vertexModel.initialize was taking 117s to complete, too slow for napari integration with 2D images. Profiling revealed multiple hot paths with redundant computations and inefficient algorithms.

Optimizations

Eliminated redundant face area computation (26.4s → ~13s saved)

• compute_face_area was called twice per face (lines 110 and 216)
• Now computed once in build_edges() and returned
• Avoided np.vstack() in loop, moved face center outside

Optimized copy operations (8.7s → ~3.5s saved)

• copy_non_mutable_attributes used deepcopy indiscriminately (40k+ calls)
• Fast-path for immutable types, shallow copy where sufficient
• Check first 3 list elements to determine if deepcopy needed

Replaced O(n²) global ID building with O(n) lookups (17.6s → ~12s saved)

• Nested loops with repeated np.isin() checks for vertex/face adjacency
• Dictionary-based lookups with tuple(sorted()) keys

Replaced determinant calculations with dot/cross products (5.7s → ~1.6s saved)

• np.linalg.det() in compute_volume_fraction and ensure_consistent_order
• Used det([y1, y2, y3]) = y1 · (y2 × y3) for ~30% speedup

Cached interface type mapping (218ms → ~200ms saved)

• get_interface recreated dictionary on every call (84k+ calls)
• Module-level _INTERFACE_TYPE_MAPPING cache

Reduced duplicate np.isin operations

• Stored boolean masks in build_edges SharedByCells computation

Expected Impact

• 25-30% reduction in initialization time (~30-35s saved from 117s baseline)
• Maintains backward compatibility
• 6 files modified: 131 insertions, 72 deletions

• Fixes Improve vertexModel.initialize efficacy #12

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