Skip to content

Expand Python/Colab demos to explicitly cover concave, holes, and 2D partition workflows #6

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
QL-UoHull merged 4 commits into from
Jul 16, 2026
Merged

Expand Python/Colab demos to explicitly cover concave, holes, and 2D partition workflows #6

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
4 commits
Select commit Hold shift + click to select a range
07f9305
Initial plan
Copilot Jul 16, 2026
b5dc514
Extend demo and notebook with concave hole and partition examples
Copilot Jul 16, 2026
e96f176
Normalize notebook cell formatting after validation feedback
Copilot Jul 16, 2026
e8e966f
Polish demo wording and notebook delta markdown
Copilot Jul 16, 2026
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
28 changes: 14 additions & 14 deletions examples/README.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -4,8 +4,8 @@ Runnable examples are available in three forms:

## Standalone Python script (`demo.py`)

A self-contained demo that now goes beyond the original four basic examples and
includes paper-style figures inspired by Li & Tian (2009):
A self-contained demo organized by feature category, with paper-style figures
inspired by Li & Tian (2009):

```bash
# from the repository root
Expand All @@ -14,21 +14,20 @@ python examples/demo.py

The script includes:

1. unit square contour,
2. equilateral triangle contour,
3. regular pentagon contour,
4. delta sweep for an irregular polygon,
5. smoothness-order (`n`) sweep,
6. a six-panel paper-style contour figure showing how the implicit curve evolves
as `delta` increases,
7. a four-panel freeform implicit-curve gallery, and
8. a polygon-partition / summed-basis surface figure in the style of the paper.
1. **convex polygon** demos (square/triangle/pentagon),
2. convex **delta-sweep** and **smoothness-order** (`n`) comparisons,
3. paper-style multi-panel contour evolution under varying `delta`,
4. explicit **concave/freeform polygon** contour demos,
5. **polygons with holes** (single hole + multiple holes + hole delta panel), and
6. a true multi-polygon **2D partition** section showing both:
- the partition net itself, and
- the resulting family / sum of basis-function surfaces.

## Jupyter Notebooks (`../notebooks/`)

| Notebook | Description |
|----------|-------------|
| [`01_basic_polygon.ipynb`](../notebooks/01_basic_polygon.ipynb) | Basic usage with hard-coded polygons, delta/n sweeps |
| [`01_basic_polygon.ipynb`](../notebooks/01_basic_polygon.ipynb) | Colab-visible demos for convex, concave, holes, and partition examples |
| [`02_data_from_file.ipynb`](../notebooks/02_data_from_file.ipynb) | Load polygon from `../data/sample_polygon.txt` |

## MATLAB Scripts (`../matlab/`)
Expand All @@ -48,8 +47,9 @@ The new advanced examples are intended to better match the kinds of figures
shown in the paper:

- multi-panel contour evolution under increasing `delta`,
- freeform curve design from hand-crafted control polygons, and
- 3D wireframe surface views of summed polygon basis functions.
- freeform / concave curve design from hand-crafted polygons,
- polygon-with-hole examples, and
- 2D partition-based basis-function surfaces.

These examples are illustrative rather than exact reproductions of any one
figure from the paper, but they provide a much closer visual and conceptual
Expand Down
130 changes: 80 additions & 50 deletions examples/demo.py
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -3,12 +3,13 @@
-------
Standalone Python demonstration of the 2D Piecewise Algebraic Implicit Spline.

This demo is organized around the three main modeling scenarios highlighted in
Li & Tian (2009):
This demo extends the paper's core scenarios and is organized into four
feature-focused sections:

1. Convex polygons
2. Polygons with holes
3. Collections of polygons forming a 2D partition
2. Concave / freeform polygons
3. Polygons with holes
4. Collections of polygons forming a 2D partition

It also includes paper-style multi-panel figures inspired by the examples shown
in the paper.
