Spline multiresolution and wavelet-like decompositions

Splines are useful tools to represent, modify and analyze curves and they play an important role in various practical applications. We present a multiresolution approach to spline curves with arbitrary knots that provides good feature detection and localization properties for non-equally distributed geometric data. In addition, we show how equidistributed data and knot sequences can be efficiently handled using signal processing techniques.     

Toughness Optimization of SBR Elastomers – Use of Fracture Mechanics Methods for Characterization

Elastomer materials are used in a wide application range and subjected to different loading from which failure of the material results. Because this failure is caused by initiation and propagation of cracks, the application of fracture mechanics methods for the assessment of the material is obvious. A short summary of the methods of technical fracture mechanics including possibilities of determination of crack resistance curves is given. Vulcanizates on the basis of SBR 1500 with various sulfur and carbon black contents were investigated. For describing the crack initiation and crack propagation behavior, several fracture mechanics examination methods were applied. Tear‐analyzer results were used to assess the crack propagation behavior under fatigue‐like loading conditions. Furthermore, for the characterization of the crack resistance of the materials under impact‐like loading conditions, instrumented tensile‐impact tests were performed. To obtain information about the initiation and propagation of a stable crack, quasi‐static fracture mechanics tests were applied. The results of the several tests are discussed in dependence on sulfur and carbon black contents. We found a non‐monotonous behavior of the toughness as a function of carbon black loading. An explanation is given in connection with a percolation‐like transition in filler morphology on larger length scales.

Schematic crack propagation curve for characterizing the fatigue behavior of the vulcanizates recorded in a TFA test.     

基于微观孔隙通道的饱和/非饱和土渗透系数模型及其应用

从微观角度揭示土体变形对饱和/非饱和渗透系数的影响机理,建立相应的预测方法,对于饱和/非饱和土的渗流分析及水力耦合研究具有重要的科学意义。利用流体力学理论,建立了微观孔隙通道渗透系数与等效孔径的关系,在此基础之上,结合毛细理论建立了饱和/非饱和渗透系数与土-水特征曲线的关系模型,并利用已有试验数据验证了模型的合理性。结合该模型与变形条件下土-水特征曲线预测方法,对变形条件下武汉黏性土饱和/非饱和渗透系数进行预测,结果表明黏性土在压缩变形条件下:饱和渗透系数呈数量级的减小,预测值与实测值均吻合较好;双对数坐标下,非饱和相对渗透系数在进气值之后随基质吸力增加而减小,不同初始孔隙比条件下其斜率近似不变,整体呈现"毛刷型"分布,相同基质吸力条件下,初始孔隙比越小,相对渗透系数越大;非饱和渗透系数,进气值之前近似为饱和渗透系数,进气值之后随基质吸力增大而减小,不同初始孔隙比的变化线近似重合。     

定量校准曲线法测定超高纯试剂丙酮中铁含量的研究

目前最常用的分析曲线法(标准曲线法、校准曲线法)、内标法、标准加入法等,对丙酮这类基体成分丰富的样品测定,其定量校准存在显著的系统误差.实验证实,通过保证标准系列中基体组成、浓度及酸度与待测样基本相同,来制作工作曲线进行定量校准(下称定量校准曲线法),能得到较为理想的结果.     

指数曲线贮仓的设计剖析

贮仓是许多工业过程中的常用设备，起拱是贮仓使用时常出现的故障，如何解决起拱问题是贮仓设计的关键，除常采取增大仓壁倾角、设置破拱装置等方法外，设计成曲线贮仓也是行之有效的措施之一。分析了指数曲线贮仓的工作原理和特点，建立了仓壁指数曲线方程，阐述了设计步骤与注意事项，并举例说明。     

Self-intersections of rational Bézier curves

Rational Bézier curves provide a curve fitting tool and are widely used in Computer Aided Geometric Design, Computer Aided Design and Geometric Modeling. The injectivity (one-to-one property) of rational Bézier curve as a mapping function is equivalent to the curve without self-intersections. We present a geometric condition on the control polygon which is equivalent to the injectivity of rational Bézier curve with this control polygon for all possible choices of weights. The proof is based on the degree elevation and toric degeneration of rational Bézier curve.     

Total curvature variation fairing for medial axis regularization

We present a new fairing method for planar curves, which is particularly well suited for the regularization of the medial axis of a planar domain. It is based on the concept of total variation regularization. The original boundary (given as a closed B-spline curve or several such curves for multiply connected domains) is approximated by another curve that possesses a smaller number of curvature extrema. Consequently, the modified curve leads to a smaller number of branches of the medial axis. In order to compute the medial axis, we use the state-of-the-art algorithm from [1] which is based on arc spline approximation and a domain decomposition approach. We improve this algorithm by using a different decomposition strategy that allows to reduce the number of base cases from 13 to only 5. Moreover, the algorithm reduces the number of conic arcs in the output by approx. 50%.     

基于GP2Y0A02距离测量的仿真与辅助设计

为了实现非接触距离测量,利用多个仿真与设计软件设计了采用GP2Y0A02模块的距离光学测试系统。在PROTEUS中测量GP2Y0A02电压值,并在Matlab中采用多元线性回归建立GP2Y0A02电压与距离的拟合曲线,最后在开发的测量程序中利用拟合曲线求解得到距离量。测试结果表明,对于非线性位置测量采用适当数据处理方法能得到满意的测量精度。     

Markov随机场与Gaussian曲线在MR图像分割中的应用

针对扫描的人脑组织MR图像边缘分辨率低、模糊性大的特点,本文提出了一种基于模糊Markov随机场和Gaussian曲线相结合的MR图像最佳阈值分割方法。该方法通过对图像的像素邻域属性的统计将模糊论引入其中,建立模糊Markov随机场,并利用Gaussian曲线对二维直方图最佳一维投影进行拟合,确定出图像中各脑组织的二维阈值点,在二维直方图上实现对脑组织的分割。通过实验表明,本算法能够有效提高脑组织的分辨率,对噪声的鲁棒性、结果区域的连通性相对于一维Otsu和二维Otsu算法都有了很大的提高。