多边形网格的非流形封闭三角形网格正则化

为了提高基于网格模型的算法与应用的效率和稳定性,提出一种将任意多边形网格模型转化为正则三角网格模型的算法.首先对输入多边形网格模型中非三角形的面片进行三角剖分,然后查找并移除模型中的重合或重叠元素,再通过模型内部三角形求交对模型进行边和面的分割,从而修正模型的拓扑结构;在求交的过程中,根据边和三角形的位置关系对共面求交进行细致的分类处理,减少了求交次数,提高了算法的稳定性;最后循环搜索在网格模型中可以确定法向的种子三角形,通过拓扑结构调整与之相邻的三角形的法向,最终构成一个或多个法向确定的闭合曲面.实验结果表明,该算法能够将多边形网格转化为正则三角形网格模型.     

Point-Based Rendering of Non-Manifold Surfaces

We are concerned with producing high‐quality images of parametric and implicit surfaces, in particular those with non‐manifold features. We present a point‐based technique for rendering implicit surfaces that uses octree spatial subdivision with a natural interval exclusion test that guarantees that no parts of the surface are missed. This allows us to render non‐manifold implicit surfaces at speeds comparable to parametric surfaces. We also derive criteria that guarantee complete pixel coverage of the surface. The point‐based method allows for hidden surface elimination using a z‐buffer, and shadow casting using a shadow buffer. We illustrate the technique with a number of surfaces, and discuss its advantages and disadvantages.     

PIGMOD: parametric and interactive geometric modeller for mechanical design

The paper describes the implementation of a geometric modelling system named PIGMOD with a parametric design capability based on non-manifold geometric modelling. The basic idea is that a set of modelling operations can be so defined that there are correspondences between the geometric constraints and the modelling operations. The geometric relations are represented internally in terms of the modelling operation sequence. The modelling operations are implemented as manipulations on a non-manifold geometric model. The methods for modifying the geometric model automatically and consistently in accordance with changed or added dimensions are implemented in a simple and unified way.     

基于特征建模技术的CAD/CAE集成方法研究

采用基于特征的非流型建模技术提出了实现CAD／CAE集成系统的的新方法，方法通过建立和使用包括CAD和CAE系统中需要的全部不同类型几何模型的单一主模型，并通过选择操作实现了从主模型中同步快速提取适用于CAD的实体模型和适用于CAE的非流型模型。本方法还通过基于特征的多分辨率和多抽象建模技术实现了不同细节层的CAD模型和不同抽象层的CAE模型建立：     

基于e1范数最小化的非流形曲线族重构

从散乱点集重构曲线族在计算机视觉、逆向工程和医学图像处理等方面有着广泛的应用,非流形曲线族重构是其中的难点问题.文中在压缩传感理论基础上,提出一种基于e1范数最小化的非流形曲线族重构方法.该方法首先将散乱点集的法矢和位置信号表示为稀疏形式,通过e1范数优化方法,重建法矢信号和位置信号;之后,根据重建的法矢和位置计算点集的双边权,在此基础上构建最小生成树(Minimum Spanning Tree,MST)来重构曲线族;最后通过后处理过程,完成对重构曲线族的开闭处理.实验表明,该算法能处理包含开、闭曲线,流形、非流形曲线,以及具有尖锐特征的曲线等复杂情况的曲线族,并且对噪声较鲁棒.     

基于非流形几何与特征树的异质材料实体可视化方法

提出一种异质材料实体可视化的方法．采用边界曲面细分技术减小材料分布的突变视觉效应;在不损失渲染质量的前提下,采用自适应曲面细分和冗余曲面滤除方法解决异质实体可视化效率差、难以实时显示的问题．给出了详细的异质实体边界网格生成算法,以显示异质实体的外部几何信息及其内部材料组分的三维分布．该算法采用基于特征树的曲面网格自适应细分策略,通过对异质实体特征树的拓扑结构分析来判定待渲染曲面的材料分布特性,仅对确实需要细分的曲面进行额外的网格细分,有效地减小了实体渲染中所需的计算量;利用非流形异质实体的表征方法,采用冗余曲面滤除方法直接滤除非相关的边界曲面,以满足实时可视化的要求．该方法已用于异质实体建模软件CAD4D中,实验结果表明,其可有效地实现异质实体的实时可视化显示．     

有限元网格自动生成的典型方法与研究前瞻

回顾了有限元网格自动生成的典型方法,分析了这些方法的优缺点,结合当前的研究现状,指出了今后一段时期内,有限元网格自动生成研究的重点和方向.     

基于顶点聚类简化外存模型的保流形算法

基于顶点聚类算法的简化方法产生的非流形部分可以分为三类：三角形片段,固有非流形边和固有非流形点,它们都可以经过简单的操作而转化为流形．在此基础上提出一种基于顶点聚类的可以保证简化结果是流形的外存模型简化算法,该算法不要求输入模型是流形,并且保持了顶点聚类算法的高效性和易实现性．     

Constructive non-regularized geometry

Solid modelling is concerned with the construction and manipulation of unambiguous computer representations of solid objects. These representations permit us to distinguish the interior, the boundary and the complement of a solid. They are conveniently specified in Constructive Solid Geometry (CSG) by a construction tree that has solid primitives as leaves and rigid body motions or regularized Boolean operations as internal nodes. Algoriths for classifying sets with respect to CSG trees and for evaluating the boundaries of the corresponding solids are known, at least for simple geometric domains. Emerging CAD applications require that we extend the domain of solid modellers to support more general and more structured geometric objects. The focus is on dimensionally non-homogeneous, non-closed pointsets with internal structures. These entities are well suited for dealing with mixed-dimensional (‘non-manifold’) objects in ⁿ that have dangling or missing boundary elements, and that may be composed of several regions. A boundary representation for such objects has been described elsewhere. We propose to specify and represent inhomogeneous objects in terms of Constructive Non-Regularized Geometry (CNRG) trees that extend the domain of CSG by supporting non-regularized primitive shapes as leaves, and by providing more general set-theoretic and topological operators at interior nodes. Filtering operations are also provided that construct CNRG objects from aggregates of selected regions of other CNRG objects. A syntax and semantics of the operators in CNRG are presented, and some basic algorithms for classifying pointsets with respect to the regions of objects represented by CNRG trees are outlined.