scholarly journals A two-level approach to implicit surface modeling with compactly supported radial basis functions

2010 ◽  
Vol 27 (3) ◽  
pp. 299-307 ◽  
Author(s):  
Rongjiang Pan ◽  
Vaclav Skala
Keyword(s):  
Radial Basis Functions ◽  
Surface Modeling ◽  
Basis Functions ◽  
Implicit Surface ◽  
Compactly Supported ◽  
Radial Basis

scholarly journals Scattered Data Interpolation and Approximation with Truncated Exponential Radial Basis Function

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1101 ◽  
Author(s):  
Qiuyan Xu ◽  
Zhiyong Liu
Keyword(s):  
Radial Basis Functions ◽  
Radial Function ◽  
Dimensional Space ◽  
Level Set Methods ◽  
Scattered Data ◽  
Surface Modeling ◽  
Basis Functions ◽  
Data Interpolation ◽  
Scattered Data Interpolation ◽  
Radial Basis

Surface modeling is closely related to interpolation and approximation by using level set methods, radial basis functions methods, and moving least squares methods. Although radial basis functions with global support have a very good approximation effect, this is often accompanied by an ill-conditioned algebraic system. The exceedingly large condition number of the discrete matrix makes the numerical calculation time consuming. The paper introduces a truncated exponential function, which is radial on arbitrary n-dimensional space R n and has compact support. The truncated exponential radial function is proven strictly positive definite on R n while internal parameter l satisfies l ≥ ⌊ n 2 ⌋ + 1 . The error estimates for scattered data interpolation are obtained via the native space approach. To confirm the efficiency of the truncated exponential radial function approximation, the single level interpolation and multilevel interpolation are used for surface modeling, respectively.

Implicit surface reconstruction with radial basis functions via PDEs

2020 ◽  
Vol 110 ◽  
pp. 95-103 ◽  
Author(s):  
Xiao-Yan Liu ◽  
Hui Wang ◽  
C.S. Chen ◽  
Qing Wang ◽  
Xiaoshuang Zhou ◽  
...  
Keyword(s):  
Radial Basis Functions ◽  
Surface Reconstruction ◽  
Basis Functions ◽  
Implicit Surface ◽  
Radial Basis
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