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692
Discrete DifferentialGeometry Operators for Triangulated 2Manifolds
, 2002
"... This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Vorono ..."
Abstract

Cited by 449 (14 self)
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Voronoi cells and the mixed FiniteElement/FiniteVolume method, and compare them to existing formulations. Building upon previous work in discrete geometry, these new operators are closely related to the continuous case, guaranteeing an appropriate extension from the continuous to the discrete setting
Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow
, 1999
"... In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating highfidelit ..."
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Cited by 542 (23 self)
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In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating high
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
Abstract

Cited by 534 (11 self)
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are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed
Computing Geodesic Paths on Manifolds
 Proc. Natl. Acad. Sci. USA
, 1998
"... The Fast Marching Method [8] is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity. A ..."
Abstract

Cited by 294 (28 self)
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The Fast Marching Method [8] is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity
ROAMing Terrain: Realtime Optimally Adapting Meshes
, 1997
"... Terrain visualization is a difficult problem for applications requiring accurate images of large datasets at high frame rates, such as flight simulation and groundbased aircraft testing using synthetic sensor stimulation. On current graphics hardware, the problem is to maintain dynamic, viewdepend ..."
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Cited by 287 (10 self)
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toframe coherence to operate at high frame rates for thousands of triangles per frame. Our method, dubbed Realtime Optimally Adapting Meshes (ROAM), uses two priority queues to drive split and merge operations that maintain continuous triangulations built from preprocessed bintree triangles. We introduce two
MAPS: Multiresolution Adaptive Parameterization of Surfaces
, 1998
"... We construct smooth parameterizations of irregular connectivity triangulations of arbitrary genus 2manifolds. Our algorithm uses hierarchical simplification to efficiently induce a parameterization of the original mesh over a base domain consisting of a small number of triangles. This initial param ..."
Abstract

Cited by 265 (12 self)
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We construct smooth parameterizations of irregular connectivity triangulations of arbitrary genus 2manifolds. Our algorithm uses hierarchical simplification to efficiently induce a parameterization of the original mesh over a base domain consisting of a small number of triangles. This initial
Persistent Triangulations
 UNDER CONSIDERATION FOR PUBLICATION IN J. FUNCTIONAL PROGRAMMING
, 2002
"... Triangulations of a surface are of fundamental importance in computational geometry, computer graphics, and engineering and scientific simulations. Triangulations are ordinarily represented as mutable graph structures for which both adding and traversing edges take constant time per operation. These ..."
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Cited by 7 (2 self)
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Triangulations of a surface are of fundamental importance in computational geometry, computer graphics, and engineering and scientific simulations. Triangulations are ordinarily represented as mutable graph structures for which both adding and traversing edges take constant time per operation
Persistent Triangulations
 Journal of Functional Programming (JFP
, 2001
"... Triangulations of a surface are of fundamental importance in computational geometry, engineering simulation, and computer graphics. For example, the convex hull of a set of points may be constructed as a triangulation, and there is a close relationship between Delaunay triangulations and Voronoi dia ..."
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diagrams in geometry. Triangulations are ordinarily represented as mutable graph structures for which both edge traversal and adding edges take constant time per operation. These representations of triangulations make it difficult to support persistence, including "multiple futures", the ability
On deletion in Delaunay triangulation
 Internat. J. Comput. Geom. Appl
, 2002
"... This paper presents how the space of spheres and shelling may be used to delete a point from a ddimensional triangulation efficiently. In dimension two, if k is the degree of the deleted vertex, the complexity is O(k log k), but we notice that this number only applies to low cost operations, while ..."
Abstract

Cited by 53 (3 self)
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This paper presents how the space of spheres and shelling may be used to delete a point from a ddimensional triangulation efficiently. In dimension two, if k is the degree of the deleted vertex, the complexity is O(k log k), but we notice that this number only applies to low cost operations, while
Modeling on Triangulations . . .
 THE VISUAL COMPUTER
"... In the first part of this paper we define a new class of curves, called geodesic Bézier curves, that are suitable for modeling on manifold triangulations. As a natural generalization of Bézier curves, the new curves are as smooth as possible. In the second part we discuss the construction of C 0 and ..."
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and C 1 piecewise Bézier splines. We also describe how to perform editing operations, such as trimming, using these curves. Special care is taken to achieve interactive rates for modeling tasks. The third part is devoted to the definition and study of convex sets on triangulated surfaces. We derive
Results 1  10
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692