3D Euler spirals for 3D curve completion

Gur Harary; Ayellet Tal

doi:10.1016/j.comgeo.2011.10.001

3D Euler spirals for 3D curve completion

Gur Harary, Ayellet Tal

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

Shape completion is an intriguing problem in geometry processing with applications in CAD and graphics. This paper defines a new type of 3D curve, which can be utilized for curve completion. It can be considered as the extension to three dimensions of the 2D Euler spiral. We prove several properties of this curve - properties that have been shown to be important for the appeal of curves. We illustrate its utility in two applications. The first is "fixing" curves detected by algorithms for edge detection on surfaces. The second is shape illustration in archaeology, where the user would like to draw curves that are missing due to the incompleteness of the input model.

Original language	English
Pages (from-to)	115-126
Number of pages	12
Journal	Computational Geometry: Theory and Applications
Volume	45
Issue number	3
DOIs	https://doi.org/10.1016/j.comgeo.2011.10.001
State	Published - Apr 2012

Keywords

3D curves
Euler spirals

All Science Journal Classification (ASJC) codes

Computational Mathematics
Control and Optimization
Geometry and Topology
Computer Science Applications
Computational Theory and Mathematics

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10.1016/j.comgeo.2011.10.001

Cite this

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title = "3D Euler spirals for 3D curve completion",

abstract = "Shape completion is an intriguing problem in geometry processing with applications in CAD and graphics. This paper defines a new type of 3D curve, which can be utilized for curve completion. It can be considered as the extension to three dimensions of the 2D Euler spiral. We prove several properties of this curve - properties that have been shown to be important for the appeal of curves. We illustrate its utility in two applications. The first is {"}fixing{"} curves detected by algorithms for edge detection on surfaces. The second is shape illustration in archaeology, where the user would like to draw curves that are missing due to the incompleteness of the input model.",

keywords = "3D curves, Euler spirals",

author = "Gur Harary and Ayellet Tal",

note = "Funding Information: This research was supported in part by the Israel Science Foundation (ISF) 628/08 , the Goldbers Fund for Electronics Research , and the Ollendorff foundation . We thank Dr. A. Gilboa and the Zinman Institute of Archaeology at the University of Haifa for providing the archaeological models. The other models are courtesy of the AIM@SHAPE Shape Repository and the MIT CSAIL database.",

year = "2012",

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doi = "10.1016/j.comgeo.2011.10.001",

language = "الإنجليزيّة",

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pages = "115--126",

journal = "Computational Geometry: Theory and Applications",

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AU - Harary, Gur

AU - Tal, Ayellet

N1 - Funding Information: This research was supported in part by the Israel Science Foundation (ISF) 628/08 , the Goldbers Fund for Electronics Research , and the Ollendorff foundation . We thank Dr. A. Gilboa and the Zinman Institute of Archaeology at the University of Haifa for providing the archaeological models. The other models are courtesy of the AIM@SHAPE Shape Repository and the MIT CSAIL database.

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Y1 - 2012/4

N2 - Shape completion is an intriguing problem in geometry processing with applications in CAD and graphics. This paper defines a new type of 3D curve, which can be utilized for curve completion. It can be considered as the extension to three dimensions of the 2D Euler spiral. We prove several properties of this curve - properties that have been shown to be important for the appeal of curves. We illustrate its utility in two applications. The first is "fixing" curves detected by algorithms for edge detection on surfaces. The second is shape illustration in archaeology, where the user would like to draw curves that are missing due to the incompleteness of the input model.

AB - Shape completion is an intriguing problem in geometry processing with applications in CAD and graphics. This paper defines a new type of 3D curve, which can be utilized for curve completion. It can be considered as the extension to three dimensions of the 2D Euler spiral. We prove several properties of this curve - properties that have been shown to be important for the appeal of curves. We illustrate its utility in two applications. The first is "fixing" curves detected by algorithms for edge detection on surfaces. The second is shape illustration in archaeology, where the user would like to draw curves that are missing due to the incompleteness of the input model.

KW - 3D curves

KW - Euler spirals

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U2 - 10.1016/j.comgeo.2011.10.001

DO - 10.1016/j.comgeo.2011.10.001

M3 - مقالة

SN - 0925-7721

VL - 45

SP - 115

EP - 126

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

IS - 3

ER -

3D Euler spirals for 3D curve completion

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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