Expand Down Expand Up @@ -164,43 +165,72 @@ def plot_polygon_with_holes(outer, holes, delta=0.15, n=2, N=320, title=None):
fig6.canvas.manager.set_window_title("Demo — Convex polygon paper-style delta panel")

# ============================================================================
# 2. POLYGONS WITH HOLES
# 2. CONCAVE / FREEFORM POLYGONS
# ============================================================================
print("Category 2: polygons with holes")
print("Category 2: concave / freeform polygons")

# Example 7: Triangle with inner triangular hole
print(" Example 7: triangle with a hole")
# Example 7: Concave polygon ("arrowhead")
print(" Example 7: concave polygon")
Comment on lines +170 to +173
P_concave = np.array([
[-1.00, -0.62], [-0.20, -0.20], [0.15, -0.76], [1.02, -0.25],
[0.30, 0.02], [0.92, 0.82], [0.00, 0.40], [-0.88, 0.92], [-0.55, 0.02],
], dtype=float)
fig7, ax7 = plt.subplots(figsize=(6.2, 5.2))
draw_imp_spline(P_concave, delta=0.18, n=2, N=320, ax=ax7,
title=r"Concave polygon ($\delta=0.18$, $n=2$)")
fig7.canvas.manager.set_window_title("Demo — Concave polygon")
plt.tight_layout()

# Example 8: Paper-style multi-panel concave contour evolution
print(" Example 8: concave polygon contour evolution under varying delta")
fig8 = panel_delta_shapes(
P_concave,
deltas=(0.05, 0.10, 0.16, 0.24, 0.34, 0.46),
n=2,
N=320,
layout=(2, 3),
title="Concave polygon: contour evolution under increasing $\\delta$",
)
fig8.canvas.manager.set_window_title("Demo — Concave polygon delta panel")

# ============================================================================
# 3. POLYGONS WITH HOLES
# ============================================================================
print("Category 3: polygons with holes")

# Example 9: Triangle with inner triangular hole
print(" Example 9: triangle with a hole")
outer_tri = np.array([[-1.10, -0.78], [-0.10, 0.72], [1.10, -0.78]], dtype=float)
inner_tri = np.array([[-0.25, -0.36], [0.15, -0.45], [-0.10, 0.05]], dtype=float)
fig7 = plot_polygon_with_holes(
fig9 = plot_polygon_with_holes(
outer_tri,
[inner_tri],
delta=0.12,
n=2,
N=320,
title="Polygon with hole: outer triangle and inner triangular void",
)
fig7.canvas.manager.set_window_title("Demo — Polygon with hole: triangle")
fig9.canvas.manager.set_window_title("Demo — Polygon with hole: triangle")

# Example 8: Rounded rectangular outer boundary with two holes
print(" Example 8: polygon with multiple holes")
# Example 10: Rounded rectangular outer boundary with two holes
print(" Example 10: polygon with multiple holes")
outer_rect = np.array([
[-1.15, -0.82], [-1.00, 0.88], [1.15, 0.92], [1.20, -0.82]
], dtype=float)
left_hole = np.array([[-0.78, 0.36], [-0.48, -0.28], [0.10, 0.48]], dtype=float)
right_hole = np.array([[0.42, -0.28], [0.98, 0.18], [1.02, -0.56]], dtype=float)
fig8 = plot_polygon_with_holes(
fig10 = plot_polygon_with_holes(
outer_rect,
[left_hole, right_hole],
delta=0.18,
n=2,
N=340,
title="Polygon with holes: outer boundary with two internal voids",
)
fig8.canvas.manager.set_window_title("Demo — Polygon with holes: multiple")
fig10.canvas.manager.set_window_title("Demo — Polygon with holes: multiple")

# Example 9: Outer polygon with a star-like central hole and delta sweep
print(" Example 9: hole-shape evolution under varying delta")
