Numerical experimentation

Supporting shapes and the closure gap

Change the cost exponent, choose a pair of cost profiles, or draw your own function in the first panel. Every curve is recomputed on the displayed finite grid.

Cost exponent p 2.00Input functionGrid points

Input f — draw here

Drag to edit. Keyboard alternative: select a sample and its height below.

Its cost transform fᶜ

Input and double transform

ffᶜᶜsupport profiles

Editable sample Sample height Show selected upper supports

Both transforms minimize over the same uniform grid on [−3,3]. The double transform is exact for this finite problem. The continuum answer can differ: a missing supporting center can create a small artificial gap even at p=2. Refine the grid to distinguish this from a genuine obstruction.