Bi-cubic spline fitting and display of tooth external surface and canal

2003 ◽  
Author(s):  
Y.C. Pao ◽  
P.-Y. Qin ◽  
Q.-S. Yuan
2019 ◽  
Vol 82 ◽  
pp. 129-139 ◽  
Author(s):  
Qing Xia ◽  
Chengju Chen ◽  
Jiarui Liu ◽  
Shuai Li ◽  
Aimin Hao ◽  
...  

1990 ◽  
Vol 7 (1-4) ◽  
pp. 293-301 ◽  
Author(s):  
Ewald Quak ◽  
Larry L. Schumaker

2014 ◽  
Vol 620 ◽  
pp. 357-362 ◽  
Author(s):  
Da Zhu Li ◽  
Lian Xia ◽  
You Yu Liu ◽  
Jiang Han

In order to solve the hobbing machining data calculation and hobbing simulation of non-circular gear with various shapes, the piecewise cubic spline fit method has been adopted to unify the polar coordinate expression of non-circular pitch curve. The method to generate hobbing machining data was deduced based on hobbing linkage mathematical model, and the machining data error caused by piecewise cubic spline fitting method was analyzed. The three-dimension software has been used as simulation tool to make secondary development, and then non-circular gear hobbing simulation was realized based on machining data, which can verify the validity of machining data and the relevant design drawbacks of non-circular gear. The work of this paper lay a good foundation for design parameters optimization and hobbing of non-circular gear.


1993 ◽  
Vol 37 ◽  
pp. 135-144
Author(s):  
J. M. Hudson ◽  
B. K. Tanner ◽  
R. Blunt

AbstractWe discuss the use of Fourier transform techniques to extract layer thickness from the interference fringes observed in high resolution X-ray diffraction rocking curves of pseudomorphic HEMT structures. The interference structure is extracted by cubic spline fitting to the extrema of the data, thereby obtaining a background envelope which is used to normalise the data. The resulting constant background is subtracted from the data and the residual Fourier transformed. Auto correlation of the residual significantly improves the result from noisy data. Satisfactory results are obtained only when the Bragg peak from the substrate is windowed out. With a limited dynamic and angular range, there is often insufficient data to separate the two closely spaced periods arising from the total layer thickness and that excluding the quantum well. The result then corresponds to the average of these two thicknesses.


Author(s):  
Michael Wodny

Given are the m points (xi,yi), i=1,2,…,m. Spline functions are introduced, and it is noticed that the interpolation task in the case of natural splines has a unique solution. The interpolating natural cubic spline is constructed. For the construction of smoothing splines, different optimization problems are formulated. A selected problem is looked at in detail. The construction of the solution is carried out in two steps. In the first step the unknown Di=s(xi) are calculated via a linear system of equations. The second step is the construction of the interpolating natural cubic spline with respect to these (xi,Di), i=1,2,…,m. Every optimization problem contains a smoothing parameter. A method of estimation of the smoothing parameter from the given data is motivated briefly.


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