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Computing Geodesics on Triangular Meshes ⋆
"... We present a new algorithm to compute a geodesic path over a triangulated surface. Based on Sethian’s Fast Marching Method and Polthier’s Straightest Geodesics theory, we are able to generate an iterative process to obtain a good discrete geodesic approximation. It can handle both convex and noncon ..."
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We present a new algorithm to compute a geodesic path over a triangulated surface. Based on Sethian’s Fast Marching Method and Polthier’s Straightest Geodesics theory, we are able to generate an iterative process to obtain a good discrete geodesic approximation. It can handle both convex and non
Multiresolution Analysis of Arbitrary Meshes
, 1995
"... In computer graphics and geometric modeling, shapes are often represented by triangular meshes. With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace. Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit. Multire ..."
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Cited by 605 (16 self)
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In computer graphics and geometric modeling, shapes are often represented by triangular meshes. With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace. Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit
QSplat: A Multiresolution Point Rendering System for Large Meshes
, 2000
"... Advances in 3D scanning technologies have enabled the practical creation of meshes with hundreds of millions of polygons. Traditional algorithms for display, simplification, and progressive transmission of meshes are impractical for data sets of this size. We describe a system for representing and p ..."
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Cited by 500 (8 self)
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Advances in 3D scanning technologies have enabled the practical creation of meshes with hundreds of millions of polygons. Traditional algorithms for display, simplification, and progressive transmission of meshes are impractical for data sets of this size. We describe a system for representing
Geodesic paths on triangular meshes
 In Proc. of SIBGRAPI/SIACG
, 2004
"... Abstract. We present a new algorithm to compute a geodesic path over a triangulated surface. Based in Sethian’s Fast Marching Method and Polthier’s Straightest Geodesics theory, we are able to generate an iterative process to obtain a good discrete geodesic approximation. It can handle convex and no ..."
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Cited by 5 (0 self)
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Abstract. We present a new algorithm to compute a geodesic path over a triangulated surface. Based in Sethian’s Fast Marching Method and Polthier’s Straightest Geodesics theory, we are able to generate an iterative process to obtain a good discrete geodesic approximation. It can handle convex
Computing geodesic distances on triangular meshes
 In Proc. of WSCG’2002
, 2002
"... We present an approximation method to compute geodesic distances on triangulated domains in the three dimensional space. Our particular approach is based on the Fast Marching Method for solving the Eikonal equation on triangular meshes. As such, the algorithm is a wavefront propagation method, a rem ..."
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Cited by 23 (2 self)
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We present an approximation method to compute geodesic distances on triangulated domains in the three dimensional space. Our particular approach is based on the Fast Marching Method for solving the Eikonal equation on triangular meshes. As such, the algorithm is a wavefront propagation method, a
Geodesic Paths on Triangular Meshes
 In Proc. of SIBGRAPI/SIACG
, 2004
"... We present a new algorithm to compute a geodesic path over a triangulated surface. Based in Sethian's Fast Marching Method and Polthier's Straightest Geodesics theory, we are able to generate an iterative process to obtain a good discrete geodesic approximation. It can handle convex and no ..."
Abstract
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We present a new algorithm to compute a geodesic path over a triangulated surface. Based in Sethian's Fast Marching Method and Polthier's Straightest Geodesics theory, we are able to generate an iterative process to obtain a good discrete geodesic approximation. It can handle convex
Mesh Optimization
, 1993
"... We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh wH, produce a mesh w, of the same topological type as wH, that fits the data well and has a small number of vertices. Our approach is to minimize an energy f ..."
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Cited by 397 (8 self)
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We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh wH, produce a mesh w, of the same topological type as wH, that fits the data well and has a small number of vertices. Our approach is to minimize an energy
LogP: Towards a Realistic Model of Parallel Computation
, 1993
"... A vast body of theoretical research has focused either on overly simplistic models of parallel computation, notably the PRAM, or overly specific models that have few representatives in the real world. Both kinds of models encourage exploitation of formal loopholes, rather than rewarding developme ..."
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Cited by 562 (15 self)
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A vast body of theoretical research has focused either on overly simplistic models of parallel computation, notably the PRAM, or overly specific models that have few representatives in the real world. Both kinds of models encourage exploitation of formal loopholes, rather than rewarding
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 ..."
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Cited by 293 (28 self)
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. As an application, we provide an optimal time algorithm for computing the geodesic distances and thereby extracting shortest paths on triangulated manifolds. 1 Introduction Sethian`s Fast Marching Method [8], is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M
Results 1  10
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53,421