基于IDL的栅格地图代数实现与应用

ArcGIS提供了功能强大的地图代数计算功能,可以有效地针对栅格数据进行空间分析。但是,由于其运算效率较低而成为一些项目应用的瓶颈。研究认为ArcGIS进行地图代数计算效率比较低的主要原因在于它在计算时首先对数据进行重采样。通过使用IDL提供的栅格数据处理功能,对数据进行预处理,建立进行地图代数计算时的模版,将进行地图代数计算的各个图层依照地图代数模版重新进行范围的分割,并根据原始栅格数据及研究内容确定像元大小,对栅格数据进行重采样,得到可以用IDL进行地图代数运算的栅格数据集。根据不同研究领域的内容,设计地图代数的算法,实现地图代数运算。最后,以使用USLE方程计算三江平原土壤侵蚀模数为例,验证了方法的有效性。     

多边形叠置分析算法研究

在二维GIS系统中经常需要对图层中的多边形进行叠置分析,为了有效地分析不同系统提供的多边形图层数据,论文研究了地理信息系统中表示多边形图层的两种数据结构——简单数据结构和拓扑数据结构,以及分别适用于这两种情况的多边形叠置算法。拓扑数据结构下的算法现在已经很成熟,论文重点介绍简单数据结构情况下的算法。     

基于模糊粗糙集的GIS数据转换方法研究

GIS按照数据结构可以分为矢量数据和栅格数据两种。GIS的空间建模大部分是基于栅格数据进行的,因此,对于一些在矢量结构中表达的属性（如人口密度等）,需要转换成栅格数据。传统的数据转换方法一般都是面积占优法,这种方法没有充分考虑空间数据的模糊性问题。采用模糊粗糙集的理论,对矢量多边形数据转换成栅格数据的方法做了探讨。基于模糊粗糙集的数据转换方法考虑到了多边形数据的边界模糊性,利用隶属函数来确定多边形边界的不确定性。     

连续法体素造型系统——ASMS

本文介绍的连续法体素造型系统又可称为代数法体素造型系统(ASMS),是用圆柱、圆台、圆锥、球和长方体等五种体素经“并”、“差”集合运算来构造三维形体。它不需要将曲面离散成一系列的平面来表示。而是直接用代数方程式表示曲面及其交线。本系统采用了新颖的数据结构,严格的集合运算规则,“穿点判断”的消隐方法。从而使之在NOVA3-Tek4014(XYNETI-CS-1200)小型计算机绘图系统上得以实现。     

时态拟序数据索引TQD-tree

讨论一种新的时态数据库索引技术TQD-tree.不同于常规的“代数”方式,TQD-tree基于“序关系”数学框架,但与“代数”方式一样能够实现“一次一集合”的数据操作.提出给定时间期间集合上线序划分概念并建立构建算法,在线序划分框架内,提出时态数据索TQD-tree,并研究了相应查询和更新算法.设计了仿真实验,对TQD-tree的性能进行了基本评估.     

SPARQL查询的关系代数表示与转换方法

为解决基于本体的数据集成系统中的查询转换问题,提出SPARQL查询的关系代数表示和转换方法。引入RDF图模式的关系代数,定义了五种基本的关系运算,给出了SPARQL查询的关系代数表示;提出了SPARQL到SQL的查询转换方法,将基于本体的SPARQL查询转换为可在关系数据库上直接执行的SQL查询,从而实现关系数据库的集成。系统实现表明,该方法能够有效地实现查询语言的转换。     

用代数系统描述数据对象及其操作方法的研究

本文旨在研究使用代数系统对CMM管理工具所需数据对象及其上操作进行统一描述的方法，结合代数系统的定义和定理，将数据对象的全体看作集合，将数据对象上的各种操作定义成该集合上的运算，从而构成代数系统，实例证明,本方法可以和已有的抽象代数系统联系起来，从而为控制数据对象上的各种操作提供可靠的理论依据。     

