Integrate paper-style examples and repair 01_basic_polygon.ipynb plotting/runtime path

[Copilot]

This PR proposes the copilot/paper-style-examples updates into main: richer, paper-style example outputs and a notebook reliability fix. It expands the examples surface/contour story and resolves the 01_basic_polygon.ipynb execution issues (3D plotting + local import-path handling).

• examples/demo.py: paper-style example expansion

  • Adds multi-panel delta evolution, smoothness-order (n) comparison, freeform curve gallery, partition/summed-basis surfaces, and an additional wireframe surface view.
  • Keeps the original basic polygon demos while extending output coverage to match Li & Tian-style figure patterns.

• python/implicit_spline/visualization.py: reusable plotting helpers for advanced figures

  • Adds/extends helpers for:
    • smoothness-order comparisons,
    • paper-style contour panel generation,
    • polygon-outline rendering,
    • partition-basis wireframe surface composition,
    • optional wireframe/view controls for 3D surfaces.

• notebooks/01_basic_polygon.ipynb: execution and plotting repair

  • Replaces 2D subplot target axes with explicit 3D axes for surface plots.
  • Makes local import setup robust across common launch locations (repo root / notebooks context).
  • Cleans the affected parameters/smoothness section and uses the helper-based smoothness comparison flow.

• examples/README.md: examples documentation refresh

  • Updates the examples overview to reflect the expanded paper-style demo capabilities.

# notebook pattern used for surface sections (3D-safe)
fig = plt.figure(figsize=(11, 4))
ax1 = fig.add_subplot(1, 2, 1)
ax2 = fig.add_subplot(1, 2, 2, projection='3d')

draw_imp_spline(P_square, delta=delta, n=n, N=N, ax=ax1, title='Contour plot')
draw_surface(P_square, delta=delta, n=n, N=80, ax=ax2, title='Surface plot')

[Copilot]

Pull request overview

This PR expands the project’s Python examples to better match the multi-panel / paper-style figures from Li & Tian (2009), and fixes reliability issues in the basic notebook (notably 3D plotting axes and local import-path handling) so it runs consistently in common environments (Colab, repo root, notebooks/).

Changes:

• Extend examples/demo.py from the original 4 examples to a larger “paper-style” set (delta panels, smoothness-order comparison, freeform gallery, partition/summed-basis surfaces, and an extra wireframe surface view).
• Add/extend reusable visualization helpers (e.g., compare_n, panel_delta_shapes, partition_basis_surfaces, and draw_surface wireframe/view controls) to support these richer figures.
• Repair notebooks/01_basic_polygon.ipynb execution by making surface plotting explicitly 3D-safe and making local imports more robust.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated no comments.

File	Description
notebooks/01_basic_polygon.ipynb	Fixes runtime reliability (robust sys.path setup) and corrects surface plotting by using explicit 3D axes; adopts helper-based smoothness comparison.
examples/demo.py	Expands the standalone demo into a richer, paper-style set of examples and uses shared plotting helpers for consistent figures.
python/implicit_spline/visualization.py	Provides/extends plotting helper functions needed by the new demo/notebook (including compare_n, multi-panel contour helpers, and 3D surface options).
examples/README.md	Updates examples documentation to reflect the expanded demo and paper-style figure capabilities.

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