四次Said-Ball曲线的扩展

给出了一个含有参数λ的五次多项式基函数,是四次Said-Ball 曲线基础函数的扩展;分析了此基函数的性质,基于该组基函数定义了带有形状参数的多项式曲线.曲线不仅具有四次Said-Ball 曲线的特性,而且具有形状的可调性和更好的逼近性.参数λ有明确的几何意义:λ越大,曲线越逼近控制多边形;当λ=0时,曲线退化为四次Said-Ball曲线.还讨论了两段曲线C1连续拼接的条件.实例表明,定义的曲线的形状是随着λ取不同的值而发生变化.     

带双参数四次Said-Ball曲线的扩展

为了使曲线易于实现光滑拼接,同时具有对应于相同控制顶点的不同形状,定义了具有凸包性、对称性、形状可调性等基本性质的新曲线.文中分析了基函数及曲线的性质和2个形状参数的几何意义,给出了2条Said-Ball型曲线的G0,G1,G2连续拼接条件.类似构造了局部形状可调的组合曲面.数值实例说明了所给方法的正确性和有效性.     

文胸模杯曲面形态特征曲线提取与分析

为获得控制文胸模杯曲面形态的特征曲线,实现模杯的正向设计,采用三维扫描仪获取模杯的点云数据,用逆向工程软件进行实体模型构建,然后根据模杯角度及特征点构建了26条模杯内外曲面形态曲线。利用各曲线拐点、峰值点、曲率最大点及最小点的分布位置一致性,提取能够反映模杯曲面特征信息的内外曲面形态特征曲线5条。结果表明:模杯结构特征曲线上的几何参数分布离散程度更小,较角度特征曲线更能反映不同类型模杯的曲面形态特征。拟合各特征曲线弧长与模杯杯深的函数关系,通过改变形态特征曲线上的几何参数可控制曲面形态结构。     

高速凸轮变系数多项式凸轮曲线的研究

提出一种七、九、十一次变系数多项式曲线设计方法,通过对凸轮曲线方程及特性参数进行计算,绘制其特性参数图谱,达到改变凸轮曲线的运动学和动力学特性,提高了凸轮曲线设计的灵活性和选择性的效果。     

非接触式测量获取背部图形的拟合及其验证

为确定非接触式人体测量获取图形的准确性,采用170/88 A 号型青年男性的背部曲线为研究对象,对获取的图形进行函数拟合和准确性验证。参考服用尺寸手工测量方法绘制其圆顺曲线,再通过多项式函数对曲线进行拟合,其中三次多项式函数的拟合优度达到0.995 62,考虑到表达式的简洁性,将其确定为标准参考曲线。经相关性验证后确定人体背部曲线与背长、胸厚具有相关性;将拟合函数转化为参数函数,利用三者之间的函数关系,按照比例进行缩放,从而通过背长和胸厚推算出背部曲线长度,再与拟合曲线的长度进行对比。实验结果表明,采用该方法拟合的背部曲线长度误差小于1 cm,远低于服装号型中人体背长的档差,能够满足服用人体测量的需求。     

翻领成型器曲面几何形状研究

翻领成型器曲面为可展曲面,用微分几何方法描述了翻领成型器曲面的数学模型,推出了肩曲面为左右对称顶点不同的锥面时的圆形料管翻领成型器的交接曲线以及边界曲线的数学模型,并用Pro/E建立其三维曲面参数化数字模型,为翻领成型器其他截面形状、其他曲面形状的研究提供新的研究方法,为翻领成型器设计制造提供一定的理论依据。     

Poisson曲线的升阶公式

在CAGD中,利用Bernstein基函数升阶公式得到的Bezier曲线升阶公式,可以增加Bezier曲线进行形状调整的灵活性。本文将Bezier曲线的这一升阶思想推广到Poisson曲线,给出了Poisson基函数升任意阶公式,得到了Poisson曲线升任意阶算法。     

含可调参数的一次有理样条插值

为了使有理插值样条在计算机图形和CAD领域有更灵活的应用,构造了带有可调参数一次有理样条函数(1/1型)。该函数可通过选取适当的形状参数使得曲线具有保形性。可以通过调整参数交互式的修改插值曲线的形状,以得到满意的曲线,并证明了此类插值函数的保单调性和给出了其误差分析。     