利用OBDD编码的快速二值图算法(英文)

对利用有序二元判定图 OBDD 编码二值图像进行了研究,该方法可以节约大量的空间,并在此基础上,提出了各种二值图的算法,包括解码和集合运算(并、交、差、对称差、包含和互补)。实验结果表明这种基于OBDD 编码的方法比现有的二值图编码方法效率更高。     

集合游程编码算法介绍与实验分析

游程编码是一种无损压缩算法,其简单、易于实现的特性也使它得到了广泛的应用.传统的游程编码选取固定的阈值区分特征字符和非特征字符,限制了压缩率的提高.从集合论的角度研究游程编码,提出了一种新的游程编码算法一集合游程,算法中不再使用阈值,而将全域字符划分成两个互不相交的集合,分别为特征字符和非特征字符,通过对特征字符进行合理的映射来表示连续出现次数,将游程编码算法的效率利用到了极限.最后,给出了集合划分的方法,并编程进行了验证,与原游程编码算法进行了比较.     

基于Strip-Tree的无级比例尺GIS多边形化简技术

无级比例尺GIS(geographicinformationsystem)多边形化简的基础是多边形弧段的线综合,而直接对多边形的弧段施加线综合操作可能造成输出数据的拓扑错误,主要表现为化简后弧段出现相交.以往的研究并未对这个问题给予足够的重视和给出自动化的解决方法.在对此问题进行全面分析的基础上,提出了一种基于Strip-Tree的多边形图层化简策略,在保持输出数据拓扑结构正确的前提下化简多边形图层,且保持了较高的时空效率.该策略成功地应用于国家863项目“时空一体化智能城建信息系统”,并获得了满意的效率和结果.     

软Vague关系再研究

给出了软Vague关系的广义交、狭义交、狭义并、相对补运算的概念,并分别研究了这些运算的若干代数性质。     

Algebraic properties on the cuts of lattice-valued regular languages

In this paper, the algebraic operations on the cuts of lattice-valued regular languages are studied. Some sufficient conditions are given to guarantee the family of the cuts of lattice-valued regular languages to be closed under such algebraic operations as union, intersection, complement, quotient, homomorphism, inverse homomorphism, concatennation, reversal, etc. This work is supported by National Science Foundation of China (Grant No.10571112), “TRAPOYT” of China and National 973 Foundation Research Program (Grant No. 2002CB312200).     

软BCK代数

提出了软BCK代数的概念,研究了软BCK代数的并,交和乘积运算,讨论了这些运算的代数性质。     

软Vague关系

提出软Vague关系的一些基本概念,研究了软Vague关系的∨、∧以及并、交、补代数运算的若干性质。     

Vague软集的一些代数性质

基于Vague集和软集现有理论以及Vague集思想与软集思想之间的联系,初步提出了Vague软集的狭义交、狭义并、相对补运算的概念,并在此基础上分别研究了这些运算的若干代数性质。     

一类四次隐式代数曲面参数化研究

隐式代数曲面的参数化是 CAGD的热点问题之一 .针对一类四次隐式代数曲面 ,提出一种基于分片的几何参数化方法 .首先对四次代数曲面进行分片 ,然后对每一个分片曲面利用一组同轴平面束与其求交线 ,通过对求得交线的参数化来完成对整个分片曲面的参数化 .该方法是一种精确的参数化方法 ,其结构直观、计算简单 ,并且具有可使分片的四次代数曲面位于 [0 ,1]× [0 ,1]参数区间内 ,以及分片曲面的边界位于等参数线上等特点 ,利用该参数曲面可以方便地实现机器作图和几何操作 .实验结果验证了文中方法的有效性 .     

