基于外载荷的B样条曲面变形

针对B样条曲面变形过程中存在变形区域不能自由选择、变形距离不能精确计算和操作效率低等问题,运用能量优化的思想,提出一种B样条曲面变形的算法,用于B样条曲面的变形.给出B样条曲面按节点矢量划分成曲面片的方法,将曲面片类比为有限单元法中薄壁面单元,并将作用在B样条曲面片上的外载荷分解成曲面片四个端点力的双线性插值.分别建立B样条曲面内部能量方程和外载荷能量方程,外载荷的改变引起B样条曲面内部能量的变化,通过求解一个使B样条曲面内部能量变化量为最小的优化问题,得到变形后B样条曲面控制顶点的变化量.给出一种求解B样条曲面变形距离的计算方法,提高B样条曲面变形的精度和变形效率.最后的实例验证所提算法的有效性和实用性.     

基于力密度方法的NURBS曲线和曲面变形框架

提出基于力密度方法的统一求解策略,实现NURBS曲线和曲面的精确变形.将控制网格类比为空间索网结构,分别建立外载荷变化最小、外载荷最小、杆阻尼长度最小和节点位移最小等四种表达不同几何和物理意义的最小化模型来驱动变形,并以控制顶点在变形前后的位移为变量,建立统一表达的目标函数方程,便于多个最小化模型组合使用,满足特定的变形需要.由于目标函数的二次性以及约束的线性化处理,优化问题可以通过Lagrange乘子法转化为线性问题进行求解.在计算中引入目标函数快速求解算法,使变形设计可以满足实时交互操作的需要.应用实例表明,该算法可以应用于细节特征设计和反求建模等复杂曲面造型.     

基于刚架模型的多张B样条曲面变形

针对由多张B-spline曲面拼接构成的曲面形状修改问题,提出了一种多张B-spline曲面变形算法。通过将曲面片控制顶点网格进行“合并”来建立多张B-spline曲面的刚架模型;以刚架节点位移为未知量,建立节点载荷最小和节点位移最小的统一优化目标函数;将曲面片之间的光滑拼接条件抽象为节点相对位置约束,结合点约束、点和法矢约束共同组成约束方程组;采用罚函数法求解得到变形后曲面新的控制顶点。变形实例表明该算法是直观有效的。     

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°。     

基于三角剖分的曲面变形

介绍一种三维空间中基于散乱数据点三角剖分的自由变形技术。运用Voronoi图和Delaunay三角剖分,将待变形曲面上的点(作用点)用控制顶点线性表示出来,移动控制顶点使作用点发生位移,从而使曲面的形状发生局部的改变。这种方法改进了诸如自由变形(FFD)、直接自由变形(DFFD)和扩展自由变形(EFFD)等传统曲面变形技术在局部变形上的应用。     

NURBS及其自由变形

在分析 NURBS曲线、曲面与其参数域之间映射关系的基础上 ,建立了 NURBS实体和其参数域之间的映射关系 ,并进一步发现了基于 URBS的由变形与三参数 NU RBS实体之间的联系和自由变形的实质 ,即对三参数 NURBS实体的参数施了形状约束。将这一思想进一步推广到控制晶格顶点和权因子 ,则是我们下一步的工作     

小波技术在曲面变形中的应用

曲面光顺过程会导致曲面形状有很大改变。介绍一种光顺变形后曲面的一种新方法,这种算法根据小波分解的原理除去局部变形后曲面的高频部分,保留其低频部分,采用B-Spline小波捕捉小波分解过程中丢失的细节信息,光顺曲面,使得变形后的曲面能够很好地保持其原有的总体形态,并且满足一定的连续性要求。小波分解,曲面局部变形产生的棱或尖点得到有效的光顺处理。小波分解的计算快速、稳定,特别适合光顺由多控制顶点定义的曲面。     

基于仿射算术和区间运算的直线与NURBS曲线/曲面求交

针对直线与参数空间NURBS曲线、直线与NURBS曲面求交问题,提出了一种改进的基于仿射算术和区间运算的直线与NURBS曲线/曲面求交的有效方法。该方法将基于边曲率或面曲率的子域分解方法应用到求交算法中,快速定位预迭代区间,减少不必要的迭代求交判断。与传统区间迭代算法相比,该求交算法为超线性收敛的快速迭代算法,在一定程度上解决了传统区间运算的“保守性”。另外,该方法放宽了对初始区间的要求,减少迭代次数,提高了迭代算法效率。通过计算区间算子判断给定直线与NURBS曲线/曲面有无交点和存在交点时的交点数目,保证了求解交点精度,为解决直线与曲线/曲面多交点判断及内外环或内外域判断等问题提供了有利条件。数值算例验证了该方法的有效性、计算精度和效率。     

立式捏合机搅拌桨曲面的NURBS表示与误差分析

依据搅拌桨水平截面轮廓线的理论坐标点,反求生成了NURBS曲线;按照搅拌桨的螺旋升角,生成了一组不同高度截面轮廓线的NURBS曲线;利用蒙皮方法,生成了搅拌桨的NURBS曲面。提出了一种新的控制顶点投影法求解点到NURBS曲面最小距离的算法,用于计算搅拌桨的NURBS曲面的重构误差。结果表明,立式捏合机搅拌桨的NURBS曲面重构精度高,研究结果可为搅拌桨曲面优化设计提供借鉴。     

