NURBS曲面的四边形网格的分割与逼近

介绍了一个用于对NURBS曲面进行四边形网格的分割与逼近的算法。该算法采用二叉树递归分割的方法分割和逼近曲面，所分割的四边形除了在高度方向和曲面边界处满足给定精度外，同时在四边形四条边界满足给定的切矢精度。实例测试结果表明，用本文所述算法生成的四边形网格具有网格逼近原曲面、网格四边形接近于规则四边形等特点。     

复杂地质曲面三维插值—逼近拟合构造方法

针对水利水电工程多源地质数据的特点,充分考虑了地质精度要求、曲面连续性和数据存储量等多方面的均衡,提出并实现了基于NURBS(non-uniform rational B-splines,非均匀有理样条曲线)技术的复杂地质曲面插值—逼近拟合构造方法。该方法对于工程关键区域集中且均匀分布的原始数据,采用NURBS蒙皮插值方法,使曲面严格通过这些数据点;对于周边区域分布离散的数据,采用NURBS逼近拟合方法,使曲面在给定精度下充分逼近原始数据;最后对整体曲面的地质结构合理性、几何性和精度进行检查分析和调整。实例表明,该方法所构造的地质曲面能满足地质工程师的实际需要,并能为进一步的三维地质建模提供基础。     

基于球面三角网格逼近的等距曲面逼近算法

给出了一种基于球面三角网格逼近的等距曲面逼近新算法。利用三角网格逼近基球面,然后计算此三角网格按中心沿在曲面扫凉而成空间区域的边界作为等距曲面的逼近。该算法计算简单,方便地解决了整体误差问题,而且所得到的逼近曲面是与原曲面同次数的NURBS曲面。     

基于MATLAB对三维激光扫描数据的精度评定

针对三维激光扫描存在对扫描精度难以评定的问题,该文提出了1种基于(结合)MATLAB的三维激光扫描数据的精度评定方法。首先,对三维激光扫描测量的数据进行预处理,获得被扫描体表面的点云数据;其次,切割被扫描体的点云曲面,获得点云剖线;再次,通过MATLAB拟合点云曲线,将其转成离散点位;最后,依托TS30高精度的特点,对三维激光扫描数据进行精度评定。     

基于Trimmed NURBS曲面几何特征的数字化自适应采样

曲面轮廓度误差评价和多边域逼近均要求对理论曲面进行数字化自适应采样。在对当前曲面数字化方法分析的基础上，针对Trimmed NURBS曲面，研究了在给定精度下的曲面数字化自适应采样方法，给出了基于曲率特征函数的曲线自适应采样和NURBS曲面多边域离散算法，提出了一种对大规模曲面网格点检测路戏优化问题很有效的进化算法一蚁群算法，并进行了计算机仿真实验验证。仿真结果表明，所提出的规划方法可显著提高数字化采样效率，具有很大的实用价值。     

NURBS曲面求交及变半径过渡曲面生成

本文探索NURBS曲面求交及构造过渡曲面的方法。基于交线跟踪算法求出NURBS曲面间的交线,算法比较稳定、可靠;采用参数化平面与等距面求交找出两曲面空间等距点,具有自然与变半径过渡曲面的定义相呼应、找点快、准确、稳定的特点;过渡曲面表示为2×3次NURBS曲面,自然、充分地利用了NURBS曲线可精确表示圆弧段的特性,过渡曲面具有表达简单、比较准确、便于采用统一的NURBS曲面处理算法对其进行各种几何处理的优点;实验证明这些方法可行,效果令人满意。     

基于单位圆弧段逼近的Bézier曲线等距线生成算法

提出一种用四次Bézier曲线逼近单位圆弧段(Unit Circular Arcs)的方法及其详细误差函数分析.使用这种方法,给出一种使用同阶Bézier曲线逼近给定Bézier曲线等距线的算法.在Matlab7.0上实现了该算法,试验表明,新算法比Lee和Ahn所提出的算法有更高的精度和计算效率.由于B样条和NURBS曲线可以认为由多段Bézier曲线组成,因此,新算法为B样条和NURBS曲线等距线的求解提供了一种新的途径.     

RCS计算中NURBS曲面和射线求交的快速计算

提出了一种基于牛顿迭代法解方程组的射线和NURBS曲面求交算法。利用预先计算射线和曲面交点个数最大值,通过折中适应性分割曲面得到迭代初始值,达到了快速计算的效果。同时,解决了射线与NURBS曲面多交点判断、自交点筛选等问题,保证了交点精度,且不会遗漏交点。     

反求点在自由曲面上投影参数值的一种稳定算法

针对反求曲线曲面上点的参数值存在数值不稳定的问题,提出了一种稳定的算法.实际应用的曲面很多采用高阶次曲面并且由很多曲面片拼接而成,采用NURBS曲面形式记录曲面信息.针对这类复杂曲面,采用牛顿迭代法求解参数值,再采用单纯形法对参数值进行优化.通过上百个数据的试验,证明该算法是反求点在自由曲面上投影的参数值的一种稳定的并有效的算法.     

