结点插值新算法

结点插值算法广泛应用开发系统样条曲线、曲面的生成表示和求交分类。本文给出的结点插值新算法不仅可以统一表示已知的Boehm算法和Oslo算法,而且算法效率上优于它们。本算法已用于三维几何造型系统GEMS中。     

实体造型的理论基础的综述

本文阐述并总结了实体造型的一些理论和关键算法,如正则集理论,基于推广的欧拉公式的表示模型,集合成员分类。然后在扼要地介绍了实体造型的现状之后,提出了几个值得注意的研究方向。     

实体造型中集合运算研究

集合运算是实体造型的重要支持手段。本文着重对集合运算效率问题进行了分析。为了使求交运算的计算量更接近交线的数目,对交线的情况进行了研究,提出了一个有效的求交次序和一个将集合运算化为局部操作的控制方案,由此形成了一个新的实现集合运算的方法。本文估计了该方法解决问题时的计算量,并给出了证明。     

三维复杂地质体的布尔运算算法研究与实现

提出一种稳定快速的三维复杂地质体的布尔运算算法。该算法不需要跟踪交线,利用带拓扑信息的交边对实体区域进行分类,避免面在体内的判断,提高运算速度。算法在进行布尔运算前解决了数值计算误差引起的相关分类间的冲突,保证运算的稳定性。将该方法应用于蓝光矿山数字化平台系统,实践结果证明其适合数据分散、数据密集及带孔洞的实体,特别是大规模、奇异的三维复杂地质体。     

三维几何造型系统—GEMS

GEMS是在32位微型计算机图形系统或CAD工作站上运行的、用长方体、圆柱、圆锥、球、环、平移体、回转体、部件等十余种体素,经几何变换和集合运算,构造成实际的比较复杂物体的三维实体造型系统。它具有分层模块结构、全交互的用户接口、形象直观的输入方式、数据表格驱动的屏幕菜单、形体的层次网状定义和调用、基于结构的实体几何(CSG)和边界表示(BReps)的存储结构、正则集合运算、与PHIGS图形标准一致的输出流水线、多种实用的变换、成角剖切、体内巡视动进、贴面处理、便于移植等特点。它可直接应用于空间布置、建筑方案设计、机械零部件的CAD/CAM、结构分析等领域,也为进一步开发模拟仿真、计算机视觉、机器人等实用系统打下了良好的基础。     

基于几何造型的有限元网络自适应生成

介绍一个基于几何造型系统的有限元分析的前处理系统。该系统可对几何造型的二维任意形体进行快速可靠的Ｄｅｌａｕｎａｙ三角剖分，提出网络自动生成的网络密度的控制和基于误差估计的自适应有限元网格生成算法，并给出了应用实例。     

基于几何造型的有限元网格的自适应生成

介绍一个基于几何造型系统的有限元分析的前处理系统。该系统可对几何造型的二维任意形体进行快速可靠的Ｄｅｌａｕｎａｙ三角剖分，提出网格自动生成的网格密度的控制和基于误差估计的自适应有限元网格生成算法，并给出了应用实例。     

论两条直线段的求交

本文给出一种用计算机求两和直线段交点的算法，较之常用算法，本算法针对计算机的计算误差和几何元素在计算机内的表示误差，构造交点模糊判断树，使求两条直线段交点的正确性和可靠性有较大改进，并用于几何造型系统ＧＥＭＳ４．０，取得了较好的效果。     

BOOL—一个基于微机的实体造型系统

BOOL系统是一个在IBM-PC/AT微型计算机上实现的实体造型软件。它采用边界表示法(B-Reps)作为实体模型的内部表示,实体模型的构造用构造性实体几何(CSG-Constrtive Solid Geometry)法和扫动(Sweeping)法来完成。实体模型的布尔运算算法采用了专门设计的局部化技术,降低了系统的运算开销。     

建立在数据库上的实体造型,曲面造型系统—HYBRID

HYBRID是一个建立在数据库上的实体造型及曲面造型系统,该系统是在北京航天航空大学的PANDA实体造型系统的基础上开发的。HYBRID以集合运算(交、并、差)为工具,由简单物体——基本体素及二维图形,形成复杂物体。系统采用了CSG、B-rep数据结构充分地表示了体的几何信息及拓扑信息。数据库的使用使系统存储量增大,管理统一、方便,图形及非图形信息容易统一处理。曲面造型采用了非均匀有理B样条曲面插值,通过路径、截面的定义形成曲面。HYBRID适用于作为机械、建筑计算机辅助设计的支撑工具及管道的曲面设计。     

A topologically robust algorithm for Boolean operations on polyhedral shapes using approximate arithmetic

We present a topologically robust algorithm for Boolean operations on polyhedral boundary models. The algorithm can be proved always to generate a result with valid connectivity if the input shape representations have valid connectivity, irrespective of the type of arithmetic used or the extent of numerical errors in the computations or input data. The main part of the algorithm is based on a series of interdependent operations. The relationship between these operations ensures a consistency in the intermediate results that guarantees correct connectivity in the final result. Either a triangle mesh or polygon mesh can be used. Although the basic algorithm may generate geometric artifacts, principally gaps and slivers, a data smoothing post-process can be applied to the result to remove such artifacts, thereby making the combined process a practical and reliable way of performing Boolean operations.     

