Knowledge-based CNC torch path generation for laser cutting of planar shapes

In this paper, we propose a knowledge-based method for generating a CNC torch path for laser cutting of the outlines of planar shapes. The proposed method consists of two main phases: laser cutting knowledge construction and CNC torch path generation using the knowledge. In the first phase, laser cutting experiments are conducted on various operating parameters, and then empirical data are stored and analyzed to make up the knowledge of laser cutting. With this knowledge, we can inquire what a kerf width is for specific operating parameters. In the second phase, using the knowledge of laser cutting, the CNC torch path is generated for cutting the outlines of the given planar shapes. This phase is basically based on the offset generation of each outline by a sequence of arc splines, where the offset distance is the same as the half of the kerf width determined from the constructed knowledge. The proposed method based on laser cutting knowledge makes full use of arc interpolators in CNC torch path generation. The method can efficiently reduce the number of path segments while keeping the torch path within the desired accuracy.     

Dual bases for spline spaces on cells

The purpose of this paper is twofold. First, we extend the basic dimension result for spline spaces on simple cells to a class of spline spaces which satisfy additional smoothness conditions at the interior vertex. This extension is useful for the study of super spline spaces. Secondly, and more importantly, we show how to choose minimal determining sets of Bézier coordinates for these spaces. These in turn are useful for constructing explicit locally supported bases for spline spaces on general triangulations.     

基于样条修匀公式的图像边缘检测

本文给出了一类基于Ｂ样条修匀公式的图像边缘检测算子,其过程是先利用等距Ｂ样条函数对图像｛ｆ（ｉ,ｊ）｝Ｎ－１ｉ,ｊ＝０做一个全息光滑曲面公式,进一步利用Ｂ样条函数的局部支撑性质导出,该曲面公式可以严格地局限于每点的某变邻域内计算,即Ｓ（ｘ,ｙ）＝∑（ｉ,ｊ）∈Ｎｋ,ｌ（ｘ,ｙ）ｆ（ｉ,ｊ）Ωｋ（ｘ－ｉ）Ωｌ（ｙ－ｊ）该曲面既有足够的光滑性,又有良好的保凸性;然后,基于这个光滑曲面Ｓ（ｘ,ｙ）,再通过求｜Ｓ｜的局部极大值点或求２Ｓ的零交叉来检测边缘．数值实验表明,这是一类十分成功的边缘检测算法,它简捷、可靠,便于实时处理,如可用于计算机视觉系统中的特征提取、图像分割、纹理分析等．     

开圆弧样条的保形插值算法

提出一种G1圆弧样条插值算法.该算法选取部分满足条件的型值点构造初始圆,然后过剩下的型值点分别构造相邻初始圆的公切圆.在此过程中,让所有型值点均为相应圆弧的内点,且每段圆弧尽量通过2个型值点.在型值点列满足较弱的条件下,曲线具有在事先给定首末切向的情况下圆弧总段数比型值点个数少且保形的特点.     

基于离散插值样条的提升小波变换

文中引入了一种对信号递归滤波的提升方法,该方法与通常的提升方法不同之处是使用IIR滤波器.探讨了空间域中基于离散插值样条的预测算子和更新算子的设计.提出的方法以插值为基础,只涉及信号的采样,不要求使用正交公式,更适合信号的处理.最后由数值仿真验证了该算法的性能,对于软阈值法小波系数去噪,提升小波变换T12同B9/7相比,前者略优于后者,提升方法的优点在于其设计上的灵活性和计算花费少.     

