一种基于离散数据的自由曲面建模方法

提出一种基于离散数据的自由曲面建模方法。该算法采用平行网格构造曲面,利用三次样条函数和参数样条对列表点进行行列两个方面的插补,采用局部回弹法进行曲线光顺,从而构造出适于数控加工的网格曲面,由于采用参数样条进行插补,可保证插值曲线通过所有型值点,曲线具有一、二阶导数连续的性质,可保证曲线的整体连续平滑。该方法的特点是方便了直角坐标下平行行切加工的数控编程。     

非四边(N边)域曲面造型方法的研究及在汽车外形设计中的应用

在J.A.Gregory关于N边域曲面理论研究成果的基础上,提出了一种用B样条曲面理论来构造一般N边域曲面的方法。该方法的优点是,所构造的N边域曲面片能够插值于表达为三次B样条曲线的任意边界及其跨界导矢。首先根据Gregory曲面方法构造N边域曲面片,再利用计算得到的数据构造由n个矩形B样条曲面片构成的一阶几何连续的N边域曲面片。     

基于NURBS的扫描曲面造型方法的研究

由于非均匀有理Ｂ样条（ＮＵＲＢＳ）表示的曲线,曲面具有充分的灵活性,同时又统一了初等曲线,曲面和自由曲线曲面的表示,故在ＣＡＤ领域得到广泛应用。扫描曲面造型则是自由曲面造型的重要手段之一,介绍了ＮＵＲＢＳ表示曲线曲面的方法及特点,对扫描曲面造的各种情况进行了讨论,在此基础上给出了基于ＮＵＲＢＳ的扫描曲面造型算法。     

NURBS曲面造型中曲线曲面分割问题的研究

提出一种基于ＮＵＲＢＳ齐次坐标表示来计算曲线曲面分割问题的方法，把ＮＵＲＢＳ总是转化为四维空间非有理Ｂ样条问题，就用Ｂ样条分割算法来解决，其几何意义明确，求解过程简便易行，便于在ＣＡＤ／ＣＡＭ系统中实现。     

NURBS曲面造型中曲线曲面分割问题研究

提出一种基于ＮＵＲＢＳ齐次坐标表示来计算曲线曲面分割问题的方法，把ＮＵＲＢＳ问题转化为四维空间里非有理Ｂ样条问题，就可利用Ｂ样条分割算法来解决，其几何意义明确，求解过程简便易行，便于在ＣＡＤ／ＣＡＭ系统中实现。     

G^2连续的三次有理Bezier样条插值曲线

有理插值问题至今没有得到完善解决本文探讨了局部有理插值,给出了利用每个型值点处的曲率Ｋ１为调节参数,来得到Ｇ＾２连续的保凸插值三次有理Ｂｅｚｉｅｒ样条曲线的方法。     

注塑模CAD/CAE中曲面造型的关键技术

基于表面模型构造二维绘图、三维线框和自由曲面之间递升的层次关系。系统曲面生成的主要功能有构造管道型曲面,超限插值曲面、旋转曲面和直纹面等。构造Ｇ＾１连续的过渡曲面,实现曲面求交,裁剪和拼接等编辑功能,从线框模型上构造曲面模型。曲面造型系统输出的几何模型可以生成有限元网格,将网格数据传给ＣＡＥ分析程序就可用于注塑成形的流动,保压,冷却和翘曲分析。     

B样条曲面造型设计新方法的研究

根据构造均匀双三次Ｂ样条曲面的基本理论，提出用扫描变换形式自动获取Ｂ样条曲面的特征网格顶点信息及直接生成各种Ｂ样条曲面的新方法，并研究其实用程序设计方法。     

用于大型CAD/CAE/CAM软件Anvil-5000中的贝齐尔曲面设计

着重研究Ｂｅｚｉｅｒ曲线、曲面的性质，进而提出了一种简易的Ｂｅｚｉｅｒ曲面边界联接方法，并借助大型ＣＡＤ／ＣＡＥ／ＣＡＭ软件Ａａｖｉｌ－５０００，使这种方法在计算机辅助几何设计（ＣＡＧＤ）领域得到了成功的应用。     