基于Hermite多项式的打纬运动学方程及其应用

为使打纬机构运行平稳,性能达到理想的织造要求,采用由理想运动学方程反求机构参数的方法,用4段光滑拼接的三次Hermite多项式建立剑杆织机打纬机构加速度曲线方程,再由加速度曲线方程及其边界条件推导出剑杆织机打纬机构速度、位移和跃度曲线方程,并对运动学方程中参数的计算进行了说明。将所建立的运动学方程用在共轭凸轮打纬机构的参数反求,得到了机构参数和曲率变化均匀的共轭凸轮廓线。研究结果表明,建立的运动学方程不仅能够满足共轭凸轮打纬机构参数反求的要求,而且所求共轭凸轮具有较好的力学特性。     

关于一次累积频率分布曲线意义的讨论

在纤维长度分布理论中,不但定义了频率分布函数,而且还定义了一次累积频率分布函数。笔者认为一次累积频率分布曲线下面积的意义值得讨论一下。很多文献上是这样定义一次累积频率分布函数的:在纤维长度分布曲线上(见图1)。将变数1_x 右侧的阴影面积对总面积之比分别作为纵坐标,仍以纤维长度1作横坐标作图,可画成图2的图形,这一曲线称为一次累积频率分布曲线,曲线有点像排错了方向的拜氏图。     

Detection of different shapes of lactation curve for milk yield in dairy cattle by empirical mathematical models

The study of relationships between mathematical properties of functions used to model lactation curves is usually limited to the evaluation of the goodness of fit. Problems related to the existence of different lactation curve shapes are usually neglected or solved drastically by considering shapes markedly different from the standard as biologically atypical. A deeper investigation could yield useful indications for developing technical tools aimed at modifying the lactation curve in a desirable fashion. Relationships between mathematical properties and lactation curve shapes were analyzed by fitting several common functions (Wood incomplete gamma, Wilmink's exponential, Ali and Schaeffer's polynomial regression, and fifth-order Legendre polynomials) to 229,518 test-day records belonging to 27,837 lactations of Italian Simmental cows. Among the best fits (adjusted r(2) higher than 0.75), the 3-parameter models (Wood and Wilmink) were able to detect 2 main groups of curve shape: standard and atypical. Five-parameter models (Ali and Schaeffer function and the Legendre polynomials) were able to recognize a larger number of curve shapes. The higher flexibility of 5-parameter models was accompanied by increased sensitivity to local random variation as evidenced by the bias in estimated test-day yields at the beginning and end of lactation (border effect). Meaning of parameters, range of their values and of their (co) variances are clearly different among groups of curves. Our results suggest that analysis based on comparisons between parameter values and (co)variances should be done carefully. Comparisons among parameter values and (co)variances could yield more robust, reliable, and easy to interpret results if performed within groups based on curve shape.     

基于自动测体的围度曲线拟合模型

通过拍摄人体正面和侧面的图像,提取其轮廓线形用于服装三维人体尺寸的自动测量技术。该技术成本低,转换后二维尺寸的计算简单快速,适合产品的商业化。（一般的计算方法是对人体围度进行样本分析,利用拟合方法获得不同号型样本的围度曲线函数模型,通过围度曲线的二维信息估计尺寸。）主要基于自动人体测量需要,在选取号型随机样本的试验基础上,使用指数曲线、对数曲线、二次曲线和三次曲线拟合其中胸围曲线,建立对应的围度函数模型并对其在误差和线形方面展开详细的分析与比较,论证这些模型的合理性与不足之处,为建立更适用的围度尺寸函数模型提供参考。     

New approach to the extensogram interpretation

New criteria for the evaluation of wheat qualitative properties are worked out on the basis of the study of the shape and size of the extensographic curves. Approximating the experimental curves - extensograms - to the theoretical curves which are the closest to them in their shape and equal to them in their area, it also was possible to determine their shape parameters. The theoretical curve is an ellipse inscribed over the shape of the experimental curve. It changes its shape to the case when the ellipse eccentricity becomes equal to zero and further when x-axis and y-axis exchange their places in the coordinate system. It has been determined that the extensogram area can be the best means of measuring the wheat flour quality if it has been evaluated with reference to the curve circumference which circumscribes it. The ratio of the parameters of the theoretical curve maximum (m_t) and the maximum of the theoretical curve of the ideal shape (r) is the basis for the extensogram evaluation and their classification into the qualitative range. The quantitative data of the ratio m_t/r indicate the shape, and the values for r indicate the extensogram size. On the basis of the expression (m_t/r-1)100, it is possible to evaluate accurately the extensographic curves for the first time as well as to classify wheat into the qualitative range.     

