Natural Architecture and Constructed Forms: Structure and Surfaces from Idea to Drawing

This work grew out of didactic experience in architecture classes at the universities of Florence and Parma. The comprehension of geometric schemes in regular organic objects formed the basis of teaching drawing and scientific representation, such as formal architectural synthesis. This exercise may offer also a valid starting point to help students approach mathematics, and help them to imagine and plan the increasingly complex surfaces of late contemporary architecture.     

插值边界曲线的NURBS 近似极小曲面设计

探索性地设计了一个插值给定边界曲线的NURBS 近似极小曲面算法,弥补了当前NURBS 系统无法有效地设计工程所急需的一般NURBS 极小曲面的缺陷.运用NURBS 曲面的节点插入、Hybrid 多项式逼近等多种技术,将NURBS 曲面转化为相对简单的分片Bézier 曲面求解,并运用各子曲面片的控制顶点优化、整体曲面不断更新的迭代方法,成功地得到高精度的近似分片Bézier 极小曲面.最后,可以按用户的各种要求选择运用相应不同的迭代逼近算法,求取插值给定边界曲线的近似NURBS 极小曲面.     

过测地线的近似极小直纹曲面设计

为了在服装鞋帽制造业及材料剪裁中采用过给定测地线且具有近似最小面积的直纹曲面,提出一种直纹曲面算法.该算法将过给定测地线的曲面设计和近似极小曲面的逼近技术进行有机结合,把直纹曲面表示成含2个参变量的形式;利用变分法的思想进行最优化,并分别在弧长参数和一般参数下对其进行了讨论.最后通过一些实例验证了文中算法的正确性和有效性.     

一类极小曲面的控制网格表示

给出了平面曲率线极小曲面的拟Bézier和拟B样条控制网格表示,以悬链面及Enneper曲面为特殊形式,实现了由悬链面到Enneper曲面的动态变形.该工作为将极小曲面引入CAGD/CAD造型系统,并利用拟de-Casteljau算法生成极小曲面提供了一个有力的工具.     

极小曲面力学超材料抗冲吸能特性分析

本文基于极小曲面结构构建了一类力学超材料,并研究了其准静态及动态力学特性.首先,通过对等效密度为30%、40%和50%的超材料样件进行准静态压缩试验,分析了不同等效密度下结构准静态力学特性变化规律,结果表明,结构模量及平台应力随等效密度的增长呈指数上升,其变化规律可用Gibson-Ashby模型进行精准拟合;其次,研究了不同冲击工况对极小曲面力学超材料动态力学特性的影响规律.根据动态力学特性影响因素及变化规律,分别构建了刚性-完美塑性-锁定模型和简化吸能特性预测模型,对冲击时的力学超材料强度及吸能特性进行预测.结果表明,基于三周期极小曲面的力学超材料具有良好的抗压抗冲吸能特性,且其动态力学性能可以通过建立的模型进行精确预测,为高性能防护结构设计提供了理论基础.     

基于平面的建筑物表面模型重建算法的研究

针对建筑物模型的规则性,提出了一种基于平面的建筑物模型重建算法,可以从单幅透视图像恢复建筑物的表面模型．该算法主要分为相机定标、基平面的提取、平面位置和方向的计算等几个子过程．相机定标主要用于求解相机的焦距,是一个非常重要的部分．该算法以建筑物场景中的几何结构作为约束条件,从单幅图像中求解相机的焦距;然后计算基平面位置和法向;最后通过交互式操作指明场景中各平面之间的相互关系,递归求解各平面的位置和法向,达到根据图像重建建筑物场景表面模型的目的．     

插值边界的四边网格离散极小曲面建模方法

如何实现极小曲面的快速三维建模,是几何设计与计算领域中的难点和热点问题.给定一条封闭的边界离散折线,本文研究如何构造以其为边界的四边网格离散极小曲面.首先从曲面的内蕴微分几何度量出发,给出了离散四边网格极小曲面的数学定义;然后利用保长度边界投影、四边网格生成、径向基函数插值映射和非线性优化技术,提出了由给定边界离散折线快速构造离散四边网格极小曲面的一般技术框架.最后通过若干建模实例验证了本文方法的有效性.该方法可实现四边网格极小曲面的高质量建模,在建筑几何领域具有一定的应用价值.     

