基于三坐标测量数据的点云曲面重构

基于CMM测量数据,针对鼠标数据的特点,进行了边界拟合、特征识别、分片重建、光滑拼接等技术的研究。利用三次B样条拟合边界曲线,利用微分几何方法进行曲面特征的识别与分割,利用拉伸及放样法进行曲面片重构,最后进行曲面片相交、剪裁、过渡完成最终的鼠标模型。     

参数Bezier三角曲面G1光滑拼接的相容性

本文对参数Ｂｅｚｉｅｒ三角曲面拼接的相容性问题进行了研究。给出拼接的相容性条件。实现了任意多片参数三角曲面片的一阶几何连续拼接，可对任意复杂形状进行造型。     

一类C2连续可调控的交错B样条曲面

提出一类C^2连续可调控的带参数ε的交错B样条曲面的生成方法,这种曲面具有普通3次B样条曲面的主要性质,在控制点固定时,改变参数ε的值能调控曲面的位置,当ε→0时曲面整体地逼近于控制多面体网。     

平面G2组合三次α-Bézier曲线的几何构造

对三次曲线的几何连续拼接问题做了研究.给出了构造平面G2组合三次α-Bézier曲线的几何算法.这个算法,可以对给定的一组平面控制顶点,方便地构造一条G2三次α-Bézier样条曲线.这种样条保留了B样条、β样条的性质,优点在于保持曲线G2连续,同时通过选取不同的混合因子和形状因子,局部调整曲线的形状,以满足不同的设计要求.     

用NURBS光顺原理提高曲面铣削加工质量

分析了参数连续性和几何连续性对光顺性的影响。阐述了B样条方法和NURBS方法各自的特点和相互间的不同点,分析了与传统曲线构造方法相比的优点,介绍了NURBS曲面在3D设计中的应用等。建立曲面后,通过高斯云图和反射方法图的分析,检验NURBS曲面的精度和光顺性,针对不光顺的原因,采取相应的解决方法,以生成高精度的曲面。加工时采用NURBS输出,优化刀具轨迹,简化程序,提高生产效益。     

比例边界等几何方法在断裂力学中的应用

该文将比例边界等几何方法(SBIGA)应用在断裂力学中,并就应力强度因子(SIFs)计算精度和收敛速度与传统比例边界有限元(SBFEM)进行了比较。与SBFEM不同,SBIGA采用非均匀有理B样条(NURBS)作为造型和离散的工具。主要包括了以下两个特点:一方面,有限元模型可直接继承于CAD系统,即节约划分网格的时间也避免了几何近似。另一方面,因为不需要进一步与CAD系统数据交换就可以保型细分,二维问题中自适应分析策略的实施十分方便。算例表明,SBIGA方法可以给出较SBFEM更为精确的结果和更快的收敛速度。其原因不仅得益于对曲边几何形状的精确描述,还来源于NURBS高阶的连续性。     

反向工程在NURBS曲面造型中的研究与应用

文章介绍了工程领域中叶片曲面造型在国内外的发展情况,针对曲面造型中存在的形状数据与建模所需数据不符的问题,推导了曲面初始二维数据向三维数据的转换关系,提出了一种将反向工程用于叶片曲面的NURBS几何建模方法,提高了此类曲面在实际生产中的设计精度.     

CE-Bézier曲面光滑拼接的研究与实现

针对CE-Bézier曲面造型中复杂曲面难以用单一曲面来表示的问题,通过分析CE-Bézier曲线的唯一性,提出了一种新的CE-Bézier曲面的光滑拼接技术。首先,在分析第1类CE-Bézier曲线基函数及其端点性质的基础上,对第1类CE-Bézier曲线的唯一性进行了研究,得出了对于同一条第1类CE-Bézier曲线可以有很多组不相同的控制顶点和形状参数与之对应的结论;其次,利用该结论进一步给出了两相邻第1类CE-Bézier曲面片间G1光滑拼接的一般几何条件,并通过合理地选取形状参数,进一步简化了该曲面的G1拼接条件;最后,给出了第1类CE-Bézier曲面光滑拼接的几何造型实例。实例结果表明,该方法简单、直观、易实现,有效地增强了CE-Bézier方法表达复杂曲线曲面的能力,可广泛地应用于工程复杂曲面的造型系统中。     

NURBS曲面自由型特征处理方法研究

NURBS曲面自由型特征因不具有确定的参数、准确的边界,使其表示、编辑及操作十分困难.基于一种新的小波多分辨率分析技术将NURBS曲面从单一尺度几何表示的空域变换为频域的表示形式,借助于滤波器组将模型的整体结构和局部细节变换为其全局和局部多分辨率自由型特征,实现了对NURBS曲面的自由型特征的编辑、操作和控制.该方法不仅能提高NURBS曲面几何建模的效率,而且可以克服传统NURBS曲面建模的繁琐和费时.     

