等距曲面的NURBS放样插值方法

本文给出了等距曲面的一种NURBS放样插值生成方法，该方法主要是在原始NURBS曲面上取得一个能较好反映曲面特征的型值点阵，再交这个型值点阵按某种算法矢方向外推，从而得到原始曲面的等距曲面上的型值点阵，然后，再用NURBS放样插值曲面来逼近等距曲面，本文给出的算法几何意义明显，易于编程实现，且得到的等距曲面其u向和v向参数曲线仍是NURBS曲线，且具有C^2连续性，最后，给出了一个实例。     

NURBS曲面生成算法及仿真研究

讨论了一种生成NURBS曲面的算法,用C语言实现了该算法,并利用MATLAB进行仿真对该算法进行验证。在算法中讨论了曲面及其等距面生成方法以及曲面生成技术中相关的一些技术,如曲线段间参数过渡、曲面生成模式、曲面生成的实时性、改变曲面的形状等。仿真结果证明了算法的有效性。     

Loop细分曲面的等距曲面的逼近

提出了一种生成Loop细分曲面的等距曲面的逼近方法．通过让生成的等距曲面在对应于其控制网格顶点的地方是精确的等距，作者将等距曲面的逼近问题转化为求解一个线性方程组．文中提出了一个用于快速求解该线性方程组的改进的Gauss—Jacobi迭代法．另外，该文还考虑了逼近的误差控制和等距曲面的自交问题．     

基于一元对称幂基的等距曲面有理逼近算法

给出了基于一元对称幂基的等距曲面蒙面逼近新算法。利用一元对称幂基逼近张量积Bézier曲面u向曲线的等距曲线,得到一组等距逼近曲线,取固定的v值,得到一组数据点,用反算控制顶点的方法得到过这组数据点的v向曲线。对这两组曲线用蒙面算法得到逼近的有理等距曲面。该算法计算简单,将二元等距曲面有理逼近转化为一元曲线有理逼近,同时方便地解决了整体误差问题,随着对称幂基阶数的升高,可以得到较理想的逼近效果。     

回转曲面的可展切曲面

论文系统地提出了构造回转曲面的可展切曲面及它们间映射分析的理论与 方法,建立了回转曲面可展切柱面和可展切锥面的数学模型以及曲面间的映射关系。根据回 转曲面及其可展切曲面间微分长度比的理论分析,推出了映射中极值映射曲线和等距映射曲 线的微分方程,通过整体和局部的变形分析,可以准确地掌握回转曲面与其可展切曲面间映 射中的变形情况。     

基于Bernstein函数类的Bezier曲面类

为了进一步丰富Bezier曲面理论,以及克服原有Bezier曲面理论中的一些不足,在梁锡坤提出的Bernstein函数类的基础上,对基于该类函数的Bezier曲面类的生成方法进行了研究。并给出了两种具体的Bezier曲面类曲面,这两种曲面是基于有理形式调配函数,即RB函数的实用曲面,称之为RB曲面和附权RB曲面。重点研究了RB曲面和附权RB曲面的表示方法和有关性质,同时还分析了这两种曲面之间以及与Bezier曲面之间的关系。得到了较好的结果,使Bezier曲面理论更加完善。     

NURBS边界曲面直接生成法

由于非均匀有理B样条(NURBS)曲面的复杂性,传统NURBS边界曲面的生成是先构造孔斯曲面,再由孔斯曲面向NURBS曲面转换得到,其操作过程比较烦琐。针对此问题,提出了NURBS边界曲面直接生成算法,该算法根据给定的四条NURBS边界曲线,结合孔斯曲面生成方法直接插值生成NURBS曲面,从而避免了通过孔斯曲面向NURBS曲面转换所带来的计算代价,因此同传统方法相比,具有较低的计算代价。实验结果表明:该算法简化了曲面生成步骤,减少了曲面转换过程的计算量,生成的曲面边界信息明确,且连续性好。     

基于Bernstein函数类的Bezier曲面类栽

为了进一步丰富Bezier曲面理论,以及克服原有Bezier曲面理论中的一些不足,在梁锡坤提出的Bernstein函数类的基础上,对基于该类函数的Bezier曲面类的生成方法进行了研究.并给出了两种具体的Bezier曲面类曲面,这两种曲面是基于有理形式调配函数,即RB函数的实用曲面,称之为RB曲面和附权RB曲面.重点研究了RB曲面和附权RB曲面的表示方法和有关性质,同时还分析了这两种曲面之间以及与Bezier曲面之间的关系.得到了较好的结果,使Bezier曲面理论更加完善.     