Minimal Surfaces Extend Shortest Path Segmentation Methods to 3D

Shortest paths have been used to segment object boundaries with both continuous and discrete image models. Although these techniques are well defined in 2D, the character of the path as an object boundary is not preserved in 3D. An object boundary in three dimensions is a 2D surface. However, many different extensions of the shortest path techniques to 3D have been previously proposed in which the 3D object is segmented via a collection of shortest paths rather than a minimal surface, leading to a solution which bears an uncertain relationship to the true minimal surface. Specifically, there is no guarantee that a minimal path between points on two closed contours will lie on the minimal surface joining these contours. We observe that an elegant solution to the computation of a minimal surface on a cellular complex (e.g., a 3D lattice) was given by Sullivan [47]. Sullivan showed that the discrete minimal surface connecting one or more closed contours may be found efficiently by solving a Minimum-cost Circulation Network Flow (MCNF) problem. In this work, we detail why a minimal surface properly extends a shortest path (in the context of a boundary) to three dimensions, present Sullivan's solution to this minimal surface problem via an MCNF calculation, and demonstrate the use of these minimal surfaces on the segmentation of image data.     

Embedded Voxel Colouring with Adaptive Threshold Selection Using Globally Minimal Surfaces

Image-based 3D reconstruction remains a competitive field of research as state-of-the-art algorithms continue to improve. This paper presents a voxel-based algorithm that adapts the earliest space-carving methods and utilises a minimal surface technique to obtain a cleaner result. Embedded Voxel Colouring is built in two stages: (a) progressive voxel carving is used to build a volume of embedded surfaces and (b) the volume is processed to obtain a surface that maximises photo-consistency data in the volume. This algorithm combines the strengths of classical carving techniques with those of minimal surface approaches. We require only a single pass through the voxel volume, this significantly reduces computation time and is the key to the speed of our approach. We also specify three requirements for volumetric reconstruction: monotonic carving order, causality of carving and water-tightness. Experimental results are presented that demonstrate the strengths of this approach.     

Algorithmic Minimal Sufficient Statistics: a New Approach

We introduce the notion of a strong sufficient statistic for a given data string. We show that strong sufficient statistics have better properties than just sufficient statistics. We prove that there are “strange” data strings, whose minimal strong sufficient statistic have much larger complexity than the minimal sufficient statistic.     

Images as Embedded Maps and Minimal Surfaces: Movies,Color, Texture,and Volumetric Medical Images

We extend the geometric framework introduced in Sochen et al. (IEEE Trans. on Image Processing, 7(3):310–318, 1998) for image enhancement. We analyze and propose enhancement techniques that selectively smooth images while preserving either the multi-channel edges or the orientation-dependent texture features in them. Images are treated as manifolds in a feature-space. This geometrical interpretation lead to a general way for grey level, color, movies, volumetric medical data, and color-texture image enhancement.We first review our framework in which the Polyakov action from high-energy physics is used to develop a minimization procedure through a geometric flow for images. Here we show that the geometric flow, based on manifold volume minimization, yields a novel enhancement procedure for color images. We apply the geometric framework and the general Beltrami flow to feature-preserving denoising of images in various spaces.Next, we introduce a new method for color and texture enhancement. Motivated by Gabor's geometric image sharpening method (Gabor, Laboratory Investigation, 14(6):801–807, 1965), we present a geometric sharpening procedure for color images with texture. It is based on inverse diffusion across the multi-channel edge, and diffusion along the edge.     

Minimal computer technologies and learner-centred environments: Some New Zealand experience

This paper argues that it is not the technology itself, but rather a learner-centred approach to the use of computers which will provide the opportunity for the learners to set their own academic goals, to experiment with their ideas, to explore alternative solutions to real world problems, and to think critically. We will use three New Zealand examples to illustrate how a limited number of computers can be utilized to facilitate an active learning process in a primary classroom.     

