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QL-UoHull merged 2 commits into from
Jul 16, 2026
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Integrate paper-style examples and repair 01_basic_polygon.ipynb plotting/runtime path #4

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Initial plan
Copilot Jul 16, 2026
e802e04
Enhance demo examples and fix notebook plotting/runtime issues
Copilot Jul 16, 2026
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134 changes: 90 additions & 44 deletions examples/demo.py
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Expand Up @@ -3,88 +3,134 @@
-------
Standalone Python demonstration of the 2D Piecewise Algebraic Implicit Spline.

Mirrors matlab/Demo.m — runs four examples that showcase the main features
of the Li & Tian (2009) implicit-spline construction:

Example 1 : Unit square (right-angle corners)
Example 2 : Equilateral triangle (acute corners)
Example 3 : Regular pentagon
Example 4 : Irregular pentagon — sweeping delta to show bandwidth effect

Run from the repository root::

python examples/demo.py

or from within the examples/ directory::

python demo.py

Reference
---------
Li, Q. & Tian, J. (2009). 2D Piecewise Algebraic Splines for Implicit
Modeling. ACM Transactions on Graphics, 28(3).
DOI: 10.1145/1516522.1516524
Includes both the original basic examples and paper-style visual panels inspired
by Li & Tian (2009).
"""

import sys
import os
import sys

# Allow running from examples/ or from the repo root
_here = os.path.dirname(os.path.abspath(__file__))
_python_dir = os.path.join(_here, '..', 'python')
_python_dir = os.path.join(_here, "..", "python")
if os.path.isdir(_python_dir):
sys.path.insert(0, os.path.abspath(_python_dir))

import numpy as np
import matplotlib.pyplot as plt

from implicit_spline import imp_spline_2d, draw_imp_spline
from implicit_spline.visualization import draw_surface, compare_delta
from implicit_spline import draw_imp_spline
from implicit_spline.visualization import (
compare_delta,
compare_n,
draw_surface,
panel_delta_shapes,
partition_basis_surfaces,
)


# ── Shared parameters ─────────────────────────────────────────────────────────
DELTA = 0.12 # transition bandwidth
N_ORDER = 2 # smoothness order (C^n near each edge)
N_GRID = 200 # grid resolution (N × N points)
def _set_window_title(fig, title):
manager = getattr(fig.canvas, "manager", None)
if manager is not None and hasattr(manager, "set_window_title"):
manager.set_window_title(title)


DELTA = 0.12
N_ORDER = 2
N_GRID = 200

print("=== 2D Implicit Spline Demo ===\n")

# ── Example 1: Unit square ────────────────────────────────────────────────────
print("Example 1: unit square")
P_sq = np.array([[0, 0], [1, 0], [1, 1], [0, 1]], dtype=float)

fig1, ax1 = plt.subplots(figsize=(6, 5))
fig1.canvas.manager.set_window_title("Demo — Example 1: Square")
_set_window_title(fig1, "Demo — Example 1: Square")
draw_imp_spline(P_sq, delta=DELTA, n=N_ORDER, N=N_GRID, ax=ax1,
title=rf"Example 1: Square ($\delta={DELTA}$, $n={N_ORDER}$)")
plt.tight_layout()

# ── Example 2: Equilateral triangle ──────────────────────────────────────────
print("Example 2: equilateral triangle")
P_tri = np.array([[0, 0], [2, 0], [1, np.sqrt(3)]], dtype=float)

fig2, ax2 = plt.subplots(figsize=(6, 5))
fig2.canvas.manager.set_window_title("Demo — Example 2: Triangle")
_set_window_title(fig2, "Demo — Example 2: Triangle")
draw_imp_spline(P_tri, delta=DELTA, n=N_ORDER, N=N_GRID, ax=ax2,
title=rf"Example 2: Triangle ($\delta={DELTA}$, $n={N_ORDER}$)")
plt.tight_layout()

# ── Example 3: Regular pentagon ───────────────────────────────────────────────
print("Example 3: regular pentagon")
theta = np.linspace(np.pi / 2, np.pi / 2 + 2 * np.pi, 6)[:-1] # 5 vertices, start at top
theta = np.linspace(np.pi / 2, np.pi / 2 + 2 * np.pi, 6)[:-1]
P_pent = np.column_stack([np.cos(theta), np.sin(theta)])

fig3, ax3 = plt.subplots(figsize=(6, 5))
fig3.canvas.manager.set_window_title("Demo — Example 3: Pentagon")
_set_window_title(fig3, "Demo — Example 3: Pentagon")
draw_imp_spline(P_pent, delta=DELTA, n=N_ORDER, N=N_GRID, ax=ax3,
title=rf"Example 3: Pentagon ($\delta={DELTA}$, $n={N_ORDER}$)")
plt.tight_layout()

