Hermite interpolation with simple planar PH curves by speed reparametrization

We introduce a new method of solving C¹ Hermite interpolation problems, which makes it possible to use a wider range of PH curves with potentially better shapes. By characterizing PH curves by roots of their hodographs in the complex representation, we introduce PH curves of type K(t−c)²ⁿ⁺¹+d. Next, we introduce a speed reparametrization. Finally, we show that, for C¹ Hermite data, we can use PH curves of type K(t−c)²ⁿ⁺¹+d or strongly regular PH quintics satisfying the G¹ reduction of C¹ data, and use these curves to solve the original C¹ Hermite interpolation problem.     

矩形域上有理Bezier曲面的广义离散算法及其应用

本文推广了有理Ｂｅｚｉｅｒ曲面的离散算法，得到了沿非等参数离散矩形域上有理Ｂｅｚｉｅｒ曲面的割角算法，并给出了从有理Ｂｅｚｉｅｒ矩形片到有理Ｂｅｚｉｅｒ三角片的割角转换。     

The restricted likelihood ratio test for autoregressive processes

The restricted likelihood is known to produce estimates with significantly less bias in AR(p) models with intercept and/or trend. In AR(1) models, the corresponding restricted likelihood ratio test (RLRT), unlike the t‐statistic or the usual LRT, has been recently shown to be well approximated by the chi‐square distribution even close to the unit root, thus yielding confidence intervals with good coverage properties. In this article, we extend this result to AR(p) processes of arbitrary order p by obtaining the expansion of the RLRT distribution around that of the limiting chi‐squared and showing that the error is bounded even as the unit root is approached. Next, we investigate the correspondence between the AR coefficients and the partial autocorrelations, which is well known in the stationary region, and extend to the more general situation of potentially multiple unit roots. In the case of one positive unit root, which is of most practical interest, the resulting parameter space is shown to be the bounded p‐dimensional hypercube (?1, 1] × (?1, 1)^p?1. This simple parameter space, in addition with a stable algorithm that we provide for computing the restricted likelihood, allows its easy computation and optimization as well as construction of confidence intervals for the sum of the AR coefficients. In simulations, the RLRT intervals are shown to have not only near exact coverage in keeping with our theoretical results, but also shorter lengths and significantly higher power against stationary alternatives than other competing interval procedures. An application to the well‐known Nelson–Plosser data yields RLRT based intervals that can be markedly different from those in the literature.     

Bernstein-Bézier类曲线和Bézier曲线的重新参数化方法

在Bernstein函数类和B啨ｚｉｅｒ曲线类的基础上 ,研究了BBC曲线和附权BBC曲线的表示方法和有关性质 对BBC曲线和附权BBC曲线理论与B啨ｚｉｅｒ曲线的关系剖析表明 :附权BBC曲线不仅是B啨ｚｉｅｒ曲线的推广形式 ,同时该理论蕴涵着系统的B啨ｚｉｅｒ曲线的重新参数化方法 ,对该方法进行了较为详尽的探讨 结果表明 ,运用附权BBC曲线理论实现B啨ｚｉｅｒ曲线的重新参数化的方法具有通用性好和计算简单等优点 ,在很大程度上弥补了B啨ｚｉｅｒ曲线理论没有系统的重新参数化方法的不足     

Interactive Shape Control of Interpolating B-splines

This paper presents a new methodfor providing interactive shape control of interpolating B-splines. The CAD designer can directly interact with geometric entities defined on the B-spline at any interpolated data point; shape adjustments can be performed either globally or locally. Our approach is based on Bλ-splines of order k (λ,k ≥1), i.e. λ-reparametrized, classical B-splines. The method presented can be easily generalised to surfaces defined either as tensor products or by using the skinning technique; interactive shape control can be provided in both surface parametric directions.     

About Shewhart control charts to monitor the Weibull mean

In this paper, a new reparametrization expressed in terms of the process mean for Weibull distribution is studied; thus, the monitoring of the process mean can be made directly. Additionally, we call attention that the asymptotic control limits for control chart by central limit theorem (CLT) may lead to a serious erroneous decision. Definitively, they can only be used to signal small/medium shifts in the process mean but with a very very large sample size. We present guidelines for practitioners about the minimum sample size needed to match out‐of‐control average run length (ARL₁) with the exact and asymptotic control limits in function of the shape parameter after an extensive simulation study. The proposed schemes are applied to monitoring the Weibull mean parameter of the strength distribution of a carbon fibber used in composite materials.     

正弦B样条类曲线及其在曲线参数化中的应用

从B样条基函数出发,导出了正弦B样条类SBSC（Sine Basic Spline Class）函数,定义了SBSC曲线,讨论了SBSC曲线和B样条曲线的关系,提供了B样条曲线重新参数化的一种有效方法。     

Partial Reparametrization of the BKW Equation of State for DNAN‐Based Melt‐Cast Explosives

DNAN‐based melt‐cast explosives are a type of new, insensitive munitions (IM) explosives. Quickly determining munitions’ explosive properties is extremely important during the formulation design stage. The aim of this study was to partially reparameterize BKW‐EOS (only β and κ were reparameterized on the basis of the parameters (α , β , κ , and θ ) of classical BKW‐RDX set and BKW‐TNT set) to more accurately predict the properties of DNAN‐based melt‐cast explosives. A new set of parameters β and κ was obtained (β =0.19, κ =9.81) according to measured detonation velocity and detonation pressure for ideal DNAN‐based melt‐cast formulations (DNAN/RDX and DNAN/HMX). For non‐ideal DNAN‐based melt‐cast formulations (DNAN/RDX/Al and DNAN/HMX/Al), aluminum oxidation degree was first determined according to the measured detonation heat; then, another new set of parameters β and κ was obtained in the same way as the ideal formulations (β =0.24, κ =8.5). The predicted detonation properties with BKW reparametrization for DNAN‐based melt‐cast explosives agreed with the measured data.     

型值点参数设定方法的研究

在反求工程中,由于型值点很多,会导致参数确定过程的计算量大幅度增加.为了提高速度,减少计算量提出反求工程中参数设定的方法,该方法通过设置给定的型值点对应的参数来反求控制点.最后,通过计算实例对该方法与其它算法得到的效果进行了比较.试验结果表明,该方法可以达到和已有方法相同的效果,并且计算量明显减少.     

Proper Reparametrization of Rational Ruled Surface

In this paper,we present a proper reparametrization algorithm for rational ruled surfaces.That is,for an improper rational parametrization of a ruled surface,we construct a proper rational parametrization for the same surface. The algorithm consists of three steps.We first reparametrize the improper rational parametrization caused by improper supports.Then the improper rational parametrization is transformed to a new one which is proper in one of the parameters. Finally,the problem is reduced to the proper reparametrization of planar rational algebraic curves.