自由变形统一模型研究

提出一个自由变形统一模型。在B样条体变形空间的基础上,通过一个统一的底层结构,使自由曲线,自由曲面和三维网格三种控制变形手段有效地结合起来。所建系统能方便地实现三维网格控制变形、自由曲线控制变形和自由曲面控制变形。     

Rapid parametric design methods for shoe-last customization

With the development of computer-aided design (CAD) technology and increasing demands of customized footwear, shoe-lasts are requested to be designed rapidly so as to speed-up the process of footwear manufacturing. Thus, this study presents a CAD system for shoe-last rapid customized design based on the piecewise reconstruction to realize the interactive deformation and separate/global shoe-last form reuse. First, piecewise remodeling method is proposed based on the multi-layer parametric definition and contour curves are extracted from the mesh. Then, five types of proper constraints to support surface manipulation are proposed, and the draft-driven deformation by the contour curve bending can realize the interactive local surface design in free angle of view. Finally, shoe-last styles can be saved and reused globally or separately to share design results between different shoe-lasts. Experimental examples show that customized shoe-lasts can be easily and rapidly generated by adopting the parametric design methods.     

Adhesion of endothelial cells using self-assembly peptides under precise deformation control of tissue-engineered vessels

The objective of this study was to anchor endothelial cells using self-assembly peptides under precise deformation control of tissue-engineered vessels. An acelluarized vascular matrix was used as the control group to examine the function of self-assembly peptides. In the experiment group, the self-assembly peptides were added to the inner surface of tissue-engineered vessels to form a monolayer. Then the endothelial cells were injected into the vascular lumen. A deformation control system was developed which was based on real-time image analysis and feedback control system. After dynamic culture by different deformation (set points 1, 5, and 10 per cent), the endothelial cell densities of experimental and control groups were compared. Both the self-assembly peptides and the extent of deformation affected the endothelial cell density on the inner surface of tissue-engineered vessels. The construct with self-assembly peptides under 5 per cent deformation gained the highest endothelial cell density. It was concluded that the deformation of assembled peptides contributes to the development and adhesion of endothelial cells in the inner surface of tissue-engineered vessels.     

一种基于能量法的自由曲面展开算法

提出了一种基于能量法的自由曲面展开算法,适用于任意复杂自由曲面的展开.根据建立的曲面能量模型,采用映射法进行曲面的Delaunay三角网格划分,并计算空间网格三角形点的变形能,然后进行变形能的释放,得到自由曲面展开后的二维平面.能量法不拘于问题的形式,可以用来求解一般的问题,该算法具有一定的通用性,适用于CAD/CAM中的曲面展开问题.     

摆环减速器环板及内齿轮副承载能力有限元分析

结合具体实例介绍了综合利用Pro/E以及ANSYS软件参数化造型、有限元分析功能,分析摆环减速器环板及内齿轮副应力与变形情况的基本思想及相关步骤。分析结果证明,环板薄弱环节仍在轮齿部分。所介绍的方法和技巧可为该类减速器设计以及强度计算提供了有益参考。     

Finite element modeling of transverse impact on a ballistic fabric

A 3D finite element analysis model is created using LS-DYNA to simulate the transverse impact of a rigid right circular cylinder onto a square patch of plain-woven Kevlar fabric. The fabric is modeled to yarn level resolution and relative motion between yarns is allowed. A frictional contact is defined between yarns and between the fabric and the projectile. Three different boundary conditions are applied on the fabric: four edges left free; two opposite edges clamped; four edges clamped. Results from the modeling effort show that during initial stage of the impact, the projectile velocity drops very quickly. There exists an abrupt momentum transfer from the projectile to the local fabric at the impact zone. When the impact velocity is low, the fabric boundary condition plays an important role at later stages of the impact. It significantly affects the fabric deformation, stress distribution, energy absorption and failure modes. When the impact velocity is high enough to cause the yarns to break instantaneously, the fabric fails along the periphery of the impact zone and the fabric boundary condition does not take any effects.     

五轴NC车铣加工自由曲面的问题

阐述用平头铣刀五轴NC车铣法加工自由曲面微机辅助编程的问题。介绍用双三次参数曲线拟合曲面、平头铣刀的直径、铣削的步长及行距选择、刀位点和刀轴矢量的计算。给出车铣机床五轴联动坐标值及转角的计算公式。     

棱体成形车刀的三维参数化设计

通过分析棱体成形车刀与工件模型的几何关系 ,提出了利用三维建模将刀具廓形的复杂计算转变为直接通过截面获得的方法 ,根据数据判断程序建立工件廓形控制矩形和控制点 ,使成形车刀设计过程不再依赖于具体的工件廓形 ,可实现棱体成形车刀尺寸和形状的全面参数化设计和制造     

CONSTRUCTION OF G^2 CONTINUOUS CURVES ON SURFACE WITH PLANAR CUBIC BEZIER CURVES

The problem of constructing curve on parametric surface (or surface that can be parameterized) such that it interpolates a sequence of points with prescribed tangent direction and curvature vector (or geodesic curvature) at every point and the issue of curve blending on this kind of surface are researched. The mapping and tangent mapping from the surface to its parametric plane are introduced and thus several conclusions with differential geometry are deduced. Based on those conclusions, the problem of interpolating (or blending) curve on a parametric surface is converted to a similar one on its parametric plane. The final solution curve of either interpolation or blending issue is explicit and can still be expressed by parametric form. And so, unlike existing methods, the presented method needs not to use any surface/surface intersection algorithms, usually a troublesome process, for displaying such interpolation curve. Experiment results show the presented methods are feasible and applicable to CAD/CAM and computer graphics.