用贝塞尔曲线拟合服装结构曲线的处理方法

尽管服装结构曲线类型很多,形态差别很大,但由于它们都要遵循服装结构设计的规律,因此具有许多共同特征,这使得同一种计算机曲线模型来拟合它们成为可能。本文通过分析服装结构曲线的这些共同点,讨论了如何用三次贝塞尔曲线对服装结构设计中可能遇到的各种类型的曲线,并概括了拟合这些曲线的一般处理方法。     

多项式拟合法在旋盖机凸轮曲线设计中的研究与应用

针对局部控制条件过多时传统多项式插值法所设计的凸轮曲线幂次过高,不利于旋盖机凸轮加工的问题,分别采用整体5次、6次及7次多项式拟合法来设计旋盖机凸轮曲线,在满足局部控制条件的同时控制多项式幂次。当凸轮曲线各项特性参数均得到优化后,构建旋盖机凸轮机构三维模型,并对其进行动力学仿真分析,综合对比机构运动学与动力学性能,确定最优的凸轮曲线。     

基于纵向轮廓曲线的青年女性体型细分研究

提取了能用于青年女性体型分类的纵向轮廓曲线,包括矢状面和冠状面轮廓曲线。建立了用轮廓曲线特征点曲率半径进行青年女性体型分类的方法。在国标体型分类的基础上,进一步细分青年女性体型,从纵向轮廓曲线形态入手,分析曲线特征点曲率半径,应用K-means聚类算法进行动态聚类,将伪F统计量作为判别函数来确定最佳类数目,最终将纵向体型分为8类,量化区分了青年女性纵向体型差异,并提出一种新的体型标识：“国标体型+纵向体型”。     

Using geometric morphometrics for the genetics analysis of shape and size of lactation curves in Israeli first-parity Holstein cattle

Our objective was to combine the methods of geometric morphometrics and multivariate quantitative genetics to genetic evaluation of the size and shape of lactation curves of milk of 3,492 Israeli first-parity Holstein cattle. Lactation records were treated as morphological data, for which 2 different lactation shape functions were evaluated, one depicted by a line graph and the other by an orbital graph. The lactation curves from both shape functions were represented by 2-dimensional Cartesian landmark coordinates. The 2 sets of landmarks were then analyzed individually for each shape function with geometric morphometrics to separate variation into components of size and shape. The analysis yielded 2 size measures and 2 sets of shape variables, and they were the inputs to estimate variance components using the MTC REML individual animal model program. Variance components were also estimated for the 305-d lactation production as a reference. Shape variables showed negligible correlation with 305-d production, providing evidence of size and shape of lactation curve as separate characters. The size measure derived from the orbital-depicted lactation curve had equal heritability (0.39 ± 0.01; ± standard error) and complete genetic and environmental correlations with 305-d production, whereas the size measure derived from the line-depicted lactation curve showed low heritability (0.09 ± 0.01) and environmental correlation (0.02 ± 0.004) and relative high genetic correlation with 305-d production (0.48 ± 0.04). This may validate both the orbital graph to depict lactation records and the use of geometric morphometrics to split variation of lactation curve into size and shape components. The maximal heritability for shape of lactation curve was 0.55 for orbital- and 0.56 for line-depicted lactation curves. The respective patterns of variations were visualized as shape changes from the mean shape in the data set. Geometric morphometrics are well grounded within the theory of shape analysis and can be paired with conventional methods in the field to characterize the patterns of phenotypic and genetic variation of shape and size of lactation curve in dairy cattle.     

BULK MECHANICAL BEHAVIOR OF COMMERCIAL PARTICLE FOOD FOAMS

The texture of 10 commercial cereal foam products, of different composition and shape, has been evaluated through the measurement of its bulk mechanical properties using a Kramer shear cell. Force–displacement curves led to repeatable measurements, characterized by low standard deviations. Discrimination among samples and relevant mechanical variables were determined by the PCA of these curves. Most of the variability in the force–displacement curves (97%) and mechanical variables (93%) were contained in the two PC1s, and the mechanical behavior of this large variety of cereal foams texture could be explained by two variables: the energy needed for crushing (area under the force–displacement curve) and the slope ratio of the curve. These variables were then respectively related to bulk density, which increased with sugar content, and to the shape factor, evaluated through geometric approximation.

PRACTICAL APPLICATIONS

The contribution of this work to the characterization of cereal foam product texture is first, to extend the validation of the Kramer shear cell for assessing the bulk behavior of real products of irregular shape. Low standard deviation and product differentiation among 10 commercial samples shows that this method is reliable enough for quality control of cereal particle foams. Then, by its ability to determine the two most relevant variables from the texture profiles, it allows a deeper look on the relationships between mechanical properties and multi-scale structure, as shown by the relation with apparent bulk density and particle shape, and the role of sugar content. Finally, the relation with former works on cornflakes also suggests the use of these variables for assessing sample crispness.