基于边界匹配的多张裁剪曲面的三角化算法研究

本文提出一种多张裁剪曲面的三角剖分算法。该算法在进行多张裁剪曲面的三角化时,首先采用匹配的方法离散各曲面的边界,确保离散后的各曲面边界在相交处重合。然后再对各曲面进行三角化,从而有效地防止了曲面相交处出现裂缝、孔洞和覆盖等现象。该算法已经成功应用于“超人ＣＡＤ／ＣＡＭ”曲面造型及加工系统,主要用于快速原型技术（ＲＰＴ） 的ＳＴＬ文件生成,算法表现稳定     

多裁剪自由曲面的修补缝合功能的实现

将初始的多个裁剪曲面粘合在一起,是从初始CAD模型转化生成为“不漏水”的网格化模型的子算法之一．首先叙述了初始多裁剪曲面的结构,然后阐述了该算法的数据结构,并给出了算法的具体实现．该算法可缝合多裁剪自由曲面,并对初始CAD模型中出现的裂缝、重叠等现象,以及不良的参数化边界曲线(如退化、折叠等现象)进行了相应的修补．程序测试表明,该算法稳定、快速．最后给出两个实例及相关数据．     

检索矩形结构化网格中裁剪单元的数值算法

裁剪等几何分析的首要任务就是检索出裁剪曲面中的裁剪单元,为此提出一种快速检索矩形结构化网格中裁剪单元的数值算法.首先将网格中每个单元的边界划分为12段区间;然后在剪裁曲线上选取适当的参数点,并将得到的离散曲线代替原剪裁曲线,对矩形结构化网格进行剪裁;根据离散剪裁曲线与单元边界交点位置的不同,将裁剪单元划分为156种不同的类型.该算法还可以根据不同情况来获取剪裁曲线上的点,当采用闭合逆时针矩形剪裁曲线对裁剪NURBS曲面参数网格进行剪裁时,该算法能够快速、有效地检索到裁剪单元,并得到剪裁曲线曲率变化大的点以及裁剪单元在物理空间中的像;悬臂梁的最优拓扑结构算例证明了该算法能够快速、有效地检索出任意矩形结构化网格中的裁剪单元.     

基于B-Rep实体模型的IGES转换为STL

提出一种将IGES文件格式转换成STL文件格式的算法.根据IGES文件内容重构几何实体信息及其拓扑关系;将几何实体的三维曲面贴合为二维平面,并将曲面上的轮廓边界转换到平面上,在二维空间中根据封闭轮廓边界裁剪曲面;根据曲面上保留的特征点及轮廓边界上的顶点信息对面进行符合STL模型一致性规则的三角剖分,生成合法的STL文件.该算法的核心是保证面与面接合处的三角化的正确性.最后介绍了该算法的转换实例.     

基于泊松方程的孔洞修补算法

传统网格生长法对孔洞数量庞大且孔洞类型复杂的三维网格模型修复效果不佳。针对该问题,将泊松方程应用于三角网格模型的孔洞修补。利用原始模型信息建立泊松方程,对输入模型曲面进行全局拟合,根据孔洞信息裁剪拟合得到的预测曲面并与原始孔洞模型缝合,通过孔洞边界区域法向量信息调整修补曲面的三角面片方向,达到特征增强的目的。实验结果表明,该算法对于结构复杂的多孔洞三维模型修补效果较好,对噪声鲁棒性强,在保留模型原始信息的同时能够准确还原孔洞区域特征。     

一种多张裁减曲面的快速三角化算法

针对多张裁减曲面的三角化问题,提出一种多张裁减曲面三角化边界的算法。该算法在进行多张裁减曲面的三角化时,采用点对应的方法离散曲面的公共边界,因而能有效地防止曲面相交处出现裂缝、孔洞和覆盖等现象,提高了多张裁减曲面三角化算法的正确性。同时采用了目前比较先进的基于局部优先的平面任意区域三角剖分算法,因而提高了三角化的效率。     

分片驱动的特征敏感曲面重建

为健壮处理包含尖锐特征或欠采样的数据点集,通过对基于边界推进曲面重建技术的扩展,提出一种分片驱动的、特征敏感的对无方向散乱数据点集进行曲面重建的算法.在一个光滑阈值的控制下,将曲面重建过程分成分片重建和特征缝合2个阶段.在分片重建中,从光滑的种子三角化区域开始进行边界推进三角化,并通过拓扑元素分类与特征检测对边界光顺和特征重定位,以进一步扩展该分片,重复该过程,得到对光滑区域三角化的一系列光滑分片;特征缝合阶段,在边界推进过程中将所有分离的分片或分片中的缝隙缝合在特征区域.这种两阶段的三角化策略可有效地处理含尖锐特征或不规则采样如不充分采样的点集,无需保证拓扑完整性的复杂数学测试,如协变分析和三角形相交检测等,基于局部光滑曲面的求交,可有效地恢复采样点集丢失的特征信息.实验结果表明,采用文中算法能健壮处理不规则采样点集,并生成特征敏感的高质量网格.     

