Survey on geometric iterative methods and their applications

Hongwei Lin; Takashi Maekawa; Chongyang Deng

doi:10.1016/j.cad.2017.10.002

Survey on geometric iterative methods and their applications

Hongwei Lin^*, Takashi Maekawa, Chongyang Deng

^*Corresponding author for this work

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

74 Citations (Scopus)

Abstract

Geometric iterative methods (GIM), including the progressive–iterative approximation (PIA) and the geometric interpolation/approximation method, are a class of iterative methods for fitting curves and surfaces with clear geometric meanings. In this paper, we provide an overview of the interpolatory and approximate geometric iteration methods, present the local properties and accelerating techniques, and show their convergence. Moreover, because it is easy to integrate geometric constraints in the iterative procedure, GIM has been widely applied in geometric design and related areas. We survey the successful applications of geometric iterative methods, including applications in geometric design, data fitting, reverse engineering, mesh and NURBS solid generation.

Original language	English
Pages (from-to)	40-51
Number of pages	12
Journal	CAD Computer Aided Design
Volume	95
DOIs	https://doi.org/10.1016/j.cad.2017.10.002
Publication status	Published - 2018 Feb
Externally published	Yes

Keywords

Geometric design
Geometric interpolation/approximation
Geometric iterative method
Progressive–iterative approximation

ASJC Scopus subject areas

Computer Science Applications
Computer Graphics and Computer-Aided Design
Industrial and Manufacturing Engineering

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10.1016/j.cad.2017.10.002

Cite this

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title = "Survey on geometric iterative methods and their applications",

abstract = "Geometric iterative methods (GIM), including the progressive–iterative approximation (PIA) and the geometric interpolation/approximation method, are a class of iterative methods for fitting curves and surfaces with clear geometric meanings. In this paper, we provide an overview of the interpolatory and approximate geometric iteration methods, present the local properties and accelerating techniques, and show their convergence. Moreover, because it is easy to integrate geometric constraints in the iterative procedure, GIM has been widely applied in geometric design and related areas. We survey the successful applications of geometric iterative methods, including applications in geometric design, data fitting, reverse engineering, mesh and NURBS solid generation.",

keywords = "Geometric design, Geometric interpolation/approximation, Geometric iterative method, Progressive–iterative approximation",

author = "Hongwei Lin and Takashi Maekawa and Chongyang Deng",

note = "Funding Information: This paper is supported by the Natural Science Foundation of China (No. 61379072 , 61370166 ), and the Fundamental Research Funds for the Central Universities ( 2017XZZX009-03 ). Publisher Copyright: {\textcopyright} 2017 Elsevier Ltd",

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doi = "10.1016/j.cad.2017.10.002",

language = "English",

volume = "95",

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AU - Lin, Hongwei

AU - Maekawa, Takashi

AU - Deng, Chongyang

N1 - Funding Information: This paper is supported by the Natural Science Foundation of China (No. 61379072 , 61370166 ), and the Fundamental Research Funds for the Central Universities ( 2017XZZX009-03 ). Publisher Copyright: © 2017 Elsevier Ltd

PY - 2018/2

Y1 - 2018/2

N2 - Geometric iterative methods (GIM), including the progressive–iterative approximation (PIA) and the geometric interpolation/approximation method, are a class of iterative methods for fitting curves and surfaces with clear geometric meanings. In this paper, we provide an overview of the interpolatory and approximate geometric iteration methods, present the local properties and accelerating techniques, and show their convergence. Moreover, because it is easy to integrate geometric constraints in the iterative procedure, GIM has been widely applied in geometric design and related areas. We survey the successful applications of geometric iterative methods, including applications in geometric design, data fitting, reverse engineering, mesh and NURBS solid generation.

AB - Geometric iterative methods (GIM), including the progressive–iterative approximation (PIA) and the geometric interpolation/approximation method, are a class of iterative methods for fitting curves and surfaces with clear geometric meanings. In this paper, we provide an overview of the interpolatory and approximate geometric iteration methods, present the local properties and accelerating techniques, and show their convergence. Moreover, because it is easy to integrate geometric constraints in the iterative procedure, GIM has been widely applied in geometric design and related areas. We survey the successful applications of geometric iterative methods, including applications in geometric design, data fitting, reverse engineering, mesh and NURBS solid generation.

KW - Geometric design

KW - Geometric interpolation/approximation

KW - Geometric iterative method

KW - Progressive–iterative approximation

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Survey on geometric iterative methods and their applications

Abstract

Keywords

ASJC Scopus subject areas

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