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| #!/usr/bin/env python3 | |
| """Debug the angles from Rivin LP vs geometric realization.""" | |
| import sys | |
| from pathlib import Path | |
| sys.path.insert(0, str(Path(__file__).parent.parent)) | |
| import numpy as np | |
| from ideal_poly_volume_toolkit.plantri_interface import find_plantri_executable | |
| from ideal_poly_volume_toolkit.planar_utils import extract_faces_from_planar_embedding | |
| from ideal_poly_volume_toolkit.rivin_delaunay import ( | |
| check_delaunay_realizability, | |
| realize_angles_as_points, | |
| compute_triangle_angle | |
| ) | |
| import subprocess | |
| def get_octahedron(): | |
| """Get the octahedron triangulation (n=6, index=6).""" | |
| plantri = find_plantri_executable() | |
| args = [plantri, '-pc3', '-a', '6'] | |
| result = subprocess.run(args, capture_output=True, text=True) | |
| triangulations = [] | |
| for line in result.stdout.split('\n'): | |
| line = line.strip() | |
| if not line or line.startswith('>'): | |
| continue | |
| parts = line.split(maxsplit=1) | |
| if len(parts) != 2: | |
| continue | |
| n = int(parts[0]) | |
| adj_str = parts[1] | |
| adj = {} | |
| for v_idx, neighbor_str in enumerate(adj_str.split(',')): | |
| neighbors = [ord(c) - ord('a') for c in neighbor_str] | |
| adj[v_idx] = neighbors | |
| closed_tri = extract_faces_from_planar_embedding(n, adj) | |
| planar_tri = [tri for tri in closed_tri if 0 not in tri] | |
| if planar_tri: | |
| triangulations.append(planar_tri) | |
| return triangulations[6] # The octahedron | |
| if __name__ == '__main__': | |
| triangles = get_octahedron() | |
| print("="*70) | |
| print("OCTAHEDRON ANGLE ANALYSIS") | |
| print("="*70) | |
| print(f"\nTriangles: {triangles}") | |
| # Check strict realizability | |
| result = check_delaunay_realizability(triangles, verbose=True, strict=True) | |
| print(f"\n{'='*70}") | |
| print("LP SOLUTION ANGLES") | |
| print(f"{'='*70}") | |
| angles = result['angles'] | |
| n_triangles = len(triangles) | |
| target_angles = angles.reshape((n_triangles, 3)) | |
| for i, tri in enumerate(triangles): | |
| print(f"\nTriangle {i}: {tri}") | |
| print(f" Angles (rad): {target_angles[i]}") | |
| print(f" Angles (deg): {np.degrees(target_angles[i])}") | |
| print(f" Sum: {target_angles[i].sum():.6f} rad (π = {np.pi:.6f})") | |
| # Try realization | |
| print(f"\n{'='*70}") | |
| print("GEOMETRIC REALIZATION") | |
| print(f"{'='*70}") | |
| realization = realize_angles_as_points(triangles, target_angles, verbose=True) | |
| if realization['success']: | |
| print(f"\n{'='*70}") | |
| print("REALIZED ANGLES") | |
| print(f"{'='*70}") | |
| points = realization['points'] | |
| vertex_list = realization['vertex_list'] | |
| vertex_to_idx = {v: i for i, v in enumerate(vertex_list)} | |
| print(f"\nPoint positions:") | |
| for i, v in enumerate(vertex_list): | |
| print(f" v{v}: ({points[i, 0]:8.5f}, {points[i, 1]:8.5f})") | |
| print(f"\nActual angles achieved:") | |
| for i, tri in enumerate(triangles): | |
| v0, v1, v2 = tri | |
| p0 = points[vertex_to_idx[v0]] | |
| p1 = points[vertex_to_idx[v1]] | |
| p2 = points[vertex_to_idx[v2]] | |
| angle0 = compute_triangle_angle(p0, p1, p2) | |
| angle1 = compute_triangle_angle(p1, p2, p0) | |
| angle2 = compute_triangle_angle(p2, p0, p1) | |
| print(f"\nTriangle {i}: {tri}") | |
| print(f" Target angles (rad): {target_angles[i]}") | |
| print(f" Target angles (deg): {np.degrees(target_angles[i])}") | |
| print(f" Actual angles (rad): [{angle0:.6f}, {angle1:.6f}, {angle2:.6f}]") | |
| print(f" Actual angles (deg): {np.degrees([angle0, angle1, angle2])}") | |
| print(f" Error (rad): {target_angles[i] - np.array([angle0, angle1, angle2])}") | |
| print(f" Error (deg): {np.degrees(target_angles[i] - np.array([angle0, angle1, angle2]))}") | |