Constructing Convexity-Preserving Interpolation Curves of Hyperbolic Polynomial B-Splines Using a Shape Parameter

2006 ◽  
Vol 43 (7) ◽  
pp. 1216
Author(s):  
Jun Chen
2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jin Xie

A geometric modeling method based on TH-type uniform B-splines which are composed of trigonometric and hyperbolic polynomial with parameters is introduced in this paper. The new splines possess many important properties of quadratic and cubic B-splines. Taking different values of the parameters, one can not only locally adjust the shape of the curves, but also change the type of some segments of a curve between trigonometric and hyperbolic functions as well. The given curves can also interpolate directly control polygon locally by selecting special parameters. Moreover, the introduced splines can represent some quadratic curves and transcendental curves with selecting proper control points and parameters.


2021 ◽  
Vol 2084 (1) ◽  
pp. 012018
Author(s):  
Nursyazni Binti Mohamad Sukri ◽  
Puteri Ainna Husna Binti Megat Mohd ◽  
Siti Musliha Binti Nor-Al-Din ◽  
Noor Khairiah Binti Razali

Abstract In Computer Aided Geometry Design (CAGD), B-splines curves are piecewise polynomial parametric curves that play an important role. CAGD involves the interpolation and approximation curves and surfaces. CAGD has been widely used which brings good impact of computers to industries in manufacturing. There are many improved methods in the B-spline curve such as extended cubic B-spline, trigonometric B-spline, quasi trigonometric B-spline, and λμ-B-spline. Each of the methods has its behaviour and advantage. In this paper, λμ-B-spline was used to be implemented in generating irregular symmetrical objects. λμ-B-spline has a shape parameter that can change the global shape by manipulating the value of the shape parameter. The bottle has been chosen as an irregular symmetrical object. The 2-dimensional symmetrical curves of Bottle design were formed by using λμ-B-spline degree 4. The curves designed are dependent on the shape parameter which can be adjusted. Then, the curves generated were revolved using the Sweep Surface method to form 3-dimensional objects. Every object has its volume and this research focused on the numerical method which was Simpson’s 3/8 to compute the volume. The volumes obtained were compared to the actual volume to determine the best shape parameter used. The results show that the λμ-B-spline curve with a shape parameter of 1 is the best shape parameter in designing symmetrical irregular objects with the desired volume.


2010 ◽  
Vol 72 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Liu Xumin ◽  
Xu Weixiang ◽  
Guan Yong ◽  
Shang Yuanyuan

2017 ◽  
Vol 10 (6) ◽  
pp. 461
Author(s):  
Mohammed-El-Amine Khodja ◽  
Ahmed Hamida Boudinar ◽  
Azeddine Bendiabdellah

Author(s):  
Nobuyuki Wakai ◽  
Yuji Kobira ◽  
Takashi Setoya ◽  
Tamotsu Oishi ◽  
Shinichi Yamasaki

Abstract An effective procedure to determine the Burn-In acceleration factors for 130nm and 90 nm processes are discussed in this paper. The relationship among yield, defect density, and reliability, is well known and well documented for defect mechanisms. In particular, it is important to determine the suitable acceleration factors for temperature and voltage to estimate the exact Burn- In conditions needed to screen these defects. The approach in this paper is found to be useful for recent Cu-processes which are difficult to control from a defectivity standpoint. Performing an evaluation with test vehicles of 130nm and 90nm technology, the following acceleration factors were obtained, Ea>0.9ev and β (Beta)>-5.85. In addition, it was determined that a lower defect density gave a lower Weibull shape parameter. As a result of failure analysis, it is found that the main failures in these technologies were caused by particles, and their Weibull shape parameter “m” was changed depending of the related defect density. These factors can be applied for an immature time period where the process and products have failure mechanisms dominated by defects. Thus, an effective Burn-In is possible with classification from the standpoint of defect density, even from a period of technology immaturity.


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