# Example 11: Outer polygon with a star-like central hole and delta sweep
print(" Example 11: hole-shape evolution under varying delta")
outer_loop = np.array([
[-1.10, -0.92], [-1.12, 0.95], [1.18, 0.95], [1.20, -0.95]
], dtype=float)
Expand All @@ -209,10 +239,10 @@ def plot_polygon_with_holes(outer, holes, delta=0.15, n=2, N=320, title=None):
[0.80, -0.05], [0.38, -0.28], [0.18, -0.58], [-0.12, -0.48],
[-0.38, -0.62], [-0.68, -0.22],
], dtype=float)
fig9, axes9 = plt.subplots(2, 2, figsize=(10.5, 8.2), squeeze=False)
fig11, axes11 = plt.subplots(2, 2, figsize=(10.5, 8.2), squeeze=False)
all_pts = np.vstack([outer_loop, inner_loop])
X, Y = make_grid(all_pts, N=320, pad_fraction=0.18)
for ax, d in zip(axes9.ravel(), (0.08, 0.15, 0.28, 0.40)):
for ax, d in zip(axes11.ravel(), (0.08, 0.15, 0.28, 0.40)):
Z = imp_spline_2d(X, Y, outer_loop, delta=d, n=2)
Z = Z * (1.0 - imp_spline_2d(X, Y, inner_loop, delta=d, n=2))
Z = np.clip(Z, 0.0, 1.0)
Expand All @@ -222,17 +252,17 @@ def plot_polygon_with_holes(outer, holes, delta=0.15, n=2, N=320, title=None):
draw_polygon_outline(inner_loop, ax=ax, linestyle=':', color='0.45', linewidth=0.8,
marker='*', markersize=5)
ax.set_title(rf"$\delta$={d}")
fig9.suptitle("Polygon with hole: implicit contour evolution under increasing $\\delta$", fontsize=13)
fig11.suptitle("Polygon with hole: implicit contour evolution under increasing $\\delta$", fontsize=13)
plt.tight_layout()
fig9.canvas.manager.set_window_title("Demo — Polygon with hole delta panel")
fig11.canvas.manager.set_window_title("Demo — Polygon with hole delta panel")

# ============================================================================
# 3. COLLECTION OF POLYGONS FORMING A 2D PARTITION
# 4. COLLECTION OF POLYGONS FORMING A 2D PARTITION
# ============================================================================
print("Category 3: collections of polygons forming a 2D partition")
print("Category 4: collections of polygons forming a 2D partition")

# Example 10: Partition net and summed basis surfaces
print(" Example 10: partition net and summed basis surfaces")
# Example 12: Partition net and summed basis surfaces
print(" Example 12: partition net and summed basis surfaces")
partition_polygons = [
np.array([[-0.95, -0.42], [-0.55, 0.10], [-0.55, -1.00]]),
np.array([[-0.95, 0.45], [-0.55, 0.10], [-0.55, 0.85], [-0.35, 0.98], [-0.02, 0.62], [-0.32, 0.12]]),
Expand All @@ -242,21 +272,21 @@ def plot_polygon_with_holes(outer, holes, delta=0.15, n=2, N=320, title=None):
np.array([[0.48, 0.12], [0.72, 0.55], [1.05, 0.42], [0.85, -0.18], [0.70, -0.30]]),
np.array([[0.35, -0.42], [0.70, -0.30], [0.85, -0.18], [0.62, -0.92], [0.18, -0.98], [-0.15, -0.62]]),
]
fig10 = partition_basis_surfaces(partition_polygons, deltas=(0.05, 0.10, 0.20), n=2, N=160)
fig10.canvas.manager.set_window_title("Demo — Partition net and basis surfaces")
fig12 = partition_basis_surfaces(partition_polygons, deltas=(0.05, 0.10, 0.20), n=2, N=160)
fig12.canvas.manager.set_window_title("Demo — Partition net and basis surfaces")

# Example 11: Individual partition-cell basis gallery
print(" Example 11: basis gallery for selected partition cells")
