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.     

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.     

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.     

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．     

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.     

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IRAM计算机结构看计算机体系结构发展的新特点

处理器与存储器之间的带宽差距越来越大,存储器带宽已经严重限制了计算机性能的有效提高。Ｃａｌｉｆｏｒｎｉａ大学贩ＩＲＡＭ（Ｉｎｔｅｌｌｉｇｅｎｔ ＲＡＭ）计算机系统结构在单个ＤＲＡＭ芯片中集成一定逻辑功能,能有效解决这一问题,代表了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。     

一个新的最优简单规则挖掘算法

关联规则的提取是知识发现和数据挖掘领域中的重要问题,粗集理论是研究规则挖掘的重要的数学工具.本文研究信息系统中最优简单关联规则挖掘算法.本文利用信息关联矩阵中元素特性,对其进行变换,直接从中发现关联规则潜在的条件元,以此作为规则挖掘算法的基础.本文的算法简单直观,能挖掘出信息系统中所有最优简单规则,而且有效地避免了通常属性约简过程中的NP-hard问题.本文以一个实例证明本方法的有效性.     

Stairs in the Architecture Notebook of Juan de Portor y Castro: An Insight into Ruled Surfaces

Historic treatises on stonecutting of the sixteenth and seventeenth centuries contributed to progress in the study and understanding of properties of the different surfaces and the intersections between them. One of the topics that contributed most towards the development of knowledge of the geometry of surfaces was the practical use of ruled surfaces. Defining the geometry of a piece of stone by surfaces that can be cut using a ruler as a guide and a check has always been considered very interesting in the field of stonecutting. This present study focuses on stairs in two Spanish treatises to illustrate how warped surfaces were treated.     

Nebula: A New Architecture and its Relationship to Computer Hardware

The Nebula architecture of the military computer family provides, through carefully controlled visibility properties, both the flexibility to incorporate hardware advances and compatibility among family members.     

CSRAID:一种新的大规模RAID系统结构

借鉴集群文件系统“分布式虚拟磁盘”的概念,针对大规模RAID提出了一种新的存储结构CSRAID,它由若干结构不同的SubRAID组成.数据可以根据负载特征的变化动态迁移到最适合的SubRAID,SubRAID的数目和结构,也可以适应系统负载的发展而调整,从而CSRAID系统能为各用户提供一个由SubRAID物理存储空间构成的、始终适应用户I/O需求的虚拟磁盘.仿真实验结果表明与传统结构大规模RAID系统相比,同样大小存储空间的CSRAID系统的I/O性能具有显著优势.