三维纺织结构增强复合材料的几何模型

基于对织物断面显微照片的观察和分析，首先建立了三维正交织物的单元结构模型，并以此为基础建立了正交接结织物的单元结构模型；利用几何模型公式推导建立几何结构特征参数与编织工艺参数之间的理论关系；在此基础上计算了纱线长度、接结经与经纱的取向角和纤维体积含量；通过几何极限条件定义了织物紧度，为进一步研究其力学性能奠定基础。     

Pictures worth a thousand tiles,a geometrical programming language for self-assembly

We present a novel way to design self-assembling systems using a notion of signal (or ray) akin to what is used in analyzing the behaviour of cellular automata. This allows purely geometrical constructions, with a smaller specification and easier analysis. We show how to design a system of signals for a given set of shapes, and how to transform these signals into a set of tiles which self-assemble into the desired shapes.     

Variable wall thickness scroll geometry modeling with use of a control volume approach

In a scroll-type compressor, compression is achieved through relative contact between two spiral curves. Since the scroll invention by Leon Creux (1905), multiple methods have been developed for calculating scroll geometry. What can generally be considered the most classical method, is defining each scroll curve as the involute of a circle. Gravesen and Henriksen (2001) introduced a new method to calculate scroll geometry by deriving each scroll curve from the radius of curvature parameterized with involute angle. This allows a wide range of involute geometries to be considered not included in the classical method. In this paper, Gravesen's method is extended to the tip region to include all tip geometries involved in a two arc configuration resulting in a more comprehensive scroll geometry definition. Lastly, with parametric representation of all scroll geometry, the pocket volume can be easily solved using a derived control volume approach.     

Electrostatic Halftoning

We introduce a new global approach for image dithering, stippling, screening and sampling. It is inspired by the physical principles of electrostatics. Repelling forces between equally charged particles create a homogeneous distribution in flat areas, while attracting forces from the image brightness values ensure a high approximation quality. Our model is transparent and uses only two intuitive parameters: One steers the granularity of our halftoning approach, and the other its regularity. We evaluate two versions of our algorithm: A discrete version for dithering that ties points to grid positions, as well as a continuous one which does not have this restriction, and can thus be used for stippling or sampling density functions. Our methods create very few visual artefacts, reveal favourable blue‐noise behaviour in the frequency domain, and have a lower approximation error under Gaussian convolution than state‐of‐the‐art methods.     

Collision Detection for Deformable Objects

Interactive environments for dynamically deforming objects play an important role in surgery simulation and entertainment technology. These environments require fast deformable models and very efficient collision handling techniques. While collision detection for rigid bodies is well investigated, collision detection for deformable objects introduces additional challenging problems. This paper focuses on these aspects and summarizes recent research in the area of deformable collision detection. Various approaches based on bounding volume hierarchies, distance fields and spatial partitioning are discussed. In addition, image‐space techniques and stochastic methods are considered. Applications in cloth modeling and surgical simulation are presented.     

Approximation of a Variable Density Cloud of Points by Shrinking a Discrete Membrane

This paper describes a method to obtain a closed surface that approximates a general 3D data point set with nonuniform density. Aside from the positions of the initial data points, no other information is used. Particularly, neither the topological relations between the points nor the normal to the surface at the data points are needed. The reconstructed surface does not exactly interpolate the initial data points, but approximates them with a bounded maximum distance. The method allows one to reconstruct closed surfaces with arbitrary genus and closed surfaces with disconnected shells.     

Translational Covering of Closed Planar Cubic B-Spline Curves

Spline curves are useful in a variety of geometric modeling and graphics applications and covering problems abound in practical settings. This work defines a class of covering decision problems for shapes bounded by spline curves. As a first step in addressing these problems, this paper treats translational spline covering for planar, uniform, cubic B‐splines. Inner and outer polygonal approximations to the spline regions are generated using enclosures that are inside two different types of piecewise‐linear envelopes. Our recent polygonal covering technique is then applied to seek translations of the covering shapes that allow them to fully cover the target shape. A feasible solution to the polygonal instance provides a feasible solution to the spline instance. We use our recent proof that 2D translational polygonal covering is NP‐hard to establish NP‐hardness of our planar translational spline covering problem. Our polygonal approximation strategy creates approximations that are tight, yet the number of vertices is only a linear function of the number of control points. Using recent results on B‐spline curve envelopes, we bound the distance from the spline curve to its approximation. We balance the two competing objectives of tightness vs. number of points in the approximation, which is crucial given the NP‐hardness of the spline problem. Examples of the results of our spline covering work are provided for instances containing as many as six covering shapes, including both convex and nonconvex regions. Our implementation uses the LEDA and CGAL C++ libraries of geometric data structures and algorithms.     

克拉玛依油田三叠系砾岩储层孔隙结构分形特征

应用沈平平、李克文等人提出的计算砂岩孔隙结构分形维数的ＭＩＦＡ法，对克拉玛依油田三叠系克下组砾岩储层的孔隙结构分形维数进行了研究。认为克拉玛依砾岩储层的孔隙结构具有分形特征，孔隙结构的分形维数可定量描述孔隙结构的复杂程度，分形维数愈接近２，孔隙表面愈光滑，储层储集性能愈好，反之，储集性能愈差。     

磨合过程中表面形貌变化的分形表征

磨合是各运动副在投入运行前为获得好的配合性、提高承载能力所必须经历的过程,表面形貌的明显变化是磨合过程中表现出的重要特征。本文引入分形理论,用分形参数表征磨合表面的形貌变化。研究表明,磨合表面变化的分形参数表征是简单有效的。     

直线加速器中电荷束团的耦合包络线方程

采用直线加速器中有限圆柱空间电荷模型，利用电荷束团所产生的纵向和横向空间电荷力，推导得到了直线加速器中计入纵向与横向耦合效应的电荷束团的耦合包络线方程；通过数值计算，给出了纵向和横向几何因子变化的计算实例。