一种混合样条插值

本文构造了一种混合样条函数,它是用一次多项式函数及指数函数的结合来表示的。文章给出了这种混合样条的一般表达式,并证明插值问题解的存在性定理和误差估计定理,由此说明这种样条函数具有良好的逼近度和物理背景。     

Mixed model-based inference in geoadditive hazard regression for interval-censored survival times

Mixed model-based estimation of additive or geoadditive regression models has become popular throughout recent years. It provides a unified and modular framework that facilitates joint estimation of nonparametric covariate effects and the corresponding smoothing parameters. Therefore, extensions of mixed model-based inference to a Cox-type regression model for the hazard rate are considered, allowing for a combination of general censoring schemes for the survival times and a flexible, geoadditive predictor. In particular, the proposed methodology allows for arbitrary combinations of right, left, and interval censoring as well as left truncation. The geoadditive predictor comprises time-varying effects, nonparametric effects of continuous covariates, spatial effects, and potentially a number of extensions such as cluster-specific frailties or interaction surfaces. In addition, all covariates are allowed to be piecewise constant time-varying. Nonlinear and time-varying effects as well as the baseline hazard rate are modeled by penalized splines. Spatial effects can be included based on either Markov random fields or stationary Gaussian random fields. Estimation is based on a reparametrization of the model as a variance component mixed model. The variance parameters, corresponding to inverse smoothing parameters, can then be determined using an approximate marginal likelihood approach. An analysis on childhood mortality in Nigeria serves as an application, where the interval censoring framework additionally allows to deal with the problem of heaped survival times. The effect of ignoring the impact of interval-censored observations is investigated in a simulation study.     

Translational Covering of Closed Planar Cubic B-Spline Curves

Spline curves are useful in a variety of geometric modeling and graphics applications and covering problems abound in practical settings. This work defines a class of covering decision problems for shapes bounded by spline curves. As a first step in addressing these problems, this paper treats translational spline covering for planar, uniform, cubic B‐splines. Inner and outer polygonal approximations to the spline regions are generated using enclosures that are inside two different types of piecewise‐linear envelopes. Our recent polygonal covering technique is then applied to seek translations of the covering shapes that allow them to fully cover the target shape. A feasible solution to the polygonal instance provides a feasible solution to the spline instance. We use our recent proof that 2D translational polygonal covering is NP‐hard to establish NP‐hardness of our planar translational spline covering problem. Our polygonal approximation strategy creates approximations that are tight, yet the number of vertices is only a linear function of the number of control points. Using recent results on B‐spline curve envelopes, we bound the distance from the spline curve to its approximation. We balance the two competing objectives of tightness vs. number of points in the approximation, which is crucial given the NP‐hardness of the spline problem. Examples of the results of our spline covering work are provided for instances containing as many as six covering shapes, including both convex and nonconvex regions. Our implementation uses the LEDA and CGAL C++ libraries of geometric data structures and algorithms.     

基于整数维约束的分维形状映射生成方法

把整数维图形研究方法与分数维图形研究方法相结合，提出一种基于整数维规则几何形状的约束的分维形状映射生成方法，有于描述自然界和工程中出现的且具有特定基本形状趋势的随机现象和随机过程，首先，任意选取一个具有调配函数的自由形状构造一个有序参数空间，确定有序参数的取值规律和区域，把有序参数空间与自适应神经网络，随机性相结合，构造一个随机离散参数空间，并建立起有序参数与随机离散参数之间的参数对应关系，最后，通过有序与无序的参数对应关系，建立一个独立于任意规则几何形状的统一的分形映射关系，对相应整数维的任意规则参数几何形状分形映射，生成宏观形态趋势可预见和可控制的分维形状，该提出的方法适有于任意参数几何形状的分形映射，生成分形图形，且方法简明，易于实现。     

Scattering Parameters Representing Imperfections in Precision Coaxial Air Lines

Scattering parameter expressions are developed for the principal mode of a coaxial air line. The model allows for skin-effect loss and dimensional variations in the inner and outer conductors. Small deviations from conductor circular cross sections are conformally mapped by the Bergman kernel technique. Numerical results are illustrated for a 7 mm air line. An error analysis reveals that the accuracy of the scattering parameters is limited primarily by the conductor radii measurement precision.