Align examples/demo.py with supported geometry semantics (convex, composed holes, convex-cell partitions)

[Copilot]

The merged demo visuals were rich but semantically misleading in two places: single concave/freeform polygon support and the 2D partition implementation. This PR reshapes those sections so the examples match the current imp_spline_2d contract while preserving paper-style figures.

• Convex-first demo structure

  • Keeps strong convex examples (single polygons, delta sweeps, smoothness (n) comparisons, multi-panel contour evolution).
  • Retains paper-style presentation while making convex behavior the explicit baseline.

• Concave/freeform correction

  • Removes the misleading single-concave-polygon section.
  • Replaces it with a clearly labeled composed field built from multiple convex components.

• Polygons with holes (explicit composition)

  • Keeps hole examples but labels them as composed implicit fields.
  • Uses convex outer/inner loops and consistent terminology to avoid implying unsupported single-polygon concave handling.

• 2D partition correction

  • Replaces loose multi-polygon composition with a valid convex-cell partition (grid cells).
  • Shows both per-cell field behavior and an aggregate view, explicitly labeled as an unnormalized sum (no partition-of-unity claim).

• Docs/helper wording updates

  • Updates examples/README.md and partition_basis_surfaces wording/title to match the corrected semantics.

# Hole example now shown as explicit composition:
Z = imp_spline_2d(X, Y, outer_loop, delta=d, n=2)
for hole in holes:
    Z *= (1.0 - imp_spline_2d(X, Y, hole, delta=d, n=2))
Z = np.clip(Z, 0.0, 1.0)

[Copilot]

Pull request overview

Aligns the example/demo materials with the actual imp_spline_2d semantics (convex-first; concave/freeform shown via explicit composition; partitions shown as convex-cell aggregates) so the visuals don’t imply unsupported single-polygon concave behavior or partition-of-unity properties.

Changes:

• Restructures examples/demo.py to remove the single concave polygon section and replace it with composed fields (convex components, explicit holes composition, convex-cell partition grid + aggregate view).
• Updates partition_basis_surfaces wording/titles to explicitly describe aggregate unnormalized sums.
• Updates examples/README.md to match the corrected semantics and terminology.

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 2 comments.

File	Description
python/implicit_spline/visualization.py	Updates partition_basis_surfaces doc/title to clarify “partition net” + “unnormalized sum” semantics.
examples/README.md	Updates example section descriptions to remove concave/single-polygon implications and clarify composed/partition semantics.
examples/demo.py	Reworks demo sections: composed freeform-like field from convex parts, explicit hole composition, and convex-cell partition + aggregate views.

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.