三维拓扑数据的生成算法与交互修改方法研究

在分析现有三维矢量拓扑关系的基础上,提出了三维矢量数据结构的要素拓扑模型（Feature Topological Mod—el,FTM）。FTM三维拓扑模型比传统三维模型的优势有3点：（1）直接引入三角形对象,更加有利于表示任意形状的三维体数据。（2）简化基本拓扑关系的定义,使用相对简单的三角形和边的拓扑关系,表达相对复杂的实体和曲线的拓扑关系;使用带拓扑关系的边的集合表示三维曲线,既表达了曲线对象,又不影响基本拓扑关系的维护。（3）使用实体之间的包含模型,解决环（洞）的拓扑关系。同时,使用FTM对三维离散三角形数据进行拓扑化处理,对其中存在的拓扑错误提出具体的解决方案。该拓扑模型成功应用于自主研发的三维勘查软件“探矿者”中。     

Multipole-refined charge density study of diopside at ambient conditions

The experimental multipole electron density, ρ(r), of diopside was derived from high-resolution single-crystal diffraction at room temperature. Its topological analysis revealed predominantly ionic Si–O bonding, as found in electron density studies of other silicates. In particular, the non-bridging Si–O bonds are slightly less ionic in character than the bridging Si–O bonds. The Ca–O and Mg–O bonds are classified as pure closed-shell ionic interactions. An analysis of –∇²ρ(r) showed the presence of maxima around the oxygen atoms, associated to lone pairs domains that are involved in bonds with the surrounding ions. Calculation of atomic basins gave net charges of –1.56(12), 3.11(17), 1.79(13) and 1.88(18) e for O (averaged), Si, Ca and Mg atoms, respectively. O···O interactions between the O atoms at the vertices of the SiO₄ tetrahedron were also detected from the topological analysis of ρ(r), and indicate a cooperative interaction among the lone pairs of neighbouring oxygen atoms. All these results were also confirmed by periodic restricted Hartree–Fock (RHF) calculations. Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Quantitative fuzzy topological relations of spatial objects by induced fuzzy topology

This paper presents a study on the modeling of fuzzy topological relations between uncertain objects in Geographic Information Systems (GIS). Based on the recently developed concept of computational fuzzy topological space, topological relations between simple fuzzy spatial objects are modeled. The fuzzy spatial objects here cover simple fuzzy region, simple fuzzy line segment and fuzzy point. To compute the topological relations between the simple spatial objects, intersection concepts and integration methods are applied and a computational 9-intersection model are proposed and developed. There are different types of intersection, and we have proposed different integration methods for computation in different cases. For example, surface integration method is applied to the case of the fuzzy region-to-fuzzy region relation, while the line integration method is used in the case of fuzzy line segment-to-fuzzy line segment relation. Moreover, this study has discovered that there are (a) sixteen topological relations between simple fuzzy region to line segment; (b) forty-six topological relations between simple fuzzy line segments; (c) three topological relations between simple fuzzy region to fuzzy point; and (d) three topological relations between simple fuzzy line segment to fuzzy point.     

钙钛矿型结构亚硝酸盐和氰化物的分子体积

 绝大部分的亚硝酸盐和氰化物属于钙钛矿型结构,但有部分化合物为“反”钙钛矿型结构,充填空洞A位的阳离子的拓扑体积为0。阴离子团NO₂^-和CN^-的拓扑体积都近乎常数,分别为41.73ų和40.03ų,标准方差σ_n-1=1.516和σ_n-1=1.25。由此,进一步证明了原来的一套离子拓扑体积数值的普适性。“反”钙钛矿型结构中A位阳离子的平均半径r_A>1.00Å时,三价阳离子会产生扩容效应,其扩容系数大约是其本身拓扑体积的2倍;正钙钛矿型结构中,当A位是由半径较大的Cs⁺充填时,Cs⁺也会产生扩容效应,其扩容系数约为24ų。氰化物中结晶水分子的拓扑体积近乎常数,为24ų或0。     

Computing the fuzzy topological relations of spatial objects based on induced fuzzy topology

For modeling the topological relations between spatial objects, the concepts of a bound on the intersection of the boundary and interior, and the boundary and exterior are defined in this paper based on the newly developed computational fuzzy topology. Furthermore, the qualitative measures for the intersections are specified based on the α‐cut induced fuzzy topology, which are (A_α∧?A)(x)<1?α and ((A^c)_α∧?A)(x)<1?α. In other words, the intersection of the interior and boundary or boundary and exterior are always bounded by 1?α, where α is a value of a level cutting. Specifically, the following areas are covered: (a) the homeomorphic invariants of the fuzzy topology; (b) a definition of the connectivity of the newly developed fuzzy topology; (c) a model of the fuzzy topological relations between simple fuzzy regions in GIS; and (d) the quantitative values of topological relations can be calculated.     

SHORT COMMUNICATION THE USE OF TOPOLOGICAL MODELS IN ANALYTICAL CHEMISTRY

In the present paper,the possible analytical applications of two topological models,the DARC modeland the group contribution model,are discussed.Both models are applied to obtain calibration laws,which relate UV and IR characteristics with the chemical structure of ethylene oxide condensates.The group contribution model is also applied to determine the contribution of each part of thedifferent compounds involved in a chemical interaction process,having established the sensitizationparameters of benzodiazepines and anionic surfactants from the micellar enhancement fluorescence.     

Metric spaces of Keplerian orbits

Several metric spaces of Keplerian orbits and a set of their most important subspaces, as well as a factor space (not distinguishing orbits with the same longitudes of nodes and pericentres) are constructed. Topological and metric properties of them are established. Simple formulae to calculate the distance are deduced. Applications to a number of problems of Celestial Mechanics are discussed.     

Extended model of topological relations between spatial objects in geographic information systems

This paper presents an extended model for describing topological relations between two sets (objects) in geographic information systems (GIS). First, based on the definition of the topological relations between two objects, we uncover a sequence of topological relations between two convex sets.Second, an extended model for topological relations between two sets is proposed based on the new definition. The topological relations between two convex sets are expressed as a sequence of 4 × 4 matrices, which are the topological properties of A^o ∩ B^o, A^o\B, B^o\A, ∂A ∩ ∂B. The model is also extended for handling the properties of the topological relations between two non-convex sets, where the factor of first fundamental group is added to A ∪ B to handle these complex relations.The results show that the number of topological relations between the two sets is not as simple as finite but infinite and can be approximated by a sequence of matrices.     

基于拓扑关系的等高线高程自动赋值方法

地面高程信息是地理信息的重要组成部分，主要通过对地图上的等高线进行数字化来获取。等高线的数字化包括获取其特征点平面坐标和高程值两个方面。本文讨论了闭合等高线之间的拓扑关系及其表示形成，给出了根据等高线的平面位置判定其拓扑关系的算法。在此基础上，提出并实现了一种自动获取闭合等高线高程值的方法。实验表示，本文所述方法是正确可行的。