基于广义能量法的截面曲线光顺

对于气动流形曲面,除了满足对原始数据的逼近精度要求之外,通常还要求曲面具有较高的光顺性能。笔者在综合分析现有光顺方法不足的基础上,提出了同时考虑曲面几何及物理等多项光顺准则的基于广义能量法的曲面整体光顺思路,建立了包含曲面截线族粗光顺、曲面精光顺两个步骤的曲面光顺方法。这种方法对于提高曲面的整体光顺性能具有良好的效果。     

NURBS曲面光顺方法综述

NURBS曲线、曲面的光顺处理是CAD/CAM中非常重要的问题。在研究了NURBS曲面光顺中的几种常用方法的基础上,针对现有光顺算法在多尺度特征并存曲面光顺中的不足,提出利用各向异性小波在表达高维信息的优势,将各向异性小波融入曲面的多分辨率分析中的思想,应用于NURBS曲面光顺,以达到对曲面特征的保存。     

基于图像的曲面光顺算法

针对目前曲面光顺算法存在的问题,提出了一种由平滑曲面在平行光照射下图像达到光顺的思想而形成的曲面光顺算法。该算法直接平滑曲面在平行光照射下的图像,然后通过光度立体技术反求出光顺后的曲面。由于能直接平滑曲面在平行光照射下的图像,使得光顺后的曲面在基于光照模型的曲面光顺准则下具有很的好光顺性质。应用实例显示,该算法能在保持原曲面形态的基础上达到很好的光顺效果。     

一种选点法和能量法相结合的曲线光顺方法

将选点修改法和能量法相结合，提出了一种新的曲线光顺方法。和传统的选点修改法以及能量法的区别是：选点修改法每次只修改一个坏点，能量法一次性地修改所有控制顶点，而本文的方法则是用能量法一次性地修改所有对坏点有影响的控制顶点。数值实例表明，这是一种有效的曲线光顺方法。     

大型浮体水弹性作用的频域分析

对大型浮体水弹性响应的频域计算方法做了综述和介绍。分别介绍了干模态法、湿模态法和直接计算方法,对于干模态法的五种结构弹性模态函数做了介绍,研究了五种模态函数下计算结果的收敛速度。对于水动力分析方法的计算量和存储量做了分析,介绍了降低计算量和存储量的一些新计算方法,实现了一种柱坐标下的多极子展开高阶边界元方法,积分方程中的固角系数和柯西主值积分均采用直接方法计算,应用该方法计算了波浪与大型弹性浮体的相互作用问题,计算结果与实验值得到很好的吻合。     

参数三次B样条曲线的一种整体光顺方法

本文在能量法的基础上，提出了一种新的目标函数，给出了参数三次Ｂ样条曲线的一种新的整体光顺方法。利用这种方法得到的曲线不仅具有较小的应变能，而且曲率变化比较均匀，具有很好的光顺效果。该方法能推广到对曲面的光顺。     

C-Bézier曲线的光顺

在工业设计和反求工程中,曲线是形状设计和数据拟合的重要对象。曲线的光顺性对最终产品的外观质量有着直接影响。文章利用文献[1]构造出带有参数调配函数的模型,用其生成三次C-Bézier曲线。在能量法的基础上,研究了控制参数α对这种新曲线形态的影响,通过调整α和控制顶点使得曲线的能量最小,得到最优的光顺逼近曲线。通过最小二乘法和非线性泛函的极小值优化计算,对平面数据点进行光顺逼近,达到光顺的目的。该算法既可以对曲线进行全局光顺又可以进行局部光顺。最后给出了由数据拟合的C-Bézier曲线光顺的实例。     

C1连续曲面重构与光顺的有限元算法

提出了一种基于离散的测量数据重建光顺自由曲面的有限元新方法。根据最佳逼近与能量光顺原理，建立正定的目标泛函，采用18自由度三角形板单元对泛函离散，进行极小化，求得最优解。根据有限元插值计算，重新构造出全场C^1连续的自由曲面。这种方法结合了能量光顺技术，有效地抑制了输入数据上误差噪声的影响，曲面重建的精度高、光顺性好，而且能给出合理的一阶导数。该方法计算简单、便于应用，所需的输入数据点少，并可用于处理曲线边界区域的问题。     

平面参数三次样条曲线的优化光顺算法

给出了基于Kjellander和离散曲率的平面参数三次样条曲线的一种优化光顺算法.首先介绍了离散曲率和Kjellander的光顺法,进而给出了一个带有修改因子λ的目标函数,并通过求解得到λ值和光顺后的型值点,最后得到光顺后的曲线.此法使曲线的曲率变化均匀,使光顺后的曲线与原曲线的偏差小,并且算法简单易行,计算量较小.     