# ── Example 4: Effect of delta (bandwidth) ────────────────────────────────────
print("Example 4: sweeping delta [0.05, 0.15, 0.30]")
print("Example 4: sweeping delta [0.05, 0.15, 0.30]")
P_irr = np.array([[0, 0], [2, 0], [2.5, 0.8], [1.5, 1.8], [-0.2, 1.2]], dtype=float)

fig4 = compare_delta(P_irr, deltas=(0.05, 0.15, 0.30), n=N_ORDER, N=N_GRID)
fig4.canvas.manager.set_window_title("Demo — Example 4: delta sweep")
_set_window_title(fig4, "Demo — Example 4: delta sweep")

print("Example 5: smoothness-order comparison [n=1,2,3]")
fig5 = compare_n(P_sq, delta=0.15, n_values=(1, 2, 3), N=N_GRID)
_set_window_title(fig5, "Demo — Example 5: smoothness comparison")

print("Example 6: paper-style six-panel delta evolution")
panel_deltas = (0.03, 0.06, 0.10, 0.16, 0.24, 0.36)
fig6 = panel_delta_shapes(
P_irr,
deltas=panel_deltas,
n=2,
N=260,
layout=(2, 3),
title=r"Paper-style contour evolution as $\delta$ increases",
)
_set_window_title(fig6, "Demo — Example 6: paper-style contour panels")

print("Example 7: freeform curve gallery")
gallery_polys = [
np.array([[0.0, 0.0], [1.6, -0.2], [2.1, 0.9], [1.1, 1.8], [-0.2, 1.2]]),
np.array([[0.0, 0.2], [0.9, -0.3], [1.8, 0.3], [1.4, 1.5], [0.3, 1.9], [-0.4, 1.0]]),
np.array([[0.0, 0.0], [0.8, -0.4], [1.8, 0.1], [2.0, 1.0], [1.2, 1.9], [0.2, 1.6], [-0.3, 0.8]]),
np.array([[0.0, 0.0], [1.4, -0.4], [2.4, 0.5], [1.7, 1.7], [0.6, 1.9], [-0.5, 1.1]]),
]
fig7, axes7 = plt.subplots(2, 2, figsize=(10, 8))
for i, (ax, poly) in enumerate(zip(axes7.ravel(), gallery_polys), start=1):
draw_imp_spline(poly, delta=0.12, n=2, N=220, ax=ax, title=f"freeform {i}")
fig7.suptitle("Freeform implicit-curve gallery", fontsize=13)
plt.tight_layout()
_set_window_title(fig7, "Demo — Example 7: freeform gallery")

print("Example 8: partition and summed-basis surfaces")
partition_polys = [
np.array([[0.0, 0.0], [1.1, 0.0], [0.95, 0.8], [0.1, 0.85]]),
np.array([[1.1, 0.0], [2.2, 0.0], [2.0, 0.95], [0.95, 0.8]]),
np.array([[0.1, 0.85], [0.95, 0.8], [0.9, 1.8], [0.0, 1.9]]),
np.array([[0.95, 0.8], [2.0, 0.95], [1.9, 1.9], [0.9, 1.8]]),
]
fig8 = partition_basis_surfaces(
partition_polys,
deltas=(0.04, 0.10, 0.22),
n=2,
N=130,
)
_set_window_title(fig8, "Demo — Example 8: partition-based surface figure")

print("Example 9: extra 3D wireframe surface view")
fig9 = plt.figure(figsize=(7, 5))
ax9 = fig9.add_subplot(111, projection="3d")
draw_surface(
P_irr,
delta=0.12,
n=2,
N=100,
ax=ax9,
wireframe=True,
elev=28,
azim=-58,
title="Wireframe view of implicit spline surface",
)
_set_window_title(fig9, "Demo — Example 9: wireframe surface")
plt.tight_layout()