细分蒙皮曲面

对细分曲面在曲面造型中的应用进行了研究，并着重于蒙皮曲面造型技术．所提方法在传统的蒙皮曲面构造过程中引入细分方法，有效地避免了因截面曲线的相容性处理而产生的数据量激增的问题；最后生成的蒙皮曲面能够精确插值预先设计的截面曲线，并且可以在指定的截面曲线处产生折痕效果．     

面向陶瓷3D打印的双尺度放样曲面建模

针对陶瓷3D打印的特点,提出基于放样曲面与周期参数曲线嵌入的双尺度轻量化交互式建模和制造工具.对于用户输入的2条封闭曲线,首先在它们之间插值生成中间截面采样点,并在免支撑、路径无干涉等陶瓷3D打印制造约束下对当前曲面形状进行调整,完成基于放样曲面的大尺度曲面建模;然后将采样点之间的直线路径用周期性曲线路径代替,通过调整曲线函数的周期和振幅完成小尺度几何纹理建模;最后按螺旋方式逐层连接各个截面采样点,直接生成单一连续的打印路径并制造.为验证文中方法的有效性,基于绘制的3组曲线进行建模并利用CERAMBOT Plus陶瓷3D打印机制造模型.实验结果表明,该工具为用户提供了充足的建模空间且模型生成效率高,能够有效地生成可直接进行陶瓷3D打印的带纹理放样曲面的G-code文件.     

基于耐撞性的前纵梁截面优化设计

前纵梁是偏置碰撞测试中重要的吸能部件之一。本文对前纵梁截面形状进行了优化设计,以提高前纵梁的耐撞性。根据前纵梁截面尺寸参数得到设计变量,构建响应面模型,利用遗传算法计算得到优化结果。将优化所得的截面尺寸应用于某三厢轿车40%偏置碰撞分析中,结果表明,前纵梁耐撞性显著提高,碰撞侧B柱加速度峰值有效降低,整车被动安全性能得到提升。     

An offset surface to reduce radar cross section for airborne antenna out‐band

To meet the needs of modern electronic warfare in better stealth performance of the weapon platform, we design an offset surface with metasurface structure, which greatly reduces the radar cross section for airborne antenna. The relation between surface unit size and attenuation frequency guides the design of offset surface that can work in the L‐band. The original strategy performed as cross‐array structure that plays well throughout the band at different angles, except 30° to 35°. An undesired reflection occurs at this angle gap. Therefore, we attempted to modify the structure as parallel‐array structure with same unit size. The results show that modification performs well at all angles in the passband, which meets the design requirements. We processed an offset surface sample and performed a joint test with an aircraft antenna to verify the superiority of the design.     

A new approach to z-level contour machining of triangulated surface models using fillet endmills

Precision z-level contour machining is important for various computer-aided manufacturing (CAM) applications such as pocket machining and high-speed machining (HSM). This paper presents a new z-level contour tool-path generation algorithm for NC machining of triangulated surface models. Traditional approaches of z-level machining rely on the creation of accurate CL (cutter location) surfaces by surface offsetting or high-density z-map generation, which is computationally expensive and memory demanding. In contrast, this paper presents a novel approach to the generation of CL data directly from the section polygon of a triangulated surface model. For each polygon vertex of the contour, the offset direction is determined by the normal to the edge, while the offset distance is not fixed but is determined from the cutter shape and the part surface. An interference-free tool-path computation algorithm using fillet endmills is developed. Since there is no need to create a complete CL surface or high-density z-map grids, this proposed method is highly efficient and more flexible, and can be directly applied to triangulated surfaces either tessellated from CAD models, or reconstructed from 3D scanned data for reverse engineering (RE) applications.     

A mapping-based approach to eliminating self-intersection of offset paths on mesh surfaces for CNC machining

Geometrically, a tool path can be generated by successively offsetting its adjacent path on the surface with a given path interval, which preferably starts from one of the surface boundaries or a primary curve. The key issues involved in offset path planning are the generation of raw offset paths and the elimination of the self-intersection of raw offset paths. Most researches available in this area are focused on how to generate the raw offset paths, however, the latter, especially how to eliminate the self-intersection of the offset paths on mesh surfaces, has not been sufficiently addressed. In this paper, a mapping-based approach to eliminating the self-intersection of offset paths is proposed for the CNC machining of mesh surfaces. The method first flattens the mesh surface onto a predefined plane by using a mesh mapping technique, and then taking the mapping as a guide, the offset paths are also naturally mapped onto the plane, from which those invalid self-intersection loops can be effectively identified and eliminated. To handle the issue of self-intersection for all types of offset path, a notion of local loop is introduced to detect and eliminate the invalid self-intersection loops. After that the planar paths are inversely mapped into the physical space and the final tool paths used for the machining of mesh surface are obtained. Meanwhile, in order to improve the kinematic and dynamic performance of the machine tool when machining along the generated offset paths, a method for rounding the sharp corners of tool paths, which result from the process of eliminating the self-intersection of raw offset paths, is also preliminarily investigated. Finally, the proposed method is validated by the results of simulations and machining experiments.     

