TY - JOUR
T1 - Survey on geometric iterative methods and their applications
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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U2 - 10.1016/j.cad.2017.10.002
DO - 10.1016/j.cad.2017.10.002
M3 - Article
AN - SCOPUS:85032736965
SN - 0010-4485
VL - 95
SP - 40
EP - 51
JO - CAD Computer Aided Design
JF - CAD Computer Aided Design
ER -