一种参数三次样条曲线光顺优化算法

论文给出了一种基于修改因子和修改角度的平面参数三次样条曲线的优化光顺算法,该算法通过求解一个带有修改因子λ和修改角度θ的目标函数得到光顺后的型值点,插值光顺后的型值点得到光顺曲线。目的是使曲线的曲率变化均匀的同时,使光顺后的曲线与原曲线的偏差尽量小,此算法简单易行,计算量较小。     

任意B样条曲面的多分辨率表示及光顺

本文着重研究具有任意 节占矢量的端点插值Ｂ样条曲线曲面的多分产率表示在Ｂ样条曲面光顺中的应用。     

一种基于GPU实现的自适应八叉树纹理绘画算法

当前,虽然基于二维图像映射定义的传统二维纹理已得到广泛应用。但是它有很多局限性。这是因为很多三维模型在纹理空间中进行参数化是非常困难的,例如隐式表面、细分表面和高密度或高细节的多边形网格。基于八叉树纹理定义,提出了一种新型的自适应八叉树纹理绘画算法。和传统的八叉树纹理映射算法相比,不但占用更少的存储空间,而且实现了基于GPU的纹理查询,有更快的查找速度。     

Fast calculation approach to semi-empirical molecular orbital method using real space division method

The authors have developed a new approach for large-scale systems including over 100,000 atoms to obtain physical strength from the viewpoint of atom–atom bonding energy. Combining the semi-empirical molecular orbital method with real space division method makes it possible to estimate structural parameters, electronic structures and bonding energy for various large systems. With this method, various quantum physical properties can be obtained quickly using the semi-empirical molecular orbital method, while adopting real space division improves the computational efficiency of parallelization. In this study, the authors applied this method to SiH₄ molecule and crystalline silica system, and carried out bond order and bonding energy analyses. In this analysis, the developed method offered almost the same analytical accuracy as the first principle method, while its calculation speed was much faster than that of the latter. The developed method was also suitable for parallel computing.     

A Memory-efficient Simulation Method of Grover's Search Algorithm

Grover's search algorithm is one of the most significant quantum algorithms, which can obtain quadratic speedup of the extensive search problems. Since Grover's search algorithm cannot be implemented on a real quantum computer at present, its quantum simulation is regarded as an effective method to study the search performance. When simulating the Grover's algorithm, the storage space required is exponential, which makes it difficult to simulate the high-qubit Grover's algorithm. To this end, we deeply study the storage problem of probability amplitude, which is the core of the Grover simulation algorithm. We propose a novel memory-efficient method via amplitudes compression, and validate the effectiveness of the method by theoretical analysis and simulation experimentation. The results demonstrate that our compressed simulation search algorithm can help to save nearly 87.5% of the storage space than the uncompressed one. Thus under the same hardware conditions, our method can dramatically reduce the required computing nodes, and at the same time, it can simulate at least 3 qubits more than the uncompressed one. Particularly, our memory-efficient simulation method can also be used to simulate other quantum algorithms to effectively reduce the storage costs required in simulation.     

B样条曲线的小波光顺法

本文研究了B样条曲线的小波光顺法。首先介绍了利用准均匀B样条曲线逼近具有任意节点矢量的B样条曲线的方法，从而将任意B样条曲线转化为多分辨率表示，进而提出了基于小波的曲线光顺误差控制算法。小波光顺法在光顺曲线的同时具有减少控制顶点的作用，兼具简单性和通用性的优点。     

Compact energy storage enabled by graphenes: Challenges,strategies and progress

Storing as much energy as possible in as compact a space as possible is an ever-increasing concern to deal with the emerging “space anxiety” in electrochemical energy storage (EES) devices like batteries, which is known as “compact energy storage”. Carbons built from graphene units can be used as active electrodes or inactive key materials acting as porous micro- or even nano-reactors that facilitate battery reactions and play a vital role in optimizing the volumetric performance of the electrode and the battery. In this review, we discuss and clarify the key issues and specific strategies for compact energy storage, especially in batteries. The use of shrinkable carbon networks to produce small yet sufficient reaction space together with smooth charge delivery is highlighted as the simplest structure–function-performance relationship when used in supercapacitors and is then extended to overcome problems in compact rechargeable lithium/sodium/potassium batteries. Special concerns about cycling stability, fast charging and safety in compact batteries are discussed in detail. Strategies for compact energy storage ranging from materials to electrodes to batteries are reviewed here to provide guidance for how to produce a compact high energy battery by densifying the electrodes using customized carbon structures.     

The B-spline finite element method applied to axi-symmetrical andnonlinear field problems

A B-spline FEM (finite-element method) using the B-spline functions for rectangular elements as shape functions is presented. It is very effective for solving two-dimensional electromagnetic field problems in regular regions. Compared with the conventional FEM, it gives more accurate potential values and due to the inherent properties of B-spline functions yields much closer field values. Both the computing time and the storage capacity are greatly reduced as well     

Landmark-free geometric methods in biological shape analysis

In this paper, we propose a new approach for computing a distance between two shapes embedded in three-dimensional space. We take as input a pair of triangulated genus zero surfaces that are topologically equivalent to spheres with no holes or handles, and construct a discrete conformal map f between the surfaces. The conformal map is chosen to minimize a symmetric deformation energy E_sd(f) which we introduce. This measures the distance of f from an isometry, i.e. a non-distorting correspondence. We show that the energy of the minimizing map gives a well-behaved metric on the space of genus zero surfaces. In contrast to most methods in this field, our approach does not rely on any assignment of landmarks on the two surfaces. We illustrate applications of our approach to geometric morphometrics using three datasets representing the bones and teeth of primates. Experiments on these datasets show that our approach performs remarkably well both in shape recognition and in identifying evolutionary patterns, with success rates similar to, and in some cases better than, those obtained by expert observers.     

结构力学中的广义力法

本文根据目前结构力学的力法原理、线性空间理论和最小应变能原理,对杆系结构的力法作了进一步的探讨,提出了静不定结构的解空间的概念,并建立了广义力法典型方程。由于可以灵活地选择不同的基本结构计算系数δ_(ij)和自由项Δ_(ip),从而使线性方程组的建立在一定程度上得以简化,同时本文进一步完善了力法原则,有助于理解超静定结构内力解空间的分析构造。