Results 1  10
of
19
Surface Reconstruction by Voronoi Filtering
 Discrete and Computational Geometry
, 1998
"... We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled ..."
Abstract

Cited by 405 (11 self)
 Add to MetaCart
We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled
Computational Topology: Ambient Isotopic Approximation of 2Manifolds
 THEORETICAL COMPUTER SCIENCE
, 2001
"... A fundamental issue in theoretical computer science is that of establishing unambiguous formal criteria for algorithmic output. This paper does so within the domain of computeraided geometric modeling. For practical geometric modeling algorithms, it is often desirable to create piecewise linear app ..."
Abstract

Cited by 40 (19 self)
 Add to MetaCart
and philosophical difficulties; we adopt the stronger notion of ambient isotopy. It is shown here, that for any C², compact, 2manifold without boundary, which is embedded in R³, there exists a piecewise linear ambient isotopic approximation. Furthermore, this isotopy has compact support, with specific bounds upon
Complete Tensor Field Topology on 2D Triangulated Manifolds embedded in 3D
"... This paper is concerned with the extraction of the surface topology of tensor fields on 2D triangulated manifolds embedded in 3D. In scientific visualization topology is a meaningful instrument to get a hold on the structure of a given dataset. Due to the discontinuity of tensor fields on a piecewis ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
dimensional tensor fields defined on the vertices of the triangulation and for piecewise constant two or threedimensional tensor fields given per triangle, e.g. rate of strain tensors of piecewise linear flow fields. Categories and Subject Descriptors (according to ACM CCS): Generation—Tensorfield visualization
UNIQUENESS OF THE EMBEDDING OF A 2COMPLEX INTO A 3MANIFOLD
"... Let a 2dimensional complex K2 embedded into a 3dimensional manifold M3 be given. Question. To which extent does K2 determine its regular neighbourhood in M3? For the restricted class of special polyhedra Casler [1] showed that in fact the thickening is unique (independently of the surrounding mani ..."
Abstract
 Add to MetaCart
to S2. One thickening has connected boundary and the other one has two boundary components. Therefore we assume that the boundary of the regular neighbourhood of K2 be connected. Glock, J., Uniqueness of the embedding of a 2complex into a 3manifold.
A combinatorial approach to diffeomorphism invariant quantum gauge theories
 J. Math. Phys
, 1997
"... Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical states are gauge and diffeomorphism invariant distributions on ..."
Abstract

Cited by 15 (1 self)
 Add to MetaCart
on the space of functions of the holonomies of the edges of a certain family of graphs. Then a family of graphs embedded in the space manifold (satisfying certain properties) induces a representation of the algebra of physical observables. We construct a quantum model from the set of piecewise linear graphs
Sparse Grids for Boundary Integral Equations
, 1998
"... The potential of sparse grid discretizations for solving boundary integral equations is studied for the screen problem on a square in IR 3 . Theoretical and numerical results on approximation rates, preconditioning, adaptivity and compression for piecewise constant and linear sparse grid spaces ar ..."
Abstract

Cited by 28 (15 self)
 Add to MetaCart
The potential of sparse grid discretizations for solving boundary integral equations is studied for the screen problem on a square in IR 3 . Theoretical and numerical results on approximation rates, preconditioning, adaptivity and compression for piecewise constant and linear sparse grid spaces
Abstract Jacobi Sets of Multiple Morse Functions
"... The Jacobi set of two Morse functions defined on a common £manifold is the set of critical points of the restrictions of one function to the level sets of the other function. Equivalently, it is the set of points where the gradients of the functions are parallel. For a generic pair of Morse functio ..."
Abstract
 Add to MetaCart
functions, the Jacobi set is a smoothly embedded 1manifold. We give a polynomialtime algorithm that computes the piecewise linear analog of the Jacobi set for functions specified at the vertices of a triangulation, and we generalize all results to more than two but at most £ Morse functions.
On regular neighbourhoods
 Proc. London Math. Soc
, 1964
"... IN (11) J. H. C. Whitehead introduced the theory of regular neighbourhoods, which has become a basic tool in combinatorial topology. We extend the theory in three ways. First we relativize the concept, and introduce the regular neighbourhood N of X mod Y in M, where X and Y are two compact polyhedr ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
that said that any two regular neighbourhoods were (piecewise linearly) homeomorphic. We strengthen this result by showing them to be isotopic, keeping a smaller regular neighbourhood fixed (Theorem 2). In fact they are ambient isotopic provided that they meet the boundary regularly (Theorem 3), which
Model Reduction via Projection onto Nonlinear Manifolds, with Applications to Analog Circuits and Biochemical Systems
 In ICCAD ’08: Proceedings of the 2008 IEEE/ACM International Conference on ComputerAided Design
, 2008
"... AbstractPrevious model order reduction methods fit into the framework of identifying the loworder linear subspace and using the linear projection to project the full state space into the loworder subspace. Despite its simplicity, the macromodel might automatically include redundancies. In this p ..."
Abstract

Cited by 9 (4 self)
 Add to MetaCart
the manifold is determined, it is embedded into a global nonlinear coordinate system. The projection function is defined in a piecewise linear manner, and the model evaluation is conducted directly in the manifold subspace using cheap matrixvector product computations. As a result, a compact model
MM&9383 87 SO3 M) +.OO c _ 1987 Pergamon Journals Lrd. A SPANNING TREE EXPANSION OF THE JONES POLYNOMIAL MOR~EN
, 1986
"... A KEW combinatorial formulation of the Jones polynomial of a link is used to establish some basic properties of this polynomial. A striking consequence of these properties is the result that a link admitting an alternating diagram with m crossings and with no “nugatory” crossing cannot be projected ..."
Abstract
 Add to MetaCart
with fewer than m crossings. $1. ISTRODUCTION AND STATEklENT OF RESULTS This article is concerned with classical links, that is to say closed lmanifolds embedded piecewiselinearly in the oriented 3sphere. The link itself may also be endowed with an orientation. Two oriented links L,, L, are isotopic
Results 1  10
of
19