Untangling

A block with a few inverted hexes, repaired by the optimizer’s delta continuation, the untangle_schedule preset.

Inverted hexes (fewer is better)

Key points

• The exact metric cannot untangle: optimize(delta=0) has a wall at zero Jacobian and leaves all 12 hexes inverted.

• untangle_schedule is a preset of optimize, not a separate untangler: 5 optimize stages with delta shrinking from 1 to 0.01; it clears all 12 inverted hexes (minimum scaled Jacobian 0.98).

• On this input Laplace clears them too (minimum 0.85, 0.02 s): a few displaced vertices in an otherwise clean block are what element averaging repairs best.

• suggest_schedule adds the preset by itself when the input has inverted hexes: 27 stages, minimum scaled Jacobian 0.98.

The numbers

method	stages	inverted	min SJ	mean SJ	time (s)
input	—	12	-0.9649	0.8681	—
Laplace	1	0	0.8497	0.9845	0.02
optimize δ=0	1	12	-0.6455	0.8290	1.45
untangle preset	5	0	0.9802	0.9893	0.49
suggested	27	0	0.9802	0.9893	0.90

Bold: the best value in each column among the results (highest scaled Jacobian; lowest count, objective, time, change or distance); the input row is for reference.

Times: a laptop, running serial.

Run python examples/smoother/hex/05_untangle.py to reproduce; it prints these numbers.