print("\nDemo complete.")
plt.show()
57 changes: 34 additions & 23 deletions notebooks/01_basic_polygon.ipynb
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Expand Up @@ -48,20 +48,29 @@
"outputs": [],
"source": [
"# If running in Google Colab, clone the repo so imports work.\n",
"import sys, os\n",
"import os\n",
"import sys\n",
"from pathlib import Path\n",
"\n",
"IN_COLAB = 'google.colab' in sys.modules\n",
"if IN_COLAB:\n",
" if not os.path.exists('Implicit-Spline'):\n",
" os.system('git clone https://github.com/QL-UoHull/Implicit-Spline.git')\n",
" sys.path.insert(0, 'Implicit-Spline/python')\n",
"else:\n",
" # Running locally: add the python/ directory to the path\n",
" repo_root = os.path.abspath(os.path.join(os.path.dirname(os.getcwd()), '..'))\n",
" python_dir = os.path.join(os.path.dirname(os.getcwd()), 'python')\n",
" if os.path.isdir(python_dir):\n",
" sys.path.insert(0, python_dir)\n",
" cwd = Path.cwd().resolve()\n",
" candidates = [\n",
" cwd,\n",
" cwd.parent,\n",
" cwd / 'Implicit-Spline',\n",
" cwd.parent / 'Implicit-Spline',\n",
" ]\n",
" for root in candidates:\n",
" python_dir = root / 'python'\n",
" if python_dir.is_dir():\n",
" sys.path.insert(0, str(python_dir))\n",
" break\n",
" else:\n",
" # Fallback: try relative to notebooks/\n",
" sys.path.insert(0, os.path.join('..', 'python'))\n"
]
},
Expand All @@ -76,7 +85,7 @@
"import matplotlib.pyplot as plt\n",
"\n",
"from implicit_spline import imp_spline_2d, draw_imp_spline\n",
"from implicit_spline.visualization import draw_surface, compare_delta\n",
"from implicit_spline.visualization import draw_surface, compare_delta, compare_n\n",
"from implicit_spline.core import H\n",
"\n",
"%matplotlib inline\n",
Expand Down Expand Up @@ -153,10 +162,12 @@
"source": [
"P_square = np.array([[0, 0], [1, 0], [1, 1], [0, 1]], dtype=float)\n",
"\n",
"fig, axes = plt.subplots(1, 2, figsize=(11, 4))\n",
"draw_imp_spline(P_square, delta=delta, n=n, N=N, ax=axes[0],\n",
"fig = plt.figure(figsize=(11, 4))\n",
"ax1 = fig.add_subplot(1, 2, 1)\n",
"ax2 = fig.add_subplot(1, 2, 2, projection='3d')\n",
"draw_imp_spline(P_square, delta=delta, n=n, N=N, ax=ax1,\n",
" title='Contour plot')\n",
"draw_surface(P_square, delta=delta, n=n, N=80, ax=axes[1],\n",
"draw_surface(P_square, delta=delta, n=n, N=80, ax=ax2,\n",
" title='Surface plot')\n",
"fig.suptitle('Unit square', fontsize=13)\n",
"plt.tight_layout(); plt.show()\n"
Expand All @@ -179,10 +190,12 @@
"source": [
"P_tri = np.array([[0, 0], [2, 0], [1, np.sqrt(3)]], dtype=float)\n",
"\n",
"fig, axes = plt.subplots(1, 2, figsize=(11, 4))\n",
"draw_imp_spline(P_tri, delta=delta, n=n, N=N, ax=axes[0],\n",
"fig = plt.figure(figsize=(11, 4))\n",
"ax1 = fig.add_subplot(1, 2, 1)\n",
"ax2 = fig.add_subplot(1, 2, 2, projection='3d')\n",
"draw_imp_spline(P_tri, delta=delta, n=n, N=N, ax=ax1,\n",
" title='Contour plot')\n",
"draw_surface(P_tri, delta=delta, n=n, N=80, ax=axes[1],\n",
"draw_surface(P_tri, delta=delta, n=n, N=80, ax=ax2,\n",
" title='Surface plot')\n",
"fig.suptitle('Equilateral triangle', fontsize=13)\n",
"plt.tight_layout(); plt.show()\n"
Expand All @@ -206,10 +219,12 @@
"theta = np.linspace(np.pi/2, np.pi/2 + 2*np.pi, 6)[:-1] # 5 vertices, start at top\n",
"P_pent = np.column_stack([np.cos(theta), np.sin(theta)])\n",
"\n",
"fig, axes = plt.subplots(1, 2, figsize=(11, 4))\n",
"draw_imp_spline(P_pent, delta=delta, n=n, N=N, ax=axes[0],\n",
"fig = plt.figure(figsize=(11, 4))\n",
"ax1 = fig.add_subplot(1, 2, 1)\n",
"ax2 = fig.add_subplot(1, 2, 2, projection='3d')\n",
"draw_imp_spline(P_pent, delta=delta, n=n, N=N, ax=ax1,\n",
" title='Contour plot')\n",
"draw_surface(P_pent, delta=delta, n=n, N=80, ax=axes[1],\n",
"draw_surface(P_pent, delta=delta, n=n, N=80, ax=ax2,\n",
" title='Surface plot')\n",
"fig.suptitle('Regular pentagon', fontsize=13)\n",
"plt.tight_layout(); plt.show()\n"
Expand Down Expand Up @@ -259,12 +274,8 @@
"P_sq = np.array([[0, 0], [1, 0], [1, 1], [0, 1]], dtype=float)\n",
"d = 0.15\n",
"\n",
"fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n",
"for ax, nn in zip(axes, [1, 2, 3]):\n",
" draw_imp_spline(P_sq, delta=d, n=nn, N=N, ax=ax,\n",
" title=rf'$n={nn}$ (C$^{{{nn}}}$)')\n",
"fig.suptitle(rf'Smoothness order $n$ \u2014 unit square, $\\delta={d}$', fontsize=13)\n",
"plt.tight_layout(); plt.show()\n"
"compare_n(P_sq, delta=d, n_values=(1, 2, 3), N=N)\n",
"plt.show()\n"
]
},
{
Expand Down