一类代数三角混合插值样条曲线

文中通过一类代数三角混合样条基函数的定义,构造了C<'1连续的代数三角混合插值样条曲线.一方面继承了多项式插值益线的特性,另一方面可以充分克服代数多项式基函数不能精确表示二次曲线及某些超越曲线曲面的弱点,以此扩大了插值型曲线曲面的表现范围.另外,利用形状控制参数可以灵活调节曲线形状,进一步增强了曲线曲面的表现能力.     

Trajectory planning of optical polishing based on optimized implementation of dwell time

This paper presents a study on the trajectory planning of optical polishing based on an optimized implementation of dwell time to improve the polishing quality and efficiency of optical surfaces. The large-scale, sparse, and ill-posed linear equation solution is transformed into a quadratic programming problem with boundary constraint, and the monotone projection gradient method is adopted to obtain an optimal dwell time solution by considering its fluctuation characteristic. Then, parametric polishing paths are constructed using cubic B-spline curves to guarantee one-to-one correspondence between each curve segment and dwell time of a removal spot. Finally, an interpolation process of polishing trajectory is proposed on the basis of the equal–proportional feed rate adjustment strategy to improve the implementation accuracy of dwell time. Simulation and experimental results show that the proposed dwell time algorithm and spline interpolation method can considerably improve the solution accuracy of dwell time and the convergence rate of the form error during polishing. These results provide important scientific basis and technical support for the high-efficiency and high-precision polishing of large-aperture aspheric optical surfaces.     

基于插补的三维网络曲面的一种光顺方法

常常要通过控制网格曲面片和控制点的法线来产生光滑、视角效果佳的多分辨率曲面.通过应用分段光滑Hermite样条曲线,为曲面网格的所有边界构造分段光滑样条曲线;然后,在初始网格上对边界进行采样,通过插补,非均匀构造分段三次Hermite样条的近似网格,并将原始曲面网格细分成多分辨率的曲面.提出了一种基于插补的、由低分辨率网格曲面产生多分辨率网格曲面的方法.     

三次B样条曲线数据采样插补器的研究

针对复杂轮廓零件数控加工的实际需求，基于数据采样插补原理，提出 了一种改进的三次B样条曲线插补器。利用此B样条曲线插补器进行数控加工，能够保证在整个加工过程中加工效率和加工质量的一致性，三次B样条曲线插补技术的实现将大大提高曲线，曲面零件数控加工的效率和加工质量。     

基于脊曲线控制的参数曲面周期变形

为得到理想的参数曲面造型效果,构造了一种新的基于多项式的伸缩因子,它不仅具有已有伸缩因子的特性,还具有区域峰值性;同时引入脊曲线的概念,对曲面进行控制变形,从而对曲面进行雕刻;然后利用脊曲线实现对曲面的周期控制变形。实验结果表明,该方法计算简单、易于控制,可以得到丰富的变形效果,适用于几何造型、计算机动画、CAD/CAM等领域。     

METABALL-BASED TRANSITION SURFACES

0 INTRODUCTIONTransition surface problems often arise in the design andmanufacture of airplane bodies, ship bodies and automobile bod-ies, as well as machine parts and sculpture parts. The surfaces areused to join two curves smoothly and to connect two ne…     

C形板预应力组合框架的预紧梁形状优化

针对某模锻液压机的1∶30模型,采用平面有限元分析模型将预紧梁与C形板接触的表面简化为一轮廓型线,进而将预紧梁表面形状优化问题简化为轮廓型线优化问题。分别以三次样条曲线、圆弧曲线和B样条曲线为目标曲线,应用序列二次规划法并借助于有限元分析软件对曲线的参数进行了优化。根据优化结果制作了不同表面形状的预紧梁,将其应用于该模锻液压机1∶30预应力组合框架实验装置并对预紧工况下的应力状态进行了测试。与测试结果比较,模拟结果的平均差值为9.87MPa,相对偏差的平均值为18.1%。测试结果与模拟分析结果均表明,以优化轮廓型线制作的曲面预紧梁,可不同程度地改善采用平面预紧梁时C形板与预紧梁接触区域的局部高应力现象。     

