Constructing G^1 interpolation curves on surfaces with Coons surface

Using a bi-cubic Coons surface, a method for G1-continuous interpolation of an arbitrary sequence of points on an implicitly or parametrically defined surface with a specified tangent direction at every point was presented. Firstly construct a G1-continuous composite Coons surface patch, and then compute the intersection of the surface patch and the given surface. The desired interpolation curve is the intersection curve. Unlike some existing methods, several free parameters were introduced into the method that can be used in subsequent interactive modification so that the last curve's shape meets the demand. Experiments demonstrate the method is simple, feasible and applicable to computer aided design and computer graphics, etc.

Positioning planning of high-intensity-focused ultrasound surgery platform using Bezier curve

A positioning volume ellipsoid method is proposed to represent tumor volume in the workspace of a high-intensity-focused ultrasound (HIFU) surgery platform during the platform's positioning motion. To this simplified tumor model, a nearest neighbor search method is used to determine intermediate configuration and goal configuration, which the treatment head and ultrasound focus must pass in their localization to target volume. Based on the decided configurations, the continuity condition of combined Bezier curve in Euclidean space and De Casteljau algorithm on Lie group SO(3) are integrated to construct a combined Bezier positioning path of C2 continuity at junctional configuration, and an illustration of different positioning path planning is analyzed based on a liver tumor case.

“毕月乌”作何解

统编高中语文第六册里的《高祖还乡》,对“毕月乌”作了如下注释:“毕月乌,二十八宿之一的毕宿,其形象是乌鸦.此处只取‘乌’之意,与毕宿无关.”查《辞海》,并无毕月乌的词条,也没有涉及毕月乌方面的任何内容.此外,这条注释的前后也有矛盾不清之处.

一种特殊的辞格——析音

所以说析音是“特殊”的辞格,乃因为这种修辞方式现在已几乎不用,因而有关修辞的书很少专门谈到它。 先请看高中《语文》第六册《[般涉凋]哨遍·高祖还乡》中的例子: (1)一面旗,白胡阑套住个迎霜兔;一面旗,红曲连打着个毕月乌。 课本注解曰:“……胡阑,环的复音,两字合起来念就是‘环’.下文‘曲连’,圈的复音。……”即“环”本来是一个音(单音),现在用两个音(复音)来代替它。

论调查和研究方言的作用

调查和研究方言具有十分重要的作用。这里结合自己调查、研究和教学现代汉语方言学的体会来谈谈。

税苑

税苑七律·赞新税制纪顺良园中春蕾又吐芳，严明稳局是天定，檐头紫燕舞欣然。搞活经济非世难。兴国不时甜梦起，吾便天年花甲发，治家有策妙琴弹。愿同岁月庆平安。七律·春至──兼贺新税制出台施行田保存肃落冷漠终非久，娇花绽唇媚来蝶，脆雷声声催春行。柔柳展眉戏流...

2000年中国农业出版社优秀图书评选揭晓

经中国农业出版社书刊评奖委员会评审,评出2000年度优秀图书特别奖1种,一等奖12种,二等奖22种。现将有关畜牧、兽医及水产方面的获奖图书介绍如下。

方音释古

先秦诸多典籍,如《诗经》、《国语》、《国策》、《论语》、《孟子》,与当时口语非常接近,今天读起来,仍朗然上口,心知其意。魏、晋之后,古代书面语与口语分道扬镳,日渐陌生。但是,由于政治、经济、文化的影响,陕西关中方言长期居于“雅言”地位,保持了大量的古代书面语的成分。本文通过几个词语、语句的分析,说明关中方言在阅读、整理古代文献资料方面的重要作用。

170名教育随笔作者获奖

第七届全国少年儿童教育随笔征文圆满结束。评出一等奖20名,他们是:张雪梅、王君琴、曲连坤、桑桂芹、冯居营、戴雅娟、李丽、矫学荣和唐功铨、尹长林、乔彦芳、刘瑞琦、薛路、周伟和练洲平、郑虹、于杰、岑福康、蔡丽青、朱卫星、高建新、卢刚;张蕾等50名作者获二等奖;

Oscillatory Criteria for a Class of Boundary Value Problem of Nonlinear Hyperbolic Equations *L

Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained.