基于单位圆弧段逼近的Bezier曲线等距线生成算法

提出一种用四次Bezier曲线逼近单位圆弧段（Unit Circular Arcs）的方法及其详细误差函数分析。使用这种方法,给出一种使用同阶Bezier曲线逼近给定Bezier曲线等距线的算法。在Matlab7．0上实现了该算法,试验表明,新算法比Lee和Ahn所提出的算法有更高的精度和计算效率。由于B样条和NURBS曲线可以认为由多段Bezier曲线组成,因此,新算法为B样条和NURBS曲线等距线的求解提供了一种新的途径。     

基于裁剪曲面表示的实体拼合运算

本文首先论述了多面体拼合运算的分割方法和法矢投影法，重点介绍后者。然后将法矢投影法推广到由裁剪曲面表示的曲面实体拼合中，初步得到满意的结果。     

Decomposition applied to layered manufacturing using critical points

Slicing represents an important step in all rapid prototyping processes. This paper proposes the use of critical points for adaptive local slicing for strataconception in particular and rapid prototyping technologies in general. The context of using critical points in rapid prototyping to optimise usual slicing is presented. Its definition on both surfaces and triangular meshings is given and extended to other geometric entities, such as edges, facets and faces. Finally, this new slicing approach is compared with the usual one on a few models manufactured through the stratoconception process.     

Decomposition applied to layered manufacturing using critical points

Slicing represents an important step in all rapid prototyping processes. This paper proposes the use of critical points for adaptive local slicing for strataconception in particular and rapid prototyping technologies in general. The context of using critical points in rapid prototyping to optimise usual slicing is presented. Its definition on both surfaces and triangular meshings is given and extended to other geometric entities, such as edges, facets and faces. Finally, this new slicing approach is compared with the usual one on a few models manufactured through the stratoconception process.     

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.     

Automatic segmentation and approximation of digitized data for reverse engineering

Reverse engineering is the process of developing a computer-aided design (CAD) model and a manufacturing database for an existing object. This process is used in CAD modelling of part prototypes, in designing moulds and in automated inspection of parts with a complex surface. This paper reports on the automatic segmentation and approximation of three-dimensional digitized points for reverse engineering. Based on an innovation that uses the properties of a non-uniform rational B-spline (NURBS) or B-spline and makes ordered digitized points be control points directly to construct a NURBS or B-spline surface, which takes less computation time than traditional algorithms in calculating surface normals and curvatures at digitized points, an algorithm was developed for automatic segmentation and NURBS surfaces fitting for digitized points.     

飞机结构件加工域单元分层识别及构造方法

加工域的自动识别是自动数控加工编程的关键技术之一。为实现飞机结构件自动数控加工程序编制过程中工序件加工域的自动识别,建立了加工域模型,提出了一种实用、可行的域元分层识别方法。首先,根据工序件构建分层面,截切零件和毛坯;其次,依据层交结果构建层域元轮廓,生成层域元;然后,建立规则合并层域元生成域元;最后,通过匹配域元间纵向关系,构建域元树状模型。通过对飞机结构件的测试,证明了该方法的有效性和实用性。     

Electrode-induced nonuniformities in the sweeping of alpha quartz

Infrared absorption and scanning electron microscopic techniques show that color-center and/or electrode-metal introduction into quartz is influenced by the porosity of evaporated metal electrodes. Thermal-stress relief of electrode-metal films, during sweeping, normally causes porosity. If the porosity is extensive, H introduction predominates and color-center and electrode-metal introduction mechanisms are suppressed. Samples swept with evaporated Au/Cr electrodes relying on thermal stress-induced porosity sometimes displayed these sweeping nonuniformities. Nonuniformities were not found when samples were swept using evaporated Au-Cr electrodes containing periodic stripe openings. Uniform sweeping was also obtained using magnetron-sputtered amorphous Y-Ba-Cu-O films.     

High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods

High-quality volumetric parameterization of computational domain plays an important role in three-dimensional isogeometric analysis. Reparameterization technique can improve the distribution of isoparametric curves/surfaces without changing the geometry. In this paper, using the reparameterization method, we investigate the high-quality construction of analysis-suitable NURBS volumetric parameterization. Firstly, we introduce the concept of volumetric reparameterization, and propose an optimal Möbius transformation to improve the quality of the isoparametric structure based on a new uniformity metric. Secondly, from given boundary NURBS surfaces, we present a two-stage scheme to construct the analysis-suitable volumetric parameterization: in the first step, uniformity-improved reparameterization is performed on the boundary surfaces to achieve high-quality isoparametric structure without changing the shape; in the second step, from a new variational harmonic metric and the reparameterized boundary surfaces, we construct the optimal inner control points and weights to achieve an analysis-suitable NURBS solid. Several examples with complicated geometry are presented to illustrate the effectiveness of proposed methods.