Theoretical background

Numerical behavior and diagnostics

Fusion moves equal-radius fiber centers closer together, then optimizes the virtual connections to restore the summed area of the original fiber polygons. This is a geometric model, rather than a general physical simulation of glass flow. Circle boundaries are polygonal approximations; resolution is the number of segments per quadrant (passed to Shapely as quad_segs).

After adding fused structures, inspect profile.fusion_diagnostics. Each entry contains area_residual (absolute area error in squared geometry units) and relative_area_residual (absolute error divided by the original polygon-area sum). FiberLine and FiberRing expose these same attributes after compute_optimal_structure(). These diagnostics measure area conservation, not agreement with experimental fibers or exact analytical circle areas. Optimizer failure or nonfinite results raise RuntimeError; a failed assembly is not appended to a profile. Solver success alone does not impose a universal residual threshold, so applications should check the reported relative error against their required accuracy.

Profile rotation uses degrees about the origin. Translation and rotation move both nominal and shifted cores exactly once and preserve areas. Position scaling moves fiber centers about the origin while retaining fiber radii. It recomputes fused connections and optimized cores; previously randomized offsets are reset for fused assemblies. Failed recomputation leaves the original profile intact. Cached unions are invalidated after profile edits. Modify profiles through their methods rather than mutating the public geometry lists directly.

randomize_core_positions(factor, seed=42) draws independent uniform shifts per coordinate in [-factor, factor] around the nominal core. Alternatively, pass a NumPy Generator using rng=. Nominal cores remain unchanged, repeated calls replace rather than accumulate offsets, and zero leaves existing shifted cores unchanged. This replaces the former positive-only, global-RNG behavior. Use the same coordinate units for the factor and geometry.

Raster masks approximate the polygon on the supplied sampling grid. Refine the grid to assess discretization error; individual refinements need not improve monotonically because boundary pixels change discretely.