https://codereview.appspot.com/7319049/diff/7001/lily/dot-column.cc
File lily/dot-column.cc (right):

https://codereview.appspot.com/7319049/diff/7001/lily/dot-column.cc#newcode206
lily/dot-column.cc:206: p += (int) robust_scm2double
(dp.dot_->get_property ("staff-position"), 0.0);
p is the position of the Dots, just before-collision resolution by this
function.  This is what I was calling the "desired position" with any
setting of Dots.staff-position being included here.

That is why I suggested building allowed_positions using p:
  allowed_positions.add_point(p)

You can extend this to have a separate allowed_positions for each chord,
finding the Stem of the Dots as you did above.

https://codereview.appspot.com/7319049/diff/7001/lily/dot-column.cc#newcode210
lily/dot-column.cc:210: cfg[p] = dp;
This enters a data structure dp representing a movable Dots into the
Dot_configuration cfg and associates it with the desired position 'p'.
(cfg is implemented as a map, cfg[p] = dp2 would enter a different Dots
at the same desired position.)

https://codereview.appspot.com/7319049/

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