Restricted Edge Connectivity of Binary Undirected Kautz Graphs

A restricted edge cut is an edge cut of a connected graph whose removal resultsin a disconnected graph without isolated vertices. The size of a minimum restricted edge cutof a graph G is called its restricted edge connectivity, and is denoted by λ′(G). Let ξ(G) bethe minimum edge degree of graph G. It is known that λ′(G) ≤ξ(G) if G contains restrictededge cuts. Graph G is called maximal restricted edge connected if the equality holds in thethe preceding inequality. In this paper, undirected Kautz graph UK(2, n) is proved to bemaximal restricted edge connected if n ≥ 2.

3-restricted connectivity of graphs with given girth

Let G = （V, E） be a connected graph. X belong to V（G） is a vertex set. X is a 3-restricted cut of G, if G- X is not connected and every component of G- X has at least three vertices. The 3-restricted connectivity κ3（G） （in short κ3） of G is the cardinality of a minimum 3-restricted cut of G. X is called κ3-cut, if ｜X｜ = κ3. A graph G is κ3-connected, if a 3-restricted cut exists. Let G be a graph girth g ≥ 4, κ3（G） is min{d（x） ＋ d（y） ＋ d（z） - 4 ： xyz is a 2-path of G}. It will be shown that κ3（G） = ξ3（G） under the condition of girth.

An efficient method for tracing planar implicit curves

This paper presents a method for tracing a planar implicit curve f（x, y）=0 on a rectangular region based on continuation scheme. First, according to the starting track-point and the starting track-direction of the curve, make a new fimction F（x, y）=0 where the same curve withf（x, y）=0 is defined. Then we trace the curve between the two domains where F（x, y）〉0 and F（x, y）〈0 alternately, according to the two rules presented in this paper. Equal step size or adaptive step size can be used, when we trace the curve. An irregular planar implicit curve （such as the curve with large curvatures at some points on the curve）, can be plotted if an adaptive step size is used. Moreover, this paper presents a scheme to search for the multiple points on the curve. Our method has the following advantages： （1） it can plot Co planar implicit curves; （2） it can plot the planar implicit curves with multiple points; （3） by the help of using the two rules, our method does not need to compute the tangent vector at the points on the curve, and directly searches for the direction of the tracing curve; （4） the tracing procedure costs only one of two evaluations of function f（x, y）=0 per moving step, while most existing similar methods cost more evaluations of the function.

Reconstruction from contour lines based on bi-cubic Bézier spline surface

A novel reconstruction method from contours lines is provided. First, we use a simple method to get rid of redundant points on every contour, then we interpolate them by using cubic Bézier spline curve. For corresponding points of different con- tours, we interpolate them by the cubic Bézier spline curve too, so the whole surface can be reconstructed by the bi-cubic Bézier spline surface. The reconstructed surface is smooth because every Bézier surface is patched with G2 continuity, the reconstruction speed is fast because we can use the forward elimination and backward substitution method to solve the system of tridiagonal equations. We give some reconstruction examples at the end of this paper. Experiments showed that our method is applicable and effective.

Microstructure and formability evolutions of AZ31 magnesium alloy sheets undergoing continuous bending process

Continuous bending (CB) process along rolling direction was performed to improve the formability of AZ31 magnesium alloy sheets. The microstructure and texture evolutions were characterized by optical microscopy (OM) and electronic backscatter diffraction (EBSD). The results reveal that the basal texture intensity of continuously bent and annealed (CBA) sample is drastically weakened. A large number of twins are induced on the concave surface by the 1st pass bending and the density of twins obviously declines during the 2nd pass bending owing to the occurrence of detwinning. Due to the asymmetric tension?compression strain states between the outer and inner regions during V-bending, twinning and detwinning are generated alternatively during the CB process. The Erichsen value is 5.2 mm which increases by 41% compared with that of as-received sample. This obvious improvement of formability can be attributed to the weakened basal texture, which leads to a smaller plastic strain ratio (r-value)together with a larger strain-hardening exponent (n-value).

