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#!/usr/bin/env python3
"""
Fix the 7-vertex analysis - check which vertices are actually used.
"""
import numpy as np
import torch
from ideal_poly_volume_toolkit.geometry import (
delaunay_triangulation_indices,
triangle_volume_from_points_torch,
)
from scipy.optimize import differential_evolution
# Run a single good optimization
def compute_volume(params):
"""Compute volume from spherical parameters."""
# Fixed vertices
Z = [complex(0, 0), complex(1, 0)]
# Add 4 parameterized vertices
for i in range(4):
theta = params[2*i]
phi = params[2*i + 1]
z = np.tan(theta/2) * np.exp(1j * phi)
Z.append(z)
Z_np = np.array(Z, dtype=np.complex128)
try:
idx = delaunay_triangulation_indices(Z_np)
# Check if all 7 vertices are used
vertices_used = set()
for (i, j, k) in idx:
vertices_used.update([i, j, k])
if len(vertices_used) < 7:
return 1000.0 # Penalty if not all vertices used
Z_torch = torch.tensor(Z_np, dtype=torch.complex128)
total = 0
for (i, j, k) in idx:
vol = triangle_volume_from_points_torch(Z_torch[i], Z_torch[j], Z_torch[k], series_terms=96)
total += vol.item()
return -total # Negative for minimization
except:
return 1000.0 # Penalty
print("Running constrained optimization (all 7 vertices must be used)...")
bounds = [(0.1, np.pi-0.1), (0, 2*np.pi)] * 4
result = differential_evolution(
compute_volume,
bounds,
maxiter=200,
popsize=20,
seed=42
)
volume = -result.fun
print(f"Optimal volume: {volume:.6f}")
# Analyze the result
Z = [complex(0, 0), complex(1, 0)]
for i in range(4):
theta = result.x[2*i]
phi = result.x[2*i + 1]
z = np.tan(theta/2) * np.exp(1j * phi)
Z.append(z)
print("\nVertex positions:")
for i, z in enumerate(Z):
print(f"z[{i}] = {z.real:+.4f} + {z.imag:+.4f}i")
Z_np = np.array(Z, dtype=np.complex128)
idx = delaunay_triangulation_indices(Z_np)
# Check which vertices are used
vertices_used = set()
for (i, j, k) in idx:
vertices_used.update([i, j, k])
print(f"\nVertices used: {sorted(vertices_used)}")
print(f"Number of faces: {len(idx)}")
# Count edges properly
edges = set()
for (a, b, c) in idx:
edges.add(tuple(sorted([a, b])))
edges.add(tuple(sorted([b, c])))
edges.add(tuple(sorted([a, c])))
V = len(vertices_used)
E = len(edges)
F = len(idx)
chi = V - E + F
print(f"\nEuler characteristic: V - E + F = {V} - {E} + {F} = {chi}")
# Vertex degrees
degrees = [0] * 7
for edge in edges:
if edge[0] < 7 and edge[1] < 7:
degrees[edge[0]] += 1
degrees[edge[1]] += 1
print(f"Vertex degrees: {degrees}")
# Volume
Z_torch = torch.tensor(Z_np, dtype=torch.complex128)
total_volume = 0
for (a, b, c) in idx:
vol = triangle_volume_from_points_torch(Z_torch[a], Z_torch[b], Z_torch[c], series_terms=96)
total_volume += vol.item()
print(f"\nTotal volume: {total_volume:.6f}")
print(f"Regular octahedron: ≈ 5.333")
print(f"Ratio: {total_volume/5.333:.3f}") |