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- Joel Hass, Jeffrey C. Lagarias, Nicholas Pippenger
- FOCS
- 1997

We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted, ie., capable of being continuously deformed without self-intersection so that it lies in a plane. We show that this problem, UNKNOTTING PROBLEM is in NP. We also consider the problem, SPLITTING PROBLEM of determining whether two or more such polygons… (More)

There is a positive constant c1 such that for any diagram D representing the unknot, there is a sequence of at most 2 c 1 n Reidemeister moves that will convert it to a trivial knot diagram, where n is the number of crossings in D. A similar result holds for elementary moves on a polyg-onal knot K embedded in the 1-skeleton of the interior of a compact,… (More)

- Alex Tsui, Devin Fenton, +6 authors Owen T. Carmichael
- IPMI
- 2013

We present a method for establishing correspondences between human cortical surfaces that exactly matches the positions of given point landmarks, while attaining the global minimum of an objective function that quantifies how far the mapping deviates from conformality. On each surface, a conformal transformation is applied to the Euclidean distance metric,… (More)

- Joel Hass, Tahl Nowik
- 2008

We construct a new order 1 invariant for knot diagrams. We use it to determine the minimal number of Reidemeister moves needed to pass between certain pairs of knot diagrams.

- Ian Agol, Joel Hass, William P. Thurston
- STOC
- 2002

We show that the problem of deciding whether a polygonal knot in a closed three-dimensional manifold bounds a surface of genus at most <i>g</i> is <b>NP</b>-complete.

- Marshall W. Bern, David Eppstein, +19 authors Denis Zorin
- ArXiv
- 1999

Here we present the results of the NSF-funded Workshop on Computational Topol-ogy, which met on June 11 and 12 in Miami Beach, Florida. This report identifies important problems involving both computation and topology.

- Xiaowen Song, Thomas W. Sederberg, Jianmin Zheng, Rida T. Farouki, Joel Hass
- Computer Aided Geometric Design
- 2004

By applying displacement maps to slightly perturb two free–form surfaces, one can ensure exact agreement between the images in 3 of parameter– domain approximations to their curve of intersection. Thus, at the expense of slightly altering the surfaces in the vicinity of their intersection, a perfect matching of the surface trimming curves is guaranteed.… (More)

- Joel Hass, Rida T. Farouki, Chang Yong Han, Xiaowen Song, Thomas W. Sederberg
- Adv. Comput. Math.
- 2007

We describe a method that serves to simultaneously determine the topological configuration of the intersection curve of two parametric surfaces and generate compatible decomposi-tions of their parameter domains, that are amenable to the application of existing perturbation schemes ensuring exact topological consistency of the trimmed surface… (More)

- Ian Agol, Joel Hass, William P. Thurston
- IEEE Conference on Computational Complexity
- 2002

- Joel Hass
- 1997

Algorithms are of interest to geometric topologists for two reasons. First, they have bearing on the decidability of a problem. Certain topological questions, such as finding a classification of four dimensional manifolds, admit no solution. It is important to know if other problems fall into this category. Secondly, the discovery of a reasonably efficient… (More)