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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)
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)
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)
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)
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)
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)
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)