72 citations · 87 across the 4 of their papers we have counts for
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math.DG2010★ 72 cited
Knot Tightening By Constrained Gradient Descent
Ted Ashton, Jason Cantarella, Michael Piatek +1
We present new computations of approximately length-minimizing polygons with fixed thickness. These curves model the centerlines of "tight" knotted tubes with minimal length and fi…
math.DG2005★ 6 cited
Self-contact Sets for 50 Tightly Knotted and Linked Tubes
Ted Ashton, Jason Cantarella, Michael Piatek +1
We report on new numerical computations of the set of self-contacts in tightly knotted tubes of uniform circular cross-section. Such contact sets have been obtained before for the…
math.DG2004★ 8 cited
A Fast Octree-Based Algorithm for Computing Ropelength
Ted Ashton, Jason Cantarella
The ropelength of a space curve is usually defined as the quotient of its length by its thickness: the radius of the largest embedded tube around the knot. This idea was extended t…