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。     

一种直线与隐式曲面求交的方法

绘制隐式曲面的光线跟踪算法,其本质问题就是直线与隐式曲面的求交,区间算术求根方法是计算直线与隐式曲面的一个很好方法。本文介绍了区间算术原理,研究了区间算术在直线与隐式曲面求交的应用,给出了相应的算法。应用区间算术,不仅可以求出直线与隐式曲面的最近交点,而且能求出所有交点。     

复合三角Bezier曲面/平面的过渡和裁剪

由初始交点出发,利用拓扑关系跟踪计算复合三角Bezier曲面与平面的交线,对一系列交点进行点对应修正,曲面片间边界点计算、交线两端交点的跟踪、截面线构造、截面线离散,构造出与基曲面达到G′连续、结构相似的过渡曲面,交点作为型值点值入复合曲面的型值点集中、对三角网格局域三角化,以交线为界分离,重新构造拓扑关系生成两张新的曲面,实现裁剪的目的,测试显示,上述方法简单可靠。     

BALL曲线曲面的离散求交

本文对飞机外形设计的CONSURF系统中曲线曲面的求交问题,提出了一种离散化算法。该方法计算简单,速度快,又避免了传统的选代法的一些缺点,因而是对CONSURF系统的扩充和发展。     

参数曲面与平面求交的一种新方法

本文提出了一种新的参数曲面与平面求交算法，基于平面的半空间性质，通过参数域平面的二向线性插值，将求交问题转化为一系列简单的离散、判断、比较、排序等运算，能较好的解决曲面片内的交线不连续和交线丢失问题，算法简便，可靠性好，计算精度高，在ＮＣ自动编程中具有广泛的应用场合。     

参数曲面线投影的求精计算

本文提出了一种新的参数曲面线投影求交计算方法，基于参数域摄动原理，将求交问题转化为一系列简单的参数摄动，映射，判断，比较等运算，能有效地解决参数曲面的线投影求交计算，大量的应用的实例表明这一算法的可靠性好，计算精度高，摄动速度快，已在复杂曲面测量造型和数控加工质量分析中取得了良好的应用效果。     

参数曲面点元离散求交法

提出了一种基于点元的参数曲面求交交互式新算法。该算法在参数曲面上进行自适应的离散点元采样,将点元组织为空间八叉树结构进行求交运算,最后进行交点排序并得到最终的求交结果。与以往的参数曲面求交方法相比,本算法更简单高效。实验结果表明,本算法稳定可靠,误差可控,而且可以达到交互速度。     

CAD/CAM中曲面求交技术的研究

提出了用几何特征量来描述二次曲面和相关的边界曲线的方法，并据此研究了求交算法，避免了代数法中频繁的坐标变换，减少了浮点运算误差出现的几率，简化了曲面求交算法，使曲面求交算法更加稳定可靠。     

曲率分析方法在曲面求交中的应用

在曲面求交的跟踪过程中，主要存在两个问题，即确定跟踪方向和计算跟踪步长。本文给出用曲率分析精确计算跟踪方向，并估计跟踪步长的方法。用曲率分析法能够处理相切这种奇异情况。本文最后给出三个实例验证。     

二次椭圆曲面平截线实形的新方法

本文重点研究二次椭圆曲面与平面相交，求交线实形的方法。该方法的关键在于给定的条件利用作辅助曲面耿定出交已知曲面所截得的新投影面投影成圆，以定出交线实形上的点。     

圆环与圆环求交算法中初始点的计算

曲面求交是CAD/CAM领域最为重要也最为复杂的问题之一。在众多的算法中,追踪法由于其易于实现、计算速度快而得到广泛应用,而追踪法最大的缺点在于很难确定每条交线的初始点。针对这个问题,笔者提出了一种专门用于解决圆环面与圆环面求交算法中初始点计算的方法。该算法以几何方法为基础,通过判断圆环中心圆之间的位置关系来判定相交区域,并运用数值分析方法精确计算出每条交线的初始点。     

Marching volume polytopes algorithm

This paper presents an algorithm for the refinement of two- or three-dimensional meshes with respect to an implicitly given domain, so that its surface is approximated by facets of the resulting polytopes. Using a Cartesian grid, the proposed algorithm may be used as a mesh generator. Initial meshes may consist of polytopes such as quadrilaterals and triangles, as well as hexahedrons, pyramids, and tetrahedrons. Given the ability to compute edge intersections with the surface of an implicitly given domain, the proposed marching volume polytopes algorithm uses predefined refinement patterns applied to individual polytopes depending on the intersection pattern of their edges. The refinement patterns take advantage of rotational symmetry. Since these patterns are applied independently to individual polytopes, the resulting mesh may encompass the so-called orientation problem, where two adjacent polytopes are rotated against one another. To allow for a repeated application of the marching volume polytopes algorithm, the proposed data structures and algorithms account for this ambiguity. A simple example illustrates the advantage of the repeated application of the proposed algorithm to approximate domains with sharp corners. Furthermore, finite element simulations for two challenging real-world problems, which require highly accurate approximations of the considered domains, demonstrate its applicability. For these simulations, a variant of the fictitious domain method is used.     

