Curves and Surfaces
8th International Conference, Paris, France, June 12-18, 2014, Revised Selected Papers
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56 Result(s)
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Jean-Daniel Boissonnat
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Article
The reach of subsets of manifolds
Kleinjohann (Archiv der Mathematik 35(1):574–582, 1980; Mathematische Zeitschrift 176(3), 327–344, 1981) and Bangert (Archiv der Mathematik 38(1):54–57, 1982) extended the reach
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Article
Open AccessLocal Criteria for Triangulating General Manifolds
We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex \({\mathscr {A}}\) ...
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Article
Open AccessThe Topological Correctness of PL Approximations of Isomanifolds
Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate multivalued smooth function
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Chapter
Topological Data Analysis
It has been observed since a long time that data are often carrying interesting topological and geometric structures. Characterizing such structures and providing efficient tools to infer and exploit them is a...
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Article
Open AccessDimensionality reduction for k-distance applied to persistent homology
Given a set P of n points and a constant k, we are interested in computing the persistent homology of the Čech filtration of P for the k-distance, and investigate the effectiveness of dimensionality reduction for...
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Article
Open AccessLocal Conditions for Triangulating Submanifolds of Euclidean Space
We consider the following setting: suppose that we are given a manifold M in \({\mathbb {R}}^d\) ...
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Article
Open AccessRandomized Incremental Construction of Delaunay Triangulations of Nice Point Sets
Randomized incremental construction (RIC) is one of the most important paradigms for building geometric data structures. Clarkson and Shor developed a general theory that led to numerous algorithms which are both...
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Article
Open AccessTriangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method
We quantise Whitney’s construction to prove the existence of a triangulation for any \(C^2\) ...
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Article
Open AccessThe reach, metric distortion, geodesic convexity and the variation of tangent spaces
In this paper we discuss three results. The first two concern general sets of positive reach: we first characterize the reach of a closed set by means of a bound on the metric distortion between the distance m...
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Article
Computing persistent homology with various coefficient fields in a single pass
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number...
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Article
Delaunay Triangulation of Manifolds
We present an algorithm for producing Delaunay triangulations of manifolds. The algorithm can accommodate abstract manifolds that are not presented as submanifolds of Euclidean space. Given a set of sample poi...
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Article
An Obstruction to Delaunay Triangulations in Riemannian Manifolds
Delaunay has shown that the Delaunay complex of a finite set of points \(P\) ...
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Chapter and Conference Paper
Tight Kernels for Covering and Hitting: Point Hyperplane Cover and Polynomial Point Hitting Set
The Point Hyperplane Cover problem in \(\mathbb {R}^d\) takes as input a set of n points in
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Article
Building Efficient and Compact Data Structures for Simplicial Complexes
The Simplex Tree (ST) is a recently introduced data structure that can represent abstract simplicial complexes of any dimension and allows efficient implementation of a large range of basic operations on simpl...
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Article
The Compressed Annotation Matrix: An Efficient Data Structure for Computing Persistent Cohomology
Persistent homology with coefficients in a field \(\mathbb {F}\) F ...
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Book and Conference Proceedings
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Chapter and Conference Paper
A Probabilistic Approach to Reducing Algebraic Complexity of Delaunay Triangulations
We propose algorithms to compute the Delaunay triangulation of a point set L using only (squared) distance comparisons (i.e., predicates of degree 2). Our approach is based on the witness complex, a weak form of ...
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Article
The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes
This paper introduces a new data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored in a trie whose nodes are...
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Chapter and Conference Paper
The Gudhi Library: Simplicial Complexes and Persistent Homology
We present the main algorithmic and design choices that have been made to represent complexes and compute persistent homology in the Gudhi library. The Gudhi library (Geometric Understanding in Higher Dimensio...
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Chapter and Conference Paper
Computing Persistent Homology with Various Coefficient Fields in a Single Pass
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number...
