B-Spline Basis Functions

2007 ◽  
Keyword(s):  
Basis Functions ◽  
B Spline ◽  
Spline Basis

scholarly journals Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2102
Author(s):  
Abdul Majeed ◽  
Muhammad Abbas ◽  
Faiza Qayyum ◽  
Kenjiro T. Miura ◽  
Md Yushalify Misro ◽  
...  
Keyword(s):  
Geometric Modeling ◽  
Shape Parameter ◽  
3D Models ◽  
Basis Functions ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curves ◽  
Spline Basis ◽  
Cubic Polynomial ◽  
2D And 3D

Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ∈[0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.

THE BOUNDARY FACE METHOD WITH VARIABLE APPROXIMATION BY B-SPLINE BASIS FUNCTION

2012 ◽  
Vol 09 (01) ◽  
pp. 1240009 ◽  
Author(s):  
JINLIANG GU ◽  
JIANMING ZHANG ◽  
XIAOMIN SHENG
Keyword(s):  
Numerical Solutions ◽  
Basis Functions ◽  
Spline Functions ◽  
Well Performance ◽  
Geometric Information ◽  
B Spline ◽  
Numerical Tests ◽  
Boundary Integration ◽  
Spline Basis ◽  
Boundary Face

B-spline basis functions as a new approximation method is introduced in the boundary face method (BFM) to obtain numerical solutions of 3D potential problems. In the BFM, both boundary integration and variable approximation are performed in the parametric spaces of the boundary surfaces, therefore, keeps the exact geometric information of a body in which the problem is defined. In this paper, local bivariate B-spline functions are proposed to alleviate the influence of B-spline tensor product that will deteriorate the exactness of numerical results. Numerical tests show that the new method has well performance in both exactness and convergence.

Research on the Key Issues of Numerical Controlled Machine Layout Design

2014 ◽  
Vol 548-549 ◽  
pp. 968-973
Author(s):  
Zhi Gang Xu
Keyword(s):  
Recursive Formula ◽  
Layout Design ◽  
Basis Functions ◽  
Nurbs Curve ◽  
B Spline ◽  
Machine Layout ◽  
Spline Basis ◽  
Key Issues ◽  
Normal Vectors

Formulas for the derivatives and normal vectors of non-rational B-spline and NURBS are proved based on de BOOR’s recursive formula. Compared with the existing approaches targeting at the non-rational B-spline basis functions, these equations are directly targeted at the controlling points, so the algorithms and programs for NURBS curve and surface can also be applied to the derivatives and normals, the calculating performance is increased. A simplified equation is also proved in this paper.

LDG approximation of a nonlinear fractional convection-diffusion equation using B-spline basis functions

2022 ◽  
Vol 171 ◽  
pp. 45-57
Author(s):  
Hamid Safdari ◽  
Majid Rajabzadeh ◽  
Moein Khalighi
Keyword(s):  
Diffusion Equation ◽  
Basis Functions ◽  
B Spline ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Spline Basis

Application of Rational B-Splines to the Synthesis of Cam-Follower Motion Programs

1993 ◽  
Vol 115 (3) ◽  
pp. 621-626 ◽  
Author(s):  
D. M. Tsay ◽  
C. O. Huey
Keyword(s):  
Basis Functions ◽  
Spline Functions ◽  
B Spline ◽  
B Splines ◽  
Motion Constraints ◽  
Cam Follower ◽  
Spline Basis

A procedure employing rational B-spline functions for the synthesis of cam-follower motion programs is presented. It differs from earlier techniques that employ spline functions by using rational B-spline basis functions to interpolate motion constraints. These rational B-splines permit greater flexibility in refining motion programs. Examples are provided to illustrate application of the approach.

Least square fitting of low resolution gamma ray spectra with cubic B-spline basis functions

2009 ◽  
Vol 33 (1) ◽  
pp. 24-30 ◽  
Author(s):  
Zhu Meng-Hua ◽  
Liu Liang-Gang ◽  
Qi Dong-Xu ◽  
You Zhong ◽  
Xu Ao-Ao
Keyword(s):  
Gamma Ray ◽  
Basis Functions ◽  
Least Square ◽  
Low Resolution ◽  
B Spline ◽  
Least Square Fitting ◽  
Spline Basis

An Adaptive Wavelet Finite Element Method with High-Order B-Spline Basis Functions

2007 ◽  
Vol 345-346 ◽  
pp. 877-880 ◽  
Author(s):  
Satoyuki Tanaka ◽  
Hiroshi Okada
Keyword(s):  
Galerkin Method ◽  
Scaling Function ◽  
Adaptive Strategy ◽  
Basis Functions ◽  
Adaptive Wavelet ◽  
B Spline ◽  
Wavelet Galerkin Method ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Spline Basis

In this paper, an adaptive strategy based on a B-spline wavelet Galerkin method is discussed. The authors have developed the wavelet Galerkin Method which utilizes quadratic and cubic B-spline scaling function/wavelet as its basis functions. The developed B-spline Galerkin Method has been proven to be very accurate in the analyses of elastostatics. Then the authors added a capability to adaptively adjust the special resolution of the basis functions by adding the wavelet basis functions where the resolution needs to be enhanced.

scholarly journals An Improvement on the Upper Bounds of the Partial Derivatives of NURBS Surfaces

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1382
Author(s):  
Ye Tian ◽  
Tao Ning ◽  
Jixing Li ◽  
Jianmin Zheng ◽  
Zhitong Chen
Keyword(s):  
Upper Bounds ◽  
Basis Functions ◽  
Nurbs Surface ◽  
Degree Reduction ◽  
B Spline ◽  
Partial Derivatives ◽  
Spline Basis ◽  
Rational Bézier Surface ◽  
Nurbs Surfaces ◽  
Derivatives Of

The Non-Uniform Rational B-spline (NURBS) surface not only has the characteristics of the rational Bézier surface, but also has changeable knot vectors and weights, which can express the quadric surface accurately. In this paper, we investigated new bounds of the first- and second-order partial derivatives of NURBS surfaces. A pilot study was performed using inequality theorems and degree reduction of B-spline basis functions. Theoretical analysis provides simple forms of the new bounds. Numerical examples are performed to illustrate that our method has sharper bounds than the existing ones.

A comment on the orthogonalization of B-spline basis functions and their derivatives

2011 ◽  
Vol 22 (1) ◽  
pp. 251-257 ◽  
Author(s):  
Andrew Redd
Keyword(s):  
Basis Functions ◽  
B Spline ◽  
Spline Basis
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