NURBS曲面(实体)扫描体的逼近算法

实现了一种NURBS曲面(实体)扫描而成的扫描体逼近方法。本方法主要通过:①用系列平面的切割,把NURBS曲面(实体)进行降维处理,变成系列平面曲线;②为曲线设置局部标架;③在局部标架下求出每一曲线在每一时刻的极值点而后转换成原曲线的奇异点;④使用fast marching cubes算法删去扫描体内部点,保留扫描体边界上的奇异点;⑤由保留的奇异点通过插值或逼近方式构建边界曲面。本算法能较好地逼近NURBS扫描体,其逼近精度可通过控制切割精度和扫描过程中时间间隔的选取而有效控制。     

Time marching integral equation method for unsteady transonic flows around airfoils

A time marching integral equation method has been proposed here which does not have the limitation of the time linearized integral equation method in that the latter method can not satisfactorily simulate the shock wave motions. Firstly, a model problem–one dimensional initial and boundary value wave problem is treated to clarify the basic idea of the new method. Then the method is implemented for two dimensional unsteady transonic flow problems. The introduction of the concept of a quasi-velocity-potential simplifies the time marching integral equations and the treatment of trailing vortex sheet condition. The numerical calculations show that the method is reasonable and reliable.     

A marching cubes based failure surface propagation concept for three‐dimensional finite elements with non‐planar embedded strong discontinuities of higher‐order kinematics

This paper presents an advanced failure surface propagation concept based on the marching cubes algorithm initially proposed in the field of computer graphics and applies it to the embedded finite element method. When modeling three‐dimensional (3D) solids at failure, the propagation of the failure surface representing a crack or shear band should not exhibit a strong sensitivity to the details of the finite element discretization. This results in the need for a propagation of the discrete failure zone through the individual finite elements, which is possible for finite elements with embedded strong discontinuities. Whereas for two‐dimensional calculations the failure zone propagation location is easily predicted by the maximal principal stress direction, more advanced strategies are needed to achieve a smooth failure surface in 3D simulations. An example for such method is the global tracking algorithm, which predicts the crack path by a scalar level set function computed on the basis of the solution of a simplified heat conduction like problem. Its prediction may though lead to various scenarios on how the failure surface may propagate through the individual finite elements. In particular, for a hexahedral eight‐node finite element, 256 such cases exist. To capture all those possibilities, the marching cubes algorithm is combined with the global tracking algorithm and the finite elements with embedded strong discontinuities in this work. In addition, because many of the possible cases result in non‐planar failure surfaces within a single finite element and because the local quantities used to describe the kinematics of the embedded strong discontinuities are physically meaningful in a strict sense only for planar failure surfaces, a remedy for such scenarios is proposed. Various 3D failure propagation simulations outline the performance of the proposed concept. Copyright © 2013 John Wiley & Sons, Ltd.     

Automatic merging of tetrahedral meshes

A generic algorithm is proposed to merge arbitrary solid tetrahedral meshes automatically into one single valid finite element mesh. The intersection segments in the form of distinct nonoverlapping loops between the boundary surfaces of the given solid objects are determined by the robust neighbor tracing technique. Each intersected triangle on the boundary surface will be triangulated to incorporate the intersection segments onto the boundary surface of the objects. The tetrahedra on the boundary surface associated with the intersected triangular facets are each divided into as many tetrahedra as the number of subtriangles on the triangulated facet. There is a natural partition of the boundary surfaces of the solid objects by the intersection loops into a number of zones. Volumes of intersection can now be identified by collected bounding surfaces from the surface patches of the partition. Whereas mesh compatibility has already been established on the boundary of the solid objects, mesh compatibility has yet to be restored on the bounding surfaces of the regions of intersection. Tetrahedra intersected by the cut surfaces are removed, and new tetrahedra can be generated to fill the volumes bounded by the cut surfaces and the portion of cavity boundary connected to the cut surfaces to restore mesh compatibility at the cut surfaces. Upon restoring compatibility on the bounding surfaces of the regions of intersection, the objects are ready to be merged together as all regions of intersection can be detached freely from the objects. All operations, besides the determination of intersections structurally in the form of loops, are virtually topological, and no parameter and tolerance is needed in the entire merging process. Examples are presented to show the steps and the details of the mesh merging procedure. Copyright © 2012 John Wiley & Sons, Ltd.     

A higher‐order potential flow method for thick bodies,thin surfaces and wakes

A higher‐order panel method for analysing the three‐dimensional potential flow fields around bodies and wakes is presented. The geometric surfaces are represented by continuous curved patches, with no discretization into panels. These geometric patches hold singularity distributions that have C2 continuity, and which are solved by applying Dirichlet or Neumann boundary conditions at discrete collocation points. While higher‐order methods have previously been developed for thick bodies and Dirichlet boundary conditions, this potential flow method is capable of modelling continuous geometry and singularity surfaces over thin bodies and wakes. The continuous surface method has a number of advantages over conventional constant panel methods. Firstly, as curved geometries are represented exactly, changing the order of the solution does not modify the physical shape of the configuration under investigation. Furthermore, the continuous singularity distributions allow velocities to be evaluated accurately across the entire surface rather than just at collocation points. This means that pressure distributions can be calculated exactly without interpolation, and streamlines can be constructed very close to surfaces without problems of divergence. Finally, body and wake surfaces do not exhibit the strong modelling singularities that can present difficulties with wake relaxation. Copyright © 2007 John Wiley & Sons, Ltd.     

构造两个曲面的拼接曲面

给出了当两个待拼接曲面的拼接线具有参数化形式或者可以参数化时,它们之间 G1光滑拼接曲面的构造方法。所得的拼接曲面是由一个空间曲线集定义的,每一条空间曲线由拼接线上的点对确定。并且拼接曲面都是参数曲面,它们的形状可以通过预设的参数很好地调整和控制。作为实例,讨论了两个截口是平面的或非平面的(由两个二次曲面定义)的二次曲面之间的拼接曲面的构造和一般的参数曲面的拼接曲面的构造。