Boolean operations on general planar polygons

Computing boolean operations between general planar polygons is one of the fundamental problems in geometric and solid modeling. In this work we present a new algorithm to calculate intersection, union and difference, valid for general planar polygons (manifold and non-manifold, with and without holes), based on a formal representation system. This formal model is based on the concept of simplicial chain, developed by Feito and Rivero (Computers & Graphics 22(5) (1998)). Using algebraic operations between simplicial chains we can obtain any general polygon and the Boolean operations between them. The fact of that our algorithm is based on simplicial chains and their operations, reduces the study of special cases, and allows us to develop a robust and efficient algorithm to calculate the intersection between general polygons.     

Signed algebraic level sets on NURBS surfaces and implicit Boolean compositions for isogeometric CAD–CAE integration

Boundary-representation (B-rep) geometrical models, often mathematically represented using Non-Uniform Rational B-Spline (NURBS) surfaces, are the starting point for complex downstream product life-cycle evaluations including Computer-Aided Engineering (CAE). Boolean operations during B-rep model generation require surface intersection computations to describe the composed entity. However, for parametric NURBS surfaces, intersection operations are non-trivial and typically carried out numerically. The numerical intersection computations introduce challenges relating to the accuracy of the resulting representation, efficiency with which the computation is carried out, and robustness of the result to small variations in geometry. Often, for downstream CAE evaluations, an implicit, procedural knowledge of the Boolean operations between the composed objects that can resolve point containment queries (exact to the original NURBS bounding surfaces) maybe sufficient during quadrature. However, common point containment queries on B-rep models are numerical, iterative and relatively expensive. Thus, the first goal of the present paper is to describe a purely algebraic, and therefore non-iterative, approach to carrying out point containment queries on complex B-rep models built using low-degree NURBS surfaces. For CAE operations, the boundary representation of B-rep solids is, in general, not convenient and as a result, the B-rep model is converted to a meshed volumetric approximation. The major challenges to such a conversion include capturing the geometric features accurately when constructing the secondary (meshed) representation, apart from the efficiency of carrying out such a mesh generation step repeatedly as the geometric shape evolves. Thus, an ideal analysis procedure would operate directly on B-rep CAD models, without needing a secondary mesh, and would procedurally unify the geometric operations during CAD as well as CAE stages. Therefore, the second and broader goal of the present paper is to demonstrate CAD–CAE integration using signed algebraic level set operations directly on B-rep models by embedding or immersing the bounding surfaces within a discretized domain while preserving the geometric accuracy of the surfaces exact to the original NURBS representation during analysis.     

Coordinate-free computer graphics

This paper describes the graphical programming language tuna. tuna is a superset of fortran IV, designed for the writing of interactive graphics programs. The datatype graphical has been added to fortran along with operators which allow the writing of graphical expressions. These operators perform coordinate-free operations such as intersection, concatenation, rotation, and superposition. Other extensions include graphical Boolean operators and statements for communicating with an interactive terminal and light pen.Graphical entities are treated as primitive, rather than as sequences of Cartesian coordinate pairs. The construction operators in tuna are more closely related to the operations of the draftsman than to the algebraic operations of analytic geometry.Pictures are logical trees of points, lines, and subpictures; either DYNAMIC (changing as their subcomponents change) or STATIC. The data structure required to implement this is completely transparent to the programmer.     

A data model and algebra for probabilistic complex values

We present a probabilistic data model for complex values. More precisely, we introduce probabilistic complex value relations, which combine the concept of probabilistic relations with the idea of complex values in a uniform framework. We elaborate a model-theoretic definition of probabilistic combination strategies, which has a rigorous foundation on probability theory. We then define an algebra for querying database instances, which comprises the operations of selection, projection, renaming, join, Cartesian product, union, intersection, and difference. We prove that our data model and algebra for probabilistic complex values generalizes the classical relational data model and algebra. Moreover, we show that under certain assumptions, all our algebraic operations are tractable. We finally show that most of the query equivalences of classical relational algebra carry over to our algebra on probabilistic complex value relations. Hence, query optimization techniques for classical relational algebra can easily be applied to optimize queries on probabilistic complex value relations.