冲压成形中凹模入口角曲线优化

冲压成形时,凹模入口角的形状对模具与工件之间的摩擦、冲压件表面质量以及模具使用寿命均有着重要的影响。为能获得最优的凹模入口角,提出了采用三次样条曲线作为凹模入口角曲线的新工艺方法。以板料与凹模入口角处的摩擦力做功为研究对象,基于响应面和试验设计方法,在满足成形质量前提下,优化凹模入口角曲线。结果表明:采用优化后的三次样条曲线进行凹模入口角设计,可以减小凹模入口角处的摩擦力做功,且摩擦力做功分布较均匀;可延长模具使用寿命,并可以提高工件表面质量。     

改进的NURBS曲面片拼接算法

研究了已网格化的曲面片之间的拼接技术并对现有的拼接算法进行了改进。首先,根据哈特利-贾德的弦长参数化算法求取非均匀有理B样条（NURBS）曲线上的节点向量,利用节点向量和曲线反求出控制顶点,并采用投影变换的方法求出权因子。其次,根据要求调整曲面片上的控制顶点,使曲面片之间达到G1连续。最后,再对已拼接好的曲面片上的控制顶点进行整体修改,重新排列整张曲面片上的控制顶点,从而实现曲面片的无缝拼接。用专业的三维造型软件对拼接后合并的曲面片进行了测试,结果表明,该方法在保证曲面片之间G1连续的情况下可使多块曲面片实现无缝拼接,无缝拼接试验中的平均误差为0.0049°。     

Adaptive tool-path generation on point-sampled surfaces

In this paper, we present a new approach to generate tool paths for machining point sampled surfaces using a direct projection algorithm, which is based on generating tool paths along planar intersection curves. In our implementation, a guide surface, with simple geometry like planes or cylinder surfaces, is first created according to the bound volume of the point cloud and initial tool paths are planned on it in terms of the motion pattern of the cutters. For each point of the initial tool paths, then, the corresponding cutter contact point (CC) of the point set surface is located by projecting the point onto the point cloud using the direct projection algorithm. In order to obtain adaptive cutter location points (CL), a least squares-based curve fitting method is applied to approximate the CC points using piecewise cubic Bezier, and a numerical method derived to estimate the length of the curve is used to adjust the position of the points along the curve, and make them evenly spaced on the curve with equal arc lengths. In addition, considering that offset curves or surfaces are necessary for locating CL points in many applications, such as machining using ball end milling cutter, torus ended milling cutters, an offset strategy for cubic Bezier curves is also studied. By testing the proposed method on several point clouds, it has been demonstrated to be promising.     

Smoothing Parametric Design of Addendum Surfaces for Sheet Metal Forming

The manual design of addendum surfaces on common CAD platforms is very tedious which requires many trialscorrections, which will certainly a ect the construction e ciency and quality of addendum surfaces, and then a ect the formability and quality of the workpiece in the process of sheet forming. In this paper, an automatic procedure based on parametric design method is proposed for the rapid construction of the addendum surfaces. The kernel of the parametric method is constructing boundary curves based on the shape of surfaces of workpiece and designing guide curves based on Hermite curve interpolation. By some simple parameters, the shape of the addendum surfaces could be controlled and adjusted easily. In addition, a minimum energy optimization method is employed to further optimize the constructed addendum surface. A finite element analysis for the sheet forming process is performed to evaluate the forming quality of constructed addendum surfaces. The instance illustrates that the addendum surface constructed by the proposed method could ensure both the overall smoothing of surfaces and the final forming quality, and it has a good e ect on springback after forming. This research proposes a smoothing parametric design method for addendum surfaces construction which could construct and optimize addendum surfaces rapidly.