旋转极小曲面中微分方程通解的解法

微分方程解析解(即通解)的求解方法十分复杂,数学领域对微分方程的研究着重在几个不同的方面,但大多数都是关心微分方程的解.只有少数简单的微分方程可以求得解析解.不过即使没有找到其解析解,仍然可以确认其解的部份性质.本文用加减消元法、微分方程解析解的求法及一些数学技巧给出了旋转极小曲面中微分方程的通解.和其他文献中该方程的解法进行比较,本文的方法更加简单易懂。     

有理三角B-B曲面多项式逼近的一个有效算法

将美国计算机图形专家Sederberg提出的有理曲线多项式逼近的思想与算法推广到工程中广泛采用的三角域上的有理曲面.主要工作是:给定一张有理三角B-B曲面,通过将多项式三角B-B曲面的控制顶点表示成相同次数的有理三角B-B曲面的形式,即将多项式曲面的移动控制顶点看作在有理三角B-B曲面上的移动点,并添加约束条件,构造了三角域上的Hybrid曲面;适当地选取有理三角B-B曲面的1次Hybrid曲面表示,推导了彼此等同但次数相邻的两张Hybrid曲面之间控制顶点的递推公式;利用Hybrid曲面移动控制顶点凸包内的一点来代替该移动控制顶点,得到了多项式三角B-B曲面逼近有理三角B-B曲面的一个算法,并在文中给出了数值实例.这些结果可以明显地提高计算机辅助几何设计系统的数据可换性与计算效率.     

一种新的曲线曲面

给出了由任意n(n≥3) 个函数构成的混合函数组,这些函数组具有非负性、规范 性、对称性,以及特殊的端点性质。由这些函数组定义的曲线具有凸包性、几何不变性、对称 性等基本性质。曲线的起点、终点分别为控制多边形首、末边的中点,曲线在起点处的一阶、 二阶导矢都平行于控制多边形的首边,在终点处的一阶、二阶导矢都平行于控制多边形的末边。 对于任意给定的m(m3)个控制顶点,可以由之定义一条曲线段,也可以由之定义由多条曲线 段构成的组合曲线,而各条曲线段可以由不同数量的控制顶点来定义,因此由同一组控制顶点 可以定义出多种不同的形状。另外,组合曲线在分段连接点处均G2 连续,可以满足工程实际中 大多数的需求。由函数组定义的张量积曲面具有类似于曲线的诸多良好性质。     

软件体系结构：一个新的研究领域

计算机软件系统中软件成分越来越复杂,系统规模不断扩大,使得软件体系结构越来越庞杂,软件系统的质量和性能已经不再仅仅取决于软件实现算法和数据结构,软件系统体系结构在一定程度上决定系统的优劣,因此软件体系结构(Software Architecture,AS)研究已经逐渐地引起计算机界的重视。软件体系结构作为一个新兴的计算机学科,它的理论体系和解决问题的方法尚未形成。加强其基础理论和应用方法的研究,不论对学科发展,还是对软件生产都具有理论意义和现实意义。     

Participation and Creativity: New Forms of Suggestion Schemes in Sweden

The idea of the suggestion scheme, its role and evolution, can be suitably examined in light of certain distinct mental models or currents of thought in industry and working life. Different perspectives can then be brought to bear on the subject.     

从Raw计算机结构看计算机体系结构发展的一种新趋势

已经能多种从不同的角度利用芯片晶体管资源的途径问世,ＭＩＴＩ计算机系统实验室提出的Ｒａｗ计算机系统结构是较有特色的一种,与其他的并行计算途径不同,Ｒａｗ结构充分考虑了微粒度并行计算。具有较好的并行效率。同时具有其自身的内在可扩展性,代表了计算机体系结构研究的一个新方向。     

MDA：新一代软件互操作体系结构

UML和MOF等建模标准的形成使得解决分布式异构环境下互操作问题的方法有了质的飞跃。为适应这种新形势，OMG提出模型驱动体系结构MDA用以明确这些新标准的相互关系，并为制定、维护和发展建模标准提供帮助。该文介绍了MDA的基础思想和基本框架，并对基于MDA的软件开发模式作了阐述。