ""+1"": 1, ""-1"": 0, ""laugh"": 0, ""hooray"": 0, ""confused"": 0, ""heart"": 0, ""rocket"": 0, ""eyes"": 0}",,,13221727,issue