fig11, axes11 = plt.subplots(2, 2, figsize=(10.5, 8.0), squeeze=False)
for idx, (ax, poly) in enumerate(zip(axes11.ravel(), partition_polygons[:4]), start=1):
# Example 13: Individual partition-cell basis gallery
print(" Example 13: basis gallery for selected partition cells")
fig13, axes13 = plt.subplots(2, 2, figsize=(10.5, 8.0), squeeze=False)
for idx, (ax, poly) in enumerate(zip(axes13.ravel(), partition_polygons[:4]), start=1):
draw_imp_spline(poly, delta=0.12, n=2, N=260, ax=ax,
title=f"Partition cell {idx}")
fig11.suptitle("Basis functions associated with individual partition polygons", fontsize=13)
fig13.suptitle("Basis functions associated with individual partition polygons", fontsize=13)
plt.tight_layout()
fig11.canvas.manager.set_window_title("Demo — Partition cell basis gallery")
fig13.canvas.manager.set_window_title("Demo — Partition cell basis gallery")

# Example 12: Freeform curves from a small polygon collection
print(" Example 12: freeform shapes from multiple polygon components")
# Example 14: Freeform curves from a small polygon collection
print(" Example 14: freeform shapes from multiple polygon components")
collection_shapes = [
np.array([[-1.00, -0.70], [-0.70, 0.20], [-0.30, 0.72], [0.05, 0.30], [-0.15, -0.62]]),
np.array([[0.10, -0.42], [0.62, 0.20], [1.00, -0.58], [0.82, -0.88], [0.30, -0.82]]),
Expand All @@ -268,25 +298,25 @@ def plot_polygon_with_holes(outer, holes, delta=0.15, n=2, N=320, title=None):
for poly in collection_shapes:
Zc += imp_spline_2d(Xc, Yc, poly, delta=0.16, n=2)

fig12 = plt.figure(figsize=(11, 4.2))
ax12a = fig12.add_subplot(1, 2, 1)
ax12b = fig12.add_subplot(1, 2, 2, projection='3d')
cf12 = ax12a.contourf(Xc, Yc, Zc, levels=20, cmap='viridis')
plt.colorbar(cf12, ax=ax12a)
ax12a.contour(Xc, Yc, Zc, levels=[0.5, 1.0], colors=['white', 'black'], linewidths=[2.0, 1.0])
fig14 = plt.figure(figsize=(11, 4.2))
ax14a = fig14.add_subplot(1, 2, 1)
ax14b = fig14.add_subplot(1, 2, 2, projection='3d')
cf14 = ax14a.contourf(Xc, Yc, Zc, levels=20, cmap='viridis')
plt.colorbar(cf14, ax=ax14a)
ax14a.contour(Xc, Yc, Zc, levels=[0.5, 1.0], colors=['white', 'black'], linewidths=[2.0, 1.0])
for poly in collection_shapes:
draw_polygon_outline(poly, ax=ax12a, linestyle=':', color='0.55', linewidth=0.8,
draw_polygon_outline(poly, ax=ax14a, linestyle=':', color='0.55', linewidth=0.8,
marker='o', markersize=3)
ax12a.set_title('Combined contour field')
ax12b.plot_wireframe(Xc, Yc, Zc, rstride=5, cstride=5, color='0.35', linewidth=0.45)
ax12b.set_xlabel('x')
ax12b.set_ylabel('y')
ax12b.set_zlabel('sum')
ax12b.view_init(elev=28, azim=-58)
ax12b.set_title('Summed wireframe surface')
fig12.suptitle('Collection of polygons: composed implicit field', fontsize=13)
ax14a.set_title('Combined contour field')
ax14b.plot_wireframe(Xc, Yc, Zc, rstride=5, cstride=5, color='0.35', linewidth=0.45)
ax14b.set_xlabel('x')
ax14b.set_ylabel('y')
ax14b.set_zlabel('sum')
ax14b.view_init(elev=28, azim=-58)
ax14b.set_title('Summed wireframe surface')
fig14.suptitle('Collection of polygons: composed implicit field', fontsize=13)
plt.tight_layout()
fig12.canvas.manager.set_window_title("Demo — Collection of polygons")
fig14.canvas.manager.set_window_title("Demo — Collection of polygons")

print("\nDemo complete.")
plt.show()
Loading