
Deciding contractibility of a nonsimple curve on the boundary of a 3manifold: A computational Loop Theorem
We present an algorithm for the following problem. Given a triangulated ...
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Tightening Curves on Surfaces Monotonically with Applications
We prove the first polynomial bound on the number of monotonic homotopy ...
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Fast and Simple Methods For Computing Control Points
The purpose of this paper is to present simple and fast methods for comp...
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Segmenting a Surface Mesh into Pants Using Morse Theory
A pair of pants is a genus zero orientable surface with three boundary c...
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Determining surfaces of revolution from their implicit equations
Results of number of geometric operations (often used in technical pract...
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3D Registration of Curves and Surfaces using Local Differential Information
This article presents for the first time a global method for registering...
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On the complexity of optimal homotopies
In this article, we provide new structural results and algorithms for th...
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Algorithms for Contractibility of Compressed Curves on 3Manifold Boundaries
In this paper we prove that the problem of deciding contractibility of an arbitrary closed curve on the boundary of a 3manifold is in NP. We emphasize that the manifold and the curve are both inputs to the problem. Moreover, our algorithm also works if the curve is given as a compressed word. Previously, such an algorithm was known for simple (noncompressed) curves, and, in very limited cases, for curves with selfintersections. Furthermore, our algorithm is fixedparameter tractable in the complexity of the input 3manifold. As part of our proof, we obtain new polynomialtime algorithms for compressed curves on surfaces, which we believe are of independent interest. We provide a polynomialtime algorithm which, given an orientable surface and a compressed loop on the surface, computes a canonical form for the loop as a compressed word. In particular, contractibility of compressed curves on surfaces can be decided in polynomial time; prior published work considered only constant genus surfaces. More generally, we solve the following normal subgroup membership problem in polynomial time: given an arbitrary orientable surface, a compressed closed curve γ, and a collection of disjoint normal curves Δ, there is a polynomialtime algorithm to decide if γ lies in the normal subgroup generated by components of Δ in the fundamental group of the surface after attaching the curves to a basepoint.
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