均匀B样条曲线曲面的小波表示

小波基为曲线曲面带来了更为灵活的表达方式,均匀B样条曲线曲面在经过小波分解以后所得到的小波在定义域边界与内部可以采用统一的表达式,在进行小波重构时仅需作乘法运算,计算效率高。本文试图从几何概念出发由浅入深地论述基于小波的均匀三次B样条曲线曲面多分辨表示的原理及其实现。     

面向IGES输出的曲面重构技术

针对反求工程中复杂曲面CAD建模专用软件（RE－SOFT）与其他商用CAD／CAM系统间进行信息流动的问题，提出一种面向IGES标准输出的复合三角Beizer曲面重构四边NURBS曲面技术；通过复合三角曲面的特征提取，对三角曲面进行分块、区域边界编辑及相邻区域光滑拼接，进而构造出G^1连续的光滑四边NURBS曲面模型并以IGES数据格式传输到其它CAD／CAM系统中进行后续处理，达到了既能充分利用三角曲面的优势又能实现专用CAD软件（RE－SOFT）与其他商用CAD／CAM系统集成的目的。     

NURBS Modeling and Curve Interpolation Optimization of 3D Graphics

In order to solve the problem of complicated Non-Uniform Rational B-Splines (NURBS) modeling and improve the real-time performance of the high-order derivative of the curve interpolation process, the method of NURBS modeling based on the slicing and layering of triangular mesh is introduced. The research and design of NURBS curve interpolation are carried out from the two aspects of software algorithm and hardware structure. Based on the analysis of the characteristics of traditional computing methods with Taylor series expansion, the Adams formula and the Runge-Kutta formula are used in the NURBS curve interpolation process, and the process is then optimized according to the characteristics of NURBS interpolation. This can ensure accuracy, and avoid the calculation of higher-order derivatives. Furthermore, the hardware modules for the Adams and Runge-Kutta formulas are designed by using the parallel hardware construction technology of Field Programmable Gate Array (FPGA) chips. The parallel computing process using FPGA is compared with the traditional serial computing process using CPUs. Simulation and experimental results show that this scheme can improve the computational speed of the system and that the algorithm is feasible.     

Patch coupling in isogeometric analysis of solids in boundary representation using a mortar approach

This contribution is concerned with a coupling approach for nonconforming NURBS patches in the framework of an isogeometric formulation for solids in boundary representation. The boundary representation modeling technique in CAD is the starting point of this approach. We parameterize the solid according to the scaled boundary finite element method and employ NURBS basis functions for the approximation of the solution. Therefore, solid surfaces consist of several sections, which can be regarded as patches and discretized independently. The main objective of this study is to derive an approach for the connection of independent sections in order to allow for local refinement and thus an accurate and efficient discretization of the computational domain. Nonconforming sections are coupled with a mortar approach within a master-slave framework. The coupling of adjacent sections ensures the equality of mutual deformations along the interface in a weak sense and is enforced by constraining the NURBS basis functions on the interface. We apply this approach to nonlinear problems in two dimensions and compare the results with conforming discretizations.     

高速凸轮NURBS廓线改进人工鱼群多目标动力学优化

为改善高速凸轮机构动力学性能,首先采用非均匀有理B样条（NURBS）重构凸轮廓线,建立高速凸轮单自由度弹性动力学模型,进行高速凸轮机构多目标动力学优化设计。然后利用改进人工鱼群算法求解该模型,获取系统Pareto最优解从而得到优化后的NURBS廓线。最后,分析和比较高速凸轮机构在NURBS和修正正弦两种廓线下的动力学响应。结果表明：改进人工鱼群算法可以有效解决多目标优化问题,优化后NURBS廓线运动学特性与修正正弦廓线相差不大,在一定程度上降低了高速凸轮机构的残余振动幅值,提高了高速凸轮机构的定位精度和动力性能,减少了振动和冲击的噪声。     

On the treatments of heterogeneities and periodic boundary conditions for isogeometric homogenization analysis