CAD模型截面的Voronoi图生成与分层面的等距线填充

目前快速成型中层面制作都是采用行扫描方式进行分层截面的填充,该扫描方式的缺点是:熔丝冷却后产生的收缩对上一层面形成切向内应力,使得物理模型容易产生翘曲变形,另外对于注重外表面的形体,行扫描方式的填充效率较低,为此提出环扫描的填充方式,将VORONOI图的理论引入模型的分层制作,用外轮廓与它的等距线为轨迹完成截面的扫描填充,基于CAD模型分层后的轮廓线及其数据结构,研究了对该区域进行VORONOI图分割的算法,在此基础上规划出它的环扫描轨迹。     

Computing non-self-intersecting offsets of NURBS surfaces

A new approach for the computation of non-self-intersecting offset surface of a single G₁ continuous NURBS surface has been presented. The approach recognizes special surfaces, i.e. planes, spheres, cones and cylinders, and offsets them precisely. An approximate offset surface within the specified tolerance is computed for a general free form surface. The method for a general free form surface consists of (1) sample offset surface based on second derivatives; (2) eliminate sample points which can give self-intersections; (3) surface fitting through the remaining sample points; and (4) removal of all the removable knots of the surface. The approach checks for self-intersections in the offset surface and removes the same automatically, if any. The non-self-intersecting offsets for surface of extrusion and surface of revolution are obtained by removing the self-intersections in the offset generator and profile curves respectively using point sampling, cleaning of sampled points, curve fitting and knot removal. The approach has better control on error. It generates offset surface with less number of control points and degree. The methodology works only for a class of problems where in the offset of a single G₁ surface is still a single connected surface without having any holes. The offset methodology has been demonstrated through three types of surfaces namely surface of revolution, surface of extrusion and a general free form surface. This approach has been extensively used in creation of offset surfaces of composite laminate components. The presented approach can also be used to check for self-intersections in any general surface and to remove the same, if any, with little modifications, as long as the cleaned surface is a single connected surface.     

Computing offsets of trimmed NURBS surfaces

Offsetting of trimmed NURBS surfaces is one of the widely used functionalities in the design and manufacture simulations of composite laminates. This paper presents an approach for the offsetting of a trimmed NURBS surface. The approach has been developed mainly to meet the stringent accuracy requirements in the simulation of composite laminate design and manufacturing processes. However, the approach is applicable for the offset of a general trimmed NURBS surface. Though the method is based on known techniques in literature, the practical approach and the treatment of the subject presented is unique and has not been reported earlier. The basic approach consists of offsetting the underlying surface, offsetting of all the trimming loops and the creation of offset trimmed surface using the offset surface and the offset trimming loops. This is a unified offset approach for trimmed surfaces where in the offset of underlying surface and the offset of trimming loops are obtained using the same approach. The approach has better error control and results in less number of control points. Further the approach can be extended to obtain offsets of a general B-Rep. The approach has been used in the creation of offset surfaces of various aircraft components.     

地铁隧道形变监测系统断面采集数据的建模及算法研究

隧道形变数据包括整体的沉降和偏移数据以及断面的形变数据.针对断面形变监测数据,结合开发的监测系统,提出一种断面监测数据融合的数学模型,将采集数据进行有效融合,能够比较准确地反映隧道变形情况,为运营隧道的形变监测提供直观可靠的数据.同时,模型具有一般性,对类似管道、隧道的分析都具有参考价值.     

Qualitative and quantitative comparisons of B-spline offset surface approximation methods

Surface offset is one of the most useful operations in Computer Aided Geometric Design (CAGD). However, an implementation of this operator is not trivial primarily because the offset surface, in general, does not have the same representation as the original surface. Hence, it is difficult or impossible to represent an exact offset in a system with limited surface forms. For this reason, some CAGD surface offset operators produce results that are, at times, unsatisfactory. In this article, we discuss surface offset approximation methods in B-spline environment: both the original surfaces and their offsets are B-spline surfaces. This article summarizes research contained in the first named author's PhD thesis.     

离散曲面的等距面生成算法

离散曲面的等距面生成问题是一个不同于传统的等距面计算的新问题。拟对该问题展开研究并提出一个有效的离散曲面的等距面生成算法。该算法通过计算离散曲面的包络面上的离散体元而生成等距面。所提算法可以有效地解决等距计算过程中发生的拓扑、自相交等现象。实验结果表明了该算法的有效性。