saraedum
commented
1 year ago This is implemented in flatsurvey in OrbitClosure._consume(). However, it's unclear what's a good value for "a little bit" and also which direction to move in directly. If that little bit is too large, a lot of flips are required to make it happen, if it is too small it can lead to coefficient blowup. Also, how quickly the seacrh terminates is extremely sensitive to this deformation in experiments.
If we start with a very symmetric locus (such as quadrilateral unfolding), then the search is hard because we have (only) SAF=0 directions where it is hard to guarantee minimality ("complete algebraic periodicity"). As soon as we found one new direction in the tangent space, we should move a little bit in that direction in order to lose this property.