组合曲面参数线五坐标加工刀具轨迹的计算

提出了组合曲面间拓扑关系的建立方法．通过对曲面相邻边界及相邻角点拓扑信息查询，完成刀具路径的合理组织；针对目前在给定加工精度时确定参数增量算法存在的不足，提出基于等参数线的走刀步长追踪法，并对曲率半径趋于无穷大的情况及直纹面加工的情况进行单独处理，保证了算法的稳定性和有效性．在此基础上，系统地阐述了组合曲面加工中刀触点、刀位点的计算以及刀具轨迹的合理化组织。     

基于FFT的三维CAD模型形状描述

针对三维CAD模型,以快速傅立叶变换为基础,建立了一种CAD模型几何形状描述方法.首先,在对模型几何面进行统一表示的基础上,根据模型边界表示中的面片邻接信息,采用完全图旅行商回路算法建立模型的面片序列,并由参考模型保证面片序列的一致性;然后,根据面片序列将模型几何信息转换为5个一维离散信号,并对信号进行采样和幅度缩放,通过快速傅立叶变换(Fast Fourier Transform,FFT)将信号转换到频域,以频域振幅作为三维CAD模型几何形状的描述.如果忽略面片序列引起的偏差,该方法描述模型几何形状的能力与FFT描述离散信号的能力类似.通过实例阐述了描述方法的直观可解释性.     

海量散乱点的曲面重建算法研究

基于海量散乱点的曲面重建在机械产品测量造型、计算机视觉、根据切片数据的医学图像重建等领域中有重要应用.给出了一种以物体表面上不附加任何几何和拓扑信息(包括测点法矢、曲面边界信息)的散乱点集为处理对象,自动生成物体表面的三角网格模型的算法.该算法首先根据测点的邻近测点估算曲面在该测点处的法矢,并采用优化的顺序对法矢方向进行调整以使各测点处的法矢都指向曲面外侧,最后用步进立方体算法输出三角网格模型.采用新的方法计算切平面,不但进一步提高了效率,而且改善了曲面边界及尖锐棱边区域的重建效果.还提出并解决了法矢方向传播中可能出现的局部“孤岛”问题.同时,提出了一种对海量数据进行空间划分的算法,从而大大提高了海量数据的处理效率.应用实例表明,算法效果良好     

Sculptured Surfaces in Solid Models: Issues and Alternative Approaches

The fields of surface modeling and solid modeling have been developing quite independently. Today users of each system find they must employ functionality traditionally present only in the other system. This article focuses on issues related to the incorporation of sculptured surface functionality into solid modeling systems. Mathematical concepts related to sculptured surface modeling are reviewed and approaches to the representation of intersection curves and trimmed surfaces are discussed. Difficulties arise from the high polynomial degree resulting from many free-form surface operations. Some methods are described that keep the surface degree low, while retaining many of the advantages of sculptured surfaces. Compromises may be required when integrating this technology into boundary representation (B-rep) and constructive solid geometry (CSG) solid modelers.     

Partitioning Trimmed Spline Surfaces into NonSelf-Occluding Regions for Visibility Computation

Computing the visible portions of curved surfaces from a given viewpoint is of great interest in many applications. It is closely related to the hidden surface removal problem in computer graphics, and machining applications in manufacturing. Most of the early work has focused on discrete methods based on polygonization or ray-tracing and hidden curve removal. In this paper we present an algorithm for decomposing a given surface into regions so that each region is either completely visible or hidden from a given viewpoint. Initially, it decomposes the domain of each surface based on silhouettes and boundary curves. To compute the exact visibility, we introduce a notion of visibility curves obtained by projection of silhouette and boundary curves and decomposition of the surface into nonoverlapping regions. These curves are computed using marching methods and we present techniques to compute all the components. The nonoverlapping and visible portions of the surface are represented as trimmed surfaces and we present a representation based on polygon trapezoidation algorithms. The algorithms presented use some recently developed algorithms from computational geometry like triangulation of simple polygons and point location. Given the nonoverlapping regions, we use an existing randomized algorithm for visibility computation. We also present results from a preliminary implementation of our algorithm.     