Modeling the Flexural Carrying Capacity of Corroded RC Beam

Considering the change of bond strength between corroded steel and concrete,flexural carrying ca- pacity of corroded reinforced concrete (RC) beam was calculated.On the basis of the condition of equilibrium of forces and compatibility of deformations for the whole beam,a model for the prediction of flexural carrying capacity of the corroded RC beam was proposed.Comparison of the model's predictions with the experimental results published in the literature shows the practicality of the proposed method.

Designing the Instrument Crank-Coupler Mechanism of Linear Output with Least Transmission Ratio Error

Movement accuracy is the key factor to be considered in designing precision instrument linkage and mini-linkage mechanisms. Although manufacturing errors, elastic deformation, kinematic pair clearance and friction factors all will have synthesis effect on the position accuracy of the mechanical system, the essential factor to guarantee the movement precision remains the kinematic dimensions. Combining the classical theory of mechanical synthesis with the modern error theory and the numerical method, the authors put forward a systematic and complete process and method of computer aided design for the instrument crank-coupler mechanism in which the follower takes the linear displacement approximately within a certain limited domain, with the design result of least transmission ratio error.

Steady State and Dynamic of Gluconic Acid Production by Aspergillus Niger

Batch and continuous fermentation ofgluconic acid production has been studied. The kinetic parameters of the fermentation process were determined from the batch experimental data. The continuous fermentation was modeled to be carried out in a stirred tank reactor. The effect of hydraulic retention time on the steady state continuous fermentation process of glucose by Aspergillus niger to produce gluconic acid was investigated. The result showed that increasing the hydraulic retention time caused the cell amount and gluconic acid concentration at the outlet stream increased but the glucose concentration at the outlet stream decreased. The steady state simulation result was useful for fermenter size determination. Dynamic behaviour of gluconic acid production through fermentation by Aspergillus niger was also studied for a fermenter with 24 h hydraulic retention time. Applying step change of inlet substrate concentration resulted in first order response of cell, substrate and product concentration with all having positive gain. On the other hand, applying step change of inlet cell concentration has resulted in positive gain for cell and product concentration and negative gain for substrate concentration with first order response for all those three parameters.

A note on equicontinuous maps of graph space

Let G be a graph and f: G→ G be a continuous map with at least one periodic point. Using the quote space method, the paper addresses that f is an equicontinuous map if and only if one of the following End(G)+2k+1 conditions holds: 1) {f jm(End(G)+2k)!}∞j=1 is uniformly convergent, in which m=1,2,…, End(G)+2k; and 2) There is a positive integer n esuring that {f jn}∞j=1 is uniformly convergent.

Study of WDM polymer planar curved waveguide couplers

A wavelength division multiplexer based on curved polymer planar waveguide is proposed. According to the coupled modetheory and the waveguide structure, the performance of the curved waveguide coupler (CWC) is analyzed. The results showthat CWC can accommodate wider multiplexing bandwidth than parallel straight waveguide coupler (SWC) due to thecompensation effect of the effective coupling length. The two variables, curvature radius and minimum spacing, increasethe design flexibility of the waveguide device. A 4-channel wavelength division multiplexing (WDM) system based onCWC is designed. The deviation of the center wavelength, due to the errors of curvature radius and minimum spacingduring fabrication process, is investigated. The smaller the curvature radius and the minimum spacing are, the larger thecentral wavelength deviation caused by the error of the curvature radius and the minimum spacing is, which provides someuseful theoretical basis for the design and the fabrication of polymer waveguide devices.