Physical
02
The same gradient becomes a force. Velocity carries motion forward; damping removes it.
force = −∇A + downward load
Momentum can overshoot. Gravity affects this solver only.
Why compare them?
At zero gravity both target stationarity of the same discrete area energy, ∇A = 0 at free vertices. Their transients and rate of convergence differ.
Try Run, reduce damping, then add gravity. A loaded physical equilibrium need not minimize area alone.
This is not a timing benchmark: Compare uses three optimizer iterations and five physical substeps per frame.
Model & measurement
A is the sum of triangle areas. The boundary is fixed and both meshes retain the same disk connectivity; there is no tearing, remeshing or topology search.
The physical update uses equal implicit vertex masses, a scaled downward load, per-substep damping and a speed limit. Its time and gravity are demonstration parameters, not calibrated material units.
Both routes include tangential mesh smoothing. Nonlinear geometry and discretization mean convergence to one identical global minimum is not guaranteed.
The coil and knot presets are topology stress cases: their radial disk mesh can degenerate and fail to settle. A general soap-film solver would need a different mesh or topology treatment.
Δy = yphysical − yoptimizer compares matched mesh vertices. They may also drift sideways: arrows and the pale zero contour are not a closest-surface distance or an exact intersection curve.
Area-normalized gradient magnitude approximates |2H| at free vertices. It reduces mesh-spacing dependence; it is still a discrete estimate. A gravity-loaded equilibrium can have nonzero area gradient.
The thin-film shader supplies optical color only. Thickness and color flow do not feed back into either solver.