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Minimum-Length Polygons in Simple Cube-Curves
[chapter]

2000
*
Lecture Notes in Computer Science
*

The

doi:10.1007/3-540-44438-6_38
fatcat:guldn7l5yrd6nnnws566hvv5dy
*length*of such a*simple*digital*curve*is defined to be the*length*of the*minimum*-*length**polygonal**curve*fully contained and complete*in*the tube of this digital*curve*. ... A critical edge is a grid edge contained*in*three consecutive*cubes*of a*simple**cube*-*curve*. ... A non-flat*simple**cube*-*curve**in*R 3 specifies exactly one*minimum*-*length**polygonal**simple**curve*(MLP,*minimum*-*length**polygon*) which is contained and complete*in*its tube [11] . ...##
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Minimum-Length Polygons of First-Class Simple Cube-Curves
[chapter]

2005
*
Lecture Notes in Computer Science
*

The curve's

doi:10.1007/11556121_40
fatcat:iyfw2jtqnvci5mbztqr453veai
*length*is defined to be that of the*minimum*-*length**polygonal**curve*(MLP) fully contained and complete*in*the tube of the*curve*. ... We consider*simple**cube*-*curves**in*the orthogonal 3D grid. The union of all cells contained*in*such a*curve*(also called the tube of this*curve*) is a polyhedrally bounded set. ... A*minimum*-*length**polygon*(MLP) of a*simple**cube*-*curve*g is a shortest*simple**curve*P which is contained and complete*in*tube g. ...##
###
Minimum-Length Polygon of a Simple Cube-Curve in 3D Space
[chapter]

2004
*
Lecture Notes in Computer Science
*

The curve's

doi:10.1007/978-3-540-30503-3_36
fatcat:62n7iegqs5em3nqrmwwntsrrxi
*length*is defined to be that of the*minimum*-*length**polygonal**curve*(MLP) fully contained and complete*in*the tube of the*curve*. ... We consider*simple**cube*-*curves**in*the orthogonal 3D grid of cells. The union of all cells contained*in*such a*curve*(also called the tube of this*curve*) is a polyhedrally bounded set. ... A*minimum*-*length**polygon*(MLP) of a*simple**cube*-*curve*g is a shortest*simple**curve*P which is contained and complete*in*tube g. ...##
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Approximation of 3D Shortest Polygons in Simple Cube Curves
[chapter]

2001
*
Lecture Notes in Computer Science
*

One possible definition of the

doi:10.1007/3-540-45576-0_17
fatcat:yfnenxld5zhw7dkkvyfinn5x44
*length*of a digitized*curve**in*3D is the*length*of the shortest*polygonal**curve*lying entirely*in*a*cube**curve*. ... One possible de nition of the*length*of a digitized*curve*i n 3D is the*length*of the shortest*polygonal**curve*lying entirely*in*a*cube**curve*. ... A non-at*simple**cube*-*curve**in*R 3 speci es exactly one*minimum*-*length**polygonal**simple**curve*(MLP) which i s c o n tained and complete*in*its tube 10]. ...##
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Shortest Paths in a Cuboidal World
[chapter]

2006
*
Lecture Notes in Computer Science
*

The shortest path through a

doi:10.1007/11774938_33
fatcat:klahkozvjjgwhdknju4wxw6irm
*simple**cube*-*curve**in*the orthogonal 3D grid is a*minimum*-*length**polygonal**curve*(MLP for short). ... to move*in*form a*simple**cube*-*curve*. ... A*minimum*-*length**curve*of a*simple**cube*-*curve*g is a shortest*simple**curve*P which is contained and complete*in*tube g. The*length*L(g) of g is defined to be the*length*L(P ). ...##
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Analysis of the rubberband algorithm

2007
*
Image and Vision Computing
*

The curve's

doi:10.1016/j.imavis.2006.06.021
fatcat:vq2nfenarva7jb7o6djbjdvngq
*length*is defined to be that of the*minimum*-*length**polygonal**curve*(MLP) contained and complete*in*the tube of the*curve*. ... We consider*simple**cube*-*curves**in*the orthogonal 3D grid of cells. The union of all cells contained*in*such a*curve*(also called the tube of this*curve*) is a polyhedrally bounded set. ... The*length*of a*simple**cube*-*curve*S*in*3D Euclidean space can be defined by the (Euclidean)*length*of the*minimum*-*length**polygonal**curve*(MLP for short) contained and complete*in*the polyhedrally bounded ...##
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Euclidean Shortest Paths in Simple Cube Curves at a Glance
[article]

2007
*
arXiv
*
pre-print

>0, and

arXiv:0704.3197v1
fatcat:p4nyxp22fvhtdczwem5ttwwtnm
*in*time complexity κ(ϵ) · O(n), where κ(ϵ) is the*length*difference between the path used for initialization and the*minimum*-*length*path, divided by ϵ. ... This paper reports about the development of two provably correct approximate algorithms which calculate the Euclidean shortest path (ESP) within a given*cube*-*curve*with arbitrary accuracy, defined by ϵ ... it is of*minimum*Euclidean*length*. ...##
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Page 6382 of Mathematical Reviews Vol. , Issue 98J
[page]