非流形几何造型的布尔运算

非流形的几何造型用统一的结构来表示线框、表面和实体,是目前几何造型系统研究的热点。而模型的构造需要一个有效的布尔算法。论文提出一种由布尔运算定义的能够快速和任意重塑几何模型的新方法。这种方法利用非流形几何造型的性能,使得人们可以反复进行交互设计,并可用于特征造型。     

Fast, Exact, Linear Booleans

We present a new system for robustly performing Boolean operations on linear, 3D polyhedra. Our system is exact, meaning that all internal numeric predicates are exactly decided in the sense of exact geometric computation. Our BSP-tree based system is 16-28× faster at performing iterative computations than CGAL's Nef Polyhedra based system, the current best practice in robust Boolean operations, while being only twice as slow as the non-robust modeler Maya. Meanwhile, we achieve a much smaller substrate of geometric subroutines than previous work, comprised of only 4 predicates, a convex polygon constructor, and a convex polygon splitting routine. The use of a BSP-tree based Boolean algorithm atop this substrate allows us to explicitly handle all geometric degeneracies without treating a large number of cases.     

一种基于特征几何元素永久命名的快速相交特征检查与判别方法及其应用

相交特征的检查与判别是特征造型领域的一个重要问题,通常的方法是通过在特征体间作布尔运算进行相交特征的检查与判别,但这种方法存在复杂、耗时的缺点,为避免大量的求交运算,提高相交特征检查与判别的效率,文中提出了一种新的相交特征的检查与判别方法,该方法以一系列的面标号查找代替了特征之间的求交运算,从而有效地提高了相交特征的检查速度。     

Robust Computation of Intersection Graph between Two Solids

We propose a new robust algorithm for Boolean operations on solid models. The algorithm produces a consistent intersection graph between two input solids whose geometrical data are represented in floating point numbers. In order to prevent numerical calculation errors and inaccuracy of input data from causing inconsistency of the output, we put higher priority on symbolical connectivity of the edge-face intersection points than their numerical nearness. Each edge-face intersection point is symbolically represented using face names, which generate connectivity relations between the intersection points and the intersection line segments. The symbols with the same connectivity are made into clusters. The intersection line segments connected together at their end clusters form the intersection graph of two solids. Inconsistency of the connectivity of the clusters is detected and the intersection graph is corrected automatically. We describe the algorithm in detail for polyhedral solids, discuss extension to curves solids, and show its effectiveness by some examples of Boolean operations for two solids whose faces intersect at a very small angle.     

Boolean set operations on non-manifold boundary representation objects

For Boolean operations on geometric models, we have developed an intersection algorithm for non-manifold boundary models with vertices, linear edges, planar faces, and volumetric regions. The algorithm operates by intersecting entities in an ordered manner, from vertex to edge, then to face elements. Singular intersections are systematically handled by determining if an entity in one object is within a tolerance region of the entity in the other object. The algorithm performs Boolean operations between objects of different dimensionality as well as solids. An implementation of the proposed algorithm and the experimental results are briefly discussed.     

基于自适应延迟切割的三角网格布尔运算优化

规则化的布尔运算被广泛应用在三维建模系统中.近年来,随着图形硬件的发展,基于三角网格的规则化布尔算法由于输出结果能直接被图形硬件处理,表现出了明显的优势.但是传统的算法由于采用CSG树局部评估策略,使得面片在相交测试中反复被切割,并且由于面片分类在切割后的模型之间直接进行,导致算法无法在保证鲁棒性的同时实现高性能.为了避免这些问题,本文呈现了一种CSG树全局评估算法来统一执行单次和连续布尔运算.算法由两部分组成：自适应的延迟切割和全局化面片分类.在自适应的延迟切割阶段,算法通过仔细处理多个三角面片相交导致的各种情况使得延迟切割被扩展到整个CSG树来避免由于面片的反复切割带来的数值误差累积并利用自适应的八叉树使得相交测试能在线性时间内完成.在全局化面片分类阶段,算法通过分治法使得分类始终在切割后的面片和原始输入模型之间进行来保证分类的精度;通过结合组分类策略和自适应的八叉树来进一步优化了分类性能。实验结果表明,本文提出的算法无论是在执行单次或连续布尔运算时都能在保证鲁棒性同时性能优于其他的算法,因此本文算法可广泛应用于交互式建模系统中,如数字雕刻、计算机辅助设计和制造（CAD/CAM）等.     

基于几何关系的椭圆图形生成算法

在常规CAD图形生成算法中，往往只考虑图形的坐标方程(包括直角坐标方程、参数方程或极坐标方程)，却忽略了图形本身所具有的特点或一种图形与另一种图形之间的几何关系，而有时这种几何关系可以简化图形生成算法。本文提出了一种新的椭圆生成算法，利用椭圆与其外接圆和内切圆之间的相互位置关系，通过先生成两个圆来生成一个椭圆。在该算法的主循环中，只有加、减法和移位运算，以此替代了速度慢的乘、开方等运算，从而降低了计算量，并且减小了误差。     

Solid Modeling Based on a New Paradigm

The technique of solid modeling is essential in CAD/CAM applications, and is currently well established. However, problems remain, such as the lack of uniformity in geometric computations and the lack of stability of Boolean operations of two solids. In this paper, we introduce a theoretical solid modeling system that operates on boundary representations of polyhedral objects and is based on a new paradigm. The characteristics of the system are the following: (I) in Boolean Operations and modeling transformations, all geometric computations are performed by the 4 × 4 determinant method or the 4 × 4 matrix method in homogeneous space, which allows the system to avoid division operations, (2) all geometric computations are performed by the exact integer arithmetic, which makes the geometric algorithms stable and simple, and (3) primitive solids are constructed consistently in the integer domain, and the consistency is assured throughout Boolean operations and transformations.