The treatments of heterogeneities and periodic boundary conditions are explored to properly perform isogeometric analysis (IGA) based on NURBS basis functions in solving homogenization problems for heterogeneous media with omni‐directional periodicity and composite plates with in‐plane periodicity. Because the treatment of the combination of different materials in IGA models is not trivial especially for periodicity constraints, the first priority is to clearly specify points at issue in the numerical modeling, or equivalently mesh generation, for IG homogenization analysis (IGHA). The most awkward, but important issue is how to generate patches for NURBS representation of the geometry of a rectangular parallelepiped unit cell to realize appropriate deformations in consideration of the convex‐hull property of IGA. The issue arises from the introduction of overlapped control points located at angular points in the heterogeneous unit cell, which must satisfy multiple point constraint (MPC) conditions associated with periodic boundary conditions (PBCs). Although two measures may be conceivable, we suggest the use of multiple patches along with double MPC that imposes PBCs and the continuity conditions between different patches simultaneously. Several numerical examples of numerical material and plate tests are presented to demonstrate the validity of the proposed strategy of IG modeling for IGHA. Copyright © 2016 John Wiley & Sons, Ltd.     

Powell–Sabin B‐splines and unstructured standard T‐splines for the solution of the Kirchhoff–Love plate theory exploiting Bézier extraction

The equations that govern Kirchhoff–Love plate theory are solved using quadratic Powell–Sabin B‐splines and unstructured standard T‐splines. Bézier extraction is exploited to make the formulation computationally efficient. Because quadratic Powell–Sabin B‐splines result in ‐continuous shape functions, they are of sufficiently high continuity to capture Kirchhoff–Love plate theory when cast in a weak form. Unlike non‐uniform rational B‐splines (NURBS), which are commonly used in isogeometric analysis, Powell–Sabin B‐splines do not necessarily capture the geometry exactly. However, the fact that they are defined on triangles instead of on quadrilaterals increases their flexibility in meshing and can make them competitive with respect to NURBS, as no bending strip method for joined NURBS patches is needed. This paper further illustrates how unstructured T‐splines can be modified such that they are ‐continuous around extraordinary points, and that the blending functions fulfil the partition of unity property. The performance of quadratic NURBS, unstructured T‐splines, Powell–Sabin B‐splines and NURBS‐to‐NURPS (non‐uniform rational Powell–Sabin B‐splines, which are obtained by a transformation from a NURBS patch) is compared in a study of a circular plate. Copyright © 2015 John Wiley & Sons, Ltd.     

5G/F5G技术对于中国电影影响的分析

随着5G/F5G时代的到来,技术赋能艺术,5G与F5G技术天地联网,双剑合璧,形成功能特点相互优化补充的态势.电影作为现代科技与艺术的综合体,技术层面的升级推动电影产业不断进步.本文通过对5G/F5G技术概念特点的阐述,梳理分析5G/F5G技术在电影摄制、发行和放映等全产业链的运用以及对于各个环节产生的影响,认为5G/...     

基于能量法的G2连续的曲面过渡

提出一种基于能量法的G2连续过渡面的构造方法,着重分析过渡曲面能量优化模型的建立,边界约束、法矢方向一致约束以及主曲率相等约束的表达和处理。将过渡曲面的能量优化模型转化为非线性等式约束的二次数学规划问题,并运用Lagrange乘子法求解过渡曲面的能量优化模型。最后给出了应用该方法生成G2连续过渡曲面的几个实例。     

G7工艺实验与研究

C7工艺是以控制灰平衡为主的一种新的印刷工艺方法,能够实现不同材料的同貌印刷效果.阐述了C7工艺原理、G7工艺实验的准备工作和实验的方法,并研究了实施G7实验时印刷机的稳定性控制,对企业实施G7工艺具有借鉴意义.     

The weak substitution method – an application of the mortar method for patch coupling in NURBS‐based isogeometric analysis

In this contribution, a mortar‐type method for the coupling of non‐conforming NURBS (Non‐Uniform Rational B‐spline) surface patches is proposed. The connection of non‐conforming patches with shared degrees of freedom requires mutual refinement, which propagates throughout the whole patch due to the tensor‐product structure of NURBS surfaces. Thus, methods to handle non‐conforming meshes are essential in NURBS‐based isogeometric analysis. The main objective of this work is to provide a simple and efficient way to couple the individual patches of complex geometrical models without altering the variational formulation. The deformations of the interface control points of adjacent patches are interrelated with a master‐slave relation. This relation is established numerically using the weak form of the equality of mutual deformations along the interface. With the help of this relation, the interface degrees of freedom of the slave patch can be condensated out of the system. A natural connection of the patches is attained without additional terms in the weak form. The proposed method is also applicable for nonlinear computations without further measures. Linear and geometrical nonlinear examples show the high accuracy and robustness of the new method. A comparison to reference results and to computations with the Lagrange multiplier method is given. Copyright © 2015 John Wiley & Sons, Ltd.