裁剪后二次曲面的光线跟踪

提出了一个对裁剪后二次曲面进行光线跟踪的新方法。在该方法中引进了一个易于由世界坐标求参数的辅助参数空间，通过预处理，事先将原参数域下的边界变换到新的参数空间。这样，光线与曲面的求交仍可按二次曲面的几何参数进行，求出交点后，再将交点变换到辅助参数空间，在新的参数域中判断交点是否在裁剪过的曲面上。     

Feature-based decomposition of trimmed surface

A trimmed surface is usually represented by a parametric surface and a set of trimming curves. Because of the complexity in manipulating trimmed surfaces, many CAD processes and algorithms cannot be applied to trimmed surfaces directly. It is thus desirable to represent a trimmed surface by a group of regular surfaces. In this paper, an algorithm for decomposing a trimmed surface is presented. First, bisectors of the Voronoï diagram developed in the parametric space are used to define an isolated region for every trimming curve. Feature points on the trimming curves are extracted by considering curvatures of the curves. Correspondence between feature points and vertices on the bisectors are established by considering the similarity between the trimming curves and the bisectors. Regions of parametric patches are then identified. Finally, a group of regular surfaces are constructed by interpolating a set of sampled surface points on each of the identified regions.     

CAD-based sampling for CMM inspection of models with sculptured features

This paper addresses sampling models for trimmed sculptured surfaces, and multiple patches with boundary conditions. A CAD-based sampling system is developed and implemented in this work. The sculptured features are sampled along their isoparametric curves. These curves are then used to re-construct the model geometry using the skinning of cross section curves. We refer to the re-constructed model as the substitute geometry. The problem is to determine the sample curve locations such that the substitute geometry satisfies certain geometric conditions. These are, the form error, and the continuity of the substitute geometry across the boundaries of adjacent surfaces. Three criteria are integrated to determine the sample locations: the surface curvature change, the substitute geometry deviation from the CAD model, and the significance of trimmed portions of the surface. A boundary representation-based methodology for the sampling of trimmed surfaces is developed and implemented. This methodology is extended to handle n-sided surfaces obtained through filling n-sided regions with quadrilateral surface patches, and models that may include multiple surface patches. Furthermore, a tool to assess the sampling plans based on the continuity of the substitute geometry across boundaries of adjacent surface patches is developed. The developed algorithms, their implementations, and case studies are presented in this paper.     

一种裁剪参数曲面的有限元网格剖分方法

在板料冲压成形模拟分析中,从CAD系统输入的模具的曲面模型包含大量的裁剪参数曲面,曲面之间的相邻关系复杂,针对这种曲面模型的特点,提出了一种裁剪参数曲面的有限元网格剖分方法,单个裁剪参数曲面采用非约束边界的等参数映射法,各个裁剪参数曲面各自独立地网格剖分产生了网格单元后,再将各个裁剪参数曲面的网格单元合并为单元相容,即单元间无裂缝和覆盖的网格模型,这种方法适合于需要大量裁剪参数曲面拼合的复杂曲面模型,如汽车覆盖件模型的网格剖分。     

隐式裁剪曲面的造型及绘制

隐式曲面没有参数域的概念,故对其裁剪问题的研究,很少有人问津.提出了一种隐式裁剪曲面的造型和绘制方法:先把投影平面变换到xy平面,将该xy平面作正交化网格剖分,由参数表示或隐式表示的裁剪曲线在该xy平面定义裁剪区域,再把裁剪后留下的区域内的网格投影到隐式曲面上,从而实现了隐式裁剪曲面的多边形化绘制.     

Efficient and accurate B-rep generation of low degree sculptured solids using exact arithmetic: II—computation

We present efficient algorithms for exact boundary computation on low degree sculptured CSG solids using exact arithmetic. These include algorithms for computing the intersection curves of low-degree trimmed parametric surfaces, decomposing them into multiple components for efficient point location queries inside the trimmed regions, and computing the boundary of the resulting solid using topological information and component classification tests. We also employ a number of previously developed algorithms such as algebraic curve classification and multivariate Sturm sequences. We present some results from a preliminary implementation of our approach. This paper follows a previous paper which described the representations used in our approach.     

Isogeometric segmentation: Construction of auxiliary curves

In the context of segmenting a boundary represented solid into topological hexahedra suitable for isogeometric analysis, it is often necessary to split an existing face by constructing auxiliary curves. We consider solids represented as a collection of trimmed spline surfaces, and design a curve which can split the domain of a trimmed surface into two pieces satisfying the following criteria: the curve must not intersect the boundary of the original domain, it must not intersect itself, the two resulting pieces should have good shape, and the endpoints and the tangents of the curve at the endpoints must be equal to specified values.     

有理多结点样条插值曲线及曲面

鉴于多结点样条曲线（MSIC）是一种点点通过的插值样条曲线,因此在多结点样条插值曲线研究的基础上,给出了有理多结点条插值曲线和有理多结点样条插值曲面的定义,并讨论了有理多结点样条的性质,对有理多结 样条曲线和有理多结点样条曲面的光滑拼接问题进行了讨论,此外,还对有理多结点样条在计算机辅助几何设计中的若干应用问题进行了说明。