1998
*
Mathematical Reviews
*

Let y be a

*simple*closed*curve*of*length*< 2z on the unit sphere S?. ... 98}:52011 that a regular simplex of edge-*length*/*in*E” has*minimum*width 1\/2/(n +1) if n is odd, and /\/2(n + 1)/n(n + 2) if n is even. G. D. ...##
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Polyhedra generation from lattice points
[chapter]

1996
*
Lecture Notes in Computer Science
*

If a digital

doi:10.1007/3-540-62005-2_11
fatcat:ojfpp6pdzzbhnfnufsn2dhzuru
*polygon*has n holes, the inside of the digital*polygon*is encircled by n + 1*simple*closed*curves*because each hole is encircled by a*simple*closed*curve*. ... to the inside of the*simple*closed*curve*. ...##
###
The Class of Simple Cube-Curves Whose MLPs Cannot Have Vertices at Grid Points
[chapter]

2005
*
Lecture Notes in Computer Science
*

The curve's

doi:10.1007/978-3-540-31965-8_18
fatcat:n3ujto322ncczoq22cnpvftfwi
*length*is defined to be that of the*minimum*-*length**polygonal**curve*(MLP) fully contained and complete*in*the tube of the*curve*. ... We consider*simple**cube*-*curves**in*the orthogonal 3D grid of cells. The union of all cells contained*in*such a*curve*(also called the tube of this*curve*) is a polyhedrally bounded set. ... A*minimum*-*length**polygon*(MLP) of a*simple**cube*-*curve*g is a shortest*simple**curve*P which is contained and complete*in*tube g. ...##
###
Polygonization of implicit surfaces

1988
*
Computer Aided Geometric Design
*

With a

doi:10.1016/0167-8396(88)90013-1
fatcat:mjf7gscr6javbfjhbrjd77psaa
*polygonal*representation of the surface available, certain computational economies result.*In*particular, the roots to the function need not be solved each time the surface is rendered. ... This paper discusses a numerical technique that approximates an implicit surface with a*polygonal*representation. ... Given the*polygon*vertices, P i , their unit*length*normals, N i , and the unit*length*normal N at the*polygon*center, the planarity of the*polygon*can be estimated by: 1, nPoints] and V i the unit*length*...##
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Finding the Shortest Path Between Two Points in a Simple Polygon by Applying a Rubberband Algorithm
[chapter]

2006
*
Lecture Notes in Computer Science
*

Let p and q be two points

doi:10.1007/11949534_28
fatcat:eutdsn5qtbbwpajnpnx7uuww24
*in*a*simple**polygon*Π. ... An open problem*in*computational geometry asks to devise a*simple*linear-time algorithm for computing a shortest path between p and q, which is contained*in*Π, such that the algorithm does not depend on ... The original rubberband algorithm was published*in*[1] and [6] , aiming at an (approximative) calculation of a*minimum*-*length**polygonal*path (MLP) contained and complete*in*a*simple**cube*-*curve*(subsequent ...##
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Approximating the Fréchet Distance for Realistic Curves in Near Linear Time

2012
*
Discrete & Computational Geometry
*

We present a

doi:10.1007/s00454-012-9402-z
fatcat:jhkejni6ovewlp7qfwjftjxohm
*simple*and practical (1 + ε)-approximation algorithm for the Fréchet distance between two*polygonal**curves**in*R d . ... We show that our algorithm has near linear running time for c-packed*polygonal**curves*, and similar results for other input models, such as low-density*polygonal**curves*. ... Acknowledgements The authors thank Mark de Berg and Marc van Kreveld for insightful discussions on the problems studied*in*this paper and related problems. ...##
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Approximating the Fréchet distance for realistic curves in near linear time

2010
*
Proceedings of the 2010 annual symposium on Computational geometry - SoCG '10
*

We present a

doi:10.1145/1810959.1811019
dblp:conf/compgeom/DriemelHW10
fatcat:o3fjc2hwefca3k7hfpkq7kd72e
*simple*and practical (1 + ε)-approximation algorithm for the Fréchet distance between two*polygonal**curves**in*R d . ... We show that our algorithm has near linear running time for c-packed*polygonal**curves*, and similar results for other input models, such as low-density*polygonal**curves*. ... Acknowledgements The authors thank Mark de Berg and Marc van Kreveld for insightful discussions on the problems studied*in*this paper and related problems. ...##
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MESH GENERATION AND OPTIMAL TRIANGULATION
[chapter]

1995
*
Lecture Notes Series on Computing
*

We especially focus on optimal triangulations of geometric domains

doi:10.1142/9789812831699_0003
fatcat:ec6436f5i5bszheuiherz452ae
*in*two-and three-dimensions. ... We brie y survey the heuristic algorithms used*in*some practical mesh generators. remove the rst edge e from the queue. If Q e is not reversed, we simply continue to the next edge. ... Conclusions We have described work*in*computational geometry motivated by nite element mesh generation. ...
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