Consider adding opt-in support for circular axes when calling `bounds_to_vertices` (related to #594)

Start by reading the bounds_to_vertices implementation and the context in issues #594 and #595. Define the expected behavior for circular_period and start, including seam rotation and periodic axes beyond longitude. Done means an opt-in API handles mixed circular coordinates without NotImplementedError while preserving existing ascending and descending behavior.

Description

The latest bounds_to_vertices() function in cf-xarray v0.10.7+ only handles core dimensions that are in ascending or descending order. Core dims that are in mixed order instead raise a NotImplementedError #595 with a message for the user to normalize coordinates to a monotonic convention (related comment).

Examples

• Ascending

  [0, 1, 2, ..., 357, 358, 359]
  

• Descending

  [359, 358, 357, ..., 2, 1, 0]
  

• Mixed (wraps at seam)

  [0, 1, 2, ..., 179, -180, -179, ..., -1]
  

bounds_to_vertices() works in the first two cases but fails in the third.

Proposed solution

For a long-term solution, it might be worth considering opt-in support for circular axes, e.g.:

bounds_to_vertices(..., circular_period=360.0, start=None)

With circular_period set, cf-xarray could:

• Detect circular monotonicity
• Rotate away from the seam
• Proceed safely as if the dimension were monotonic

While longitude (circular_period=360.0) is the most common use case, the same approach could generalize to other periodic axes (e.g. angles, phases).

Why it is useful

• Users working with model output that mixes 0–360 and −180–180 conventions may encounter NotImplementedError today and must manually normalize coordinates before downstream operations.
• This affects packages such as xESMF, which rely on bounds_to_vertices() but do not implement detection/normalization for circular axes.
• I’ve opened a related xESMF issue for visibility: https://github.com/pangeo-data/xESMF/issues/454