The general B-spline interpolation method and its application to the modification of curves and surfaces

1997 ◽  
Vol 29 (11) ◽  
pp. 779-790 ◽  
Author(s):  
Junji Ishida
Keyword(s):  
Interpolation Method ◽  
Spline Interpolation ◽  
B Spline ◽  
Curves And Surfaces

Image Interpolation Algorithm Based on Edge Features

2011 ◽  
Vol 50-51 ◽  
pp. 564-567
Author(s):  
Yun Feng Yang ◽  
Xiao Guang Wei ◽  
Zhi Xun Su
Keyword(s):  
Interpolation Method ◽  
Spline Interpolation ◽  
Weighted Average ◽  
Image Interpolation ◽  
Interpolation Process ◽  
Edge Information ◽  
B Spline ◽  
Interpolation Methods ◽  
Distance Weighted ◽  
Edge Features

Image interpolation is used widely in the computer vision. Holding edge information is main problem in the image interpolation. By using bilinear and bicubic B-spline interpolation methods, a novel image interpolation approach was proposed in this paper. Firstly, inverse distance weighted average method was used to reduce image’s noise. Secondly, edge detection operator was used to extract image's edges information. It can help us to select different interpolation methods in the image interpolation process. Finally, we selected bilinear interpolation approach at non-edge regions, and bicubic B-spline interpolation method was used near edges regions. Further more, control vertexes were computed from pixels with calculation formula which has been simplified in the B-spline interpolation process. Experiments showed the interpolated image by the proposed method had good vision results for it could hold image's edge information effectively.

Bicubic B-spline interpolation method for two-dimensional heat equation

2015 ◽  
Author(s):  
Nur Nadiah Abd. Hamid ◽  
Ahmad Abd. Majid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Heat Equation ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Two Dimensional ◽  
B Spline

Study on Five-Axis NURBS Path Generation Method and Direct-Interpolation for CNC System

2014 ◽  
Vol 621 ◽  
pp. 162-166
Author(s):  
Hui Ying Li ◽  
Liang Ji Chen
Keyword(s):  
Interpolation Method ◽  
Spline Interpolation ◽  
Experimental Result ◽  
Path Generation ◽  
B Spline ◽  
Tool Paths ◽  
Controlling System ◽  
Five Axis ◽  
The Impact ◽  
Five Axes

In this article, a new method with Non-Uniform Rational B-Spline (NURBS) technology is presented and realized in a location and federate controlling system. In the method, the tool paths and the cutter locations (CL) were represented into NURBS curves based on the same knot vector. The above CL data was firstly calculated and then transformed to five motion commands of five axes of machine through the real-time post-procession algorithm. The acceleration/deceleration controlling method is also presented to avoid the impact of machine. The proposed 5-axis spline interpolation method is realized and the experimental result of machining shows that the method is valid.

Bicubic B-spline interpolation method for two-dimensional Laplace's equations

2013 ◽  
Author(s):  
Nur Nadiah Abd Hamid ◽  
Ahmad Abd. Majid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Interpolation Method ◽  
Spline Interpolation ◽  
Two Dimensional ◽  
B Spline

scholarly journals New Cubic B-Spline Approximation for Solving Linear Two-Point Boundary-Value Problems

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1250
Author(s):  
Busyra Latif ◽  
Samsul Ariffin Abdul Abdul Karim ◽  
Ishak Hashim
Keyword(s):  
Boundary Value Problems ◽  
Least Squares Method ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Boundary Value ◽  
Spline Approximation ◽  
Second Order ◽  
Order Derivative ◽  
Point Boundary ◽  
B Spline

In this study, we introduce a new cubic B-spline (CBS) approximation method to solve linear two-point boundary value problems (BVPs). This method is based on cubic B-spline basis functions with a new approximation for the second-order derivative. The theoretical new approximation for a second-order derivative and the error analysis have been successfully derived. We found that the second-order new approximation was O(h3) accurate. By using this new second-order approximation, the proposed method was O(h5) accurate. Four numerical problems consisting of linear ordinary differential equations and trigonometric equations with different step sizes were performed to validate the accuracy of the proposed methods. The numerical results were compared with the least squares method, finite difference method, finite element method, finite volume method, B-spline interpolation method, extended cubic B-spline interpolation method and the exact solutions. By finding the maximum errors, the results consistently showed that the proposed method gave the best approximations among the existing methods. We also found that our proposed method involved simple implementation and straightforward computations. Hence, based on the results and the efficiency of our method, we can say that our method is reliable and a promising method for solving linear two-point BVPs.

scholarly journals Study on Fault Diagnosis Method of Planetary Gearbox Based on Turn Domain Resampling and Variable Multi-Scale Morphological Filtering

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 52
Author(s):  
Tongtong Liu ◽  
Lingli Cui ◽  
Chao Zhang
Keyword(s):  
Frequency Conversion ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Operating Efficiency ◽  
Planetary Gearbox ◽  
Noise Interference ◽  
Multi Scale ◽  
Morphological Filtering ◽  
Diagnosis Method ◽  
Simulation Signal

The turn domain resampling (TDR) method is proposed in the paper on the basis of the existing angle domain resampling for solving the problem of non-fixed fault frequency under variable working conditions. TDR can select the appropriate sampling order according to the influence of frequency conversion, which avoided the error caused by the spline interpolation method. It can provide accurate parameters for the subsequent calculation of the equivalent frequency order. Variable multi-scale morphological filtering (VMSMF) method is proposed for the purpose of further reducing the interference of noise in resampling signal to feature extraction. VMSMF adaptively selects structural elements according to the parameter change of impact signal to make its scale more targeted. It only needs to calculate once using the optimal structural unit for a particular impact, and the filtering accuracy and operating efficiency have been greatly improved. The main steps of this article are as follows. First, the TDR is used to resample the original signal as to get the resampling signal which is still submerged by the strong noise. In the second step, VMSMF is used to filter the resampling signal to obtain the signal with less noise interference. Finally, the fault characteristics of the filtering signal was extracted and compared with the possible fault frequency calculated by the sampling parameters provided by resampling, so as to determine the fault type of the planetary gearbox. By analyzing the simulation signal and the experimental signal respectively, this method can find out the corresponding fault characteristics effectively.

scholarly journals Analysis on the Synergy Evolutionary Development of the Collecting, Distributing, and Transporting System of Railway Heavy Haul Transportation

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Fenling Feng ◽  
Dan Lan ◽  
Liuwen Yang
Keyword(s):  
Fourth Order ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Research Result ◽  
Evolutionary Model ◽  
Evolutionary Development ◽  
Heavy Load ◽  
Heavy Haul ◽  
Load Transportation ◽  
The Empirical Analysis

A synergy evolutionary model of the collecting, distributing, and transporting system of railway heavy haul transportation is built by introducing synergy-related concepts and applying synergy evolutionary theory. Then spline interpolation method, numerical differential five-point formula, and method of least squares are used to solve synergistic coefficient, while fourth-order Rugge-kutta method and fourth-order Adams linear implicit formula method are used to solve coevolutionary curve of the system. Finally, the heavy load transportation of Daqin Railway is an example of the empirical analysis. The research result shows that the degree of order of the system and its three subsystems—collecting, transporting, and distributing—increases as the synergetic coefficient of the subsystems increases; otherwise, the degree of the order will decrease. It also shows that this model can better analyze the coevolutionary process of the heavy load collecting, distributing, and transporting system of Daqin Railway, with its rationality and applicability verified.

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