automatically set Helix rolls based on crossover locations ("relax" the rolls)

[dave-doty]

Unlike "set helix coordinates based on crossovers", this would not adjust helix positions, only their rolls.

Keep each helix in the same position, but adjust the roll to minimize "something" about the strain. One way to do this is to calculate how far is each crossover from being perfect, e.g., if a crossover goes from helix i to j, but instead of the backbone angle pointing straight at j, it is 20 degrees off, then the "error" is 20 degrees. We could minimize the sum of squared errors for each crossover, for instance. This should be a straightforward linear algebra calculation to compute this roll for each helix.

See also UC-Davis-molecular-computing/scadnano-python-package#257

[dave-doty]

Release notes

automatically set Helix rolls based on crossover locations ("relax" the rolls)

In this design, the crossovers are well placed relative to each other, but the helix rolls need to be rotated. As the slice bar shows, with the default roll of 0, the crossovers do not point at the helices they connect to:

By selecting "Edit-->Helix rolls-->Set helix rolls to unstrain crossovers":

The helix rolls are set to minimize "strain" in the crossovers:

Formally, the strain is defined as the square of the angular distance between the "ideal" angle for the crossover (i.e., the relative angle of the other helix to which it is connecting) and the crossover's current angle. The roll is set so as to minimize this total strain across all crossovers in each helix.