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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)

A knot is an embedding of a circle S in a 3-manifold M , usually taken to be R or S. In the 1920’s Alexander and Briggs [2, §4] and Reidemeister [23] observed that questions about ambient isotopy of polygonal knots in R can be reduced to combinatorial questions about knot diagrams. These are labeled planar graphs with overcrossings and undercrossings… (More)

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

Here we present the results of the NSF-funded Workshop on Computational Topology, which met on June 11 and 12 in Miami Beach, Florida. This report identifies important problems involving both computation and topology. ∗Author affiliations: Marshall Bern, Xerox Palo Alto Research Ctr., bern@parc.xerox.com. David Eppstein, Univ. of California, Irvine, Dept.… (More)

- 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)

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

One of the central questions in topology is determining whether a given curve is knotted or unknotted. An algorithm to decide this question was given by Haken in 1961, using the technique of normal surfaces. These surfaces are rigid, discretized surfaces, well suited for algorithmic analysis. Any oriented surface without boundary can be obtained from a… (More)

- Patrice Koehl, Joel Hass
- IEEE Transactions on Pattern Analysis and Machine…
- 2014

A new algorithm is presented that provides a constructive way to conformally warp a triangular mesh of genus zero to a destination surface with minimal metric deformation, as well as a means to compute automatically a measure of the geometric difference between two surfaces of genus zero. The algorithm takes as input a pair of surfaces that are topological… (More)

For each integer n ≥ 1 we construct a closed unknotted Piecewise Linear curve Kn in R 3 having less than 11n edges with the property that any Piecewise Linear triangluated disk spanning the curve contains at least 2 triangles.

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

Joel Hass a, Rida T. Farouki b, Chang Yong Han b, Xiaowen Song c and Thomas W. Sederberg d a Department of Mathematics, University of California, Davis, CA 95616, USA E-mail: hass@math.ucdavis.edu b Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA 95616, USA E-mail: {farouki,cyhan}@ucdavis.edu c College of… (More)

The classical isoperimetric inequality states that the surface of smallest area enclosing a given volume in R3 is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 2π/3.

- 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)