基于地图代数的最小生成树实现方法

本文介绍了最小生成树及其常见的算法,对比栅格算法分析了基于矢量的最小生成树算法的缺点,介绍了地图代数的距离变换和基于地图代数的距离变换图生成Voronoi图、Delaunay三角网,然后根据最小生成树MST是Delaunay三角剖分的一个子集,逐次删掉Delaunay三角网中每个三角形的最长边,从而得到最小生成树,该方法不仅适用于欧氏非障碍空间,同样也适用于障碍空间的情况,解决了以往最小生成树在障碍空间下(尤其是当障碍空间中的障碍是全形态的条件下)难以求解的问题,具有一定的理论意义。     

Inferring seismic hazard in Sichuan-Yunnan region of China based on the modern earthquake catalogue (1980-2019)*

Based on the modern earthquake catalogue, the incomplete centroidal voronoi tessellation (ICVT) method was used in this study to estimate the seismic hazard in Sichuan-Yunnan region of China. We calculated spatial distributions of the total seismic hazard and background seismic hazard in this area. The Bayesian delaunay tessellation smoothing method put forward by Ogata was used to calculate the spatial distributions of b-value. The results show that seismic hazards in Sichuan-Yunnan region are high, and areas with relatively high hazard values are distributed along the main faults, while seismic hazards in Sichuan basin are relatively low.     

一种顾及重要性意义和空间分布特征的兴趣点选取方法

针对地图上的兴趣点,提出了一种兼顾个体重要性和点群空间分布特征的选取方法。根据单个点的地理特征、地理意义来评估点的重要性程度;通过反复构造加权Voronoi图保持点群的空间分布特征,并在此基础上评估单个兴趣点的选取概率。最后,结合实际数据进行实验,实验表明该方法合理有效。     

多阶三角形数据结构的高阶Voronoi图算法研究

针对大多数传统高阶Voronoi算法复杂且运行效率低下,缺乏拓扑关系与多种邻近查询以及地理空间可视化交互与分析上的问题,该文借助Delaunay三角形天然优势,首先建立了一种k阶Delaunay三角形数据结构,利用k阶Delaunay三角剖分与k阶的Voronoi图存在的间接性对偶关系,提出了一种k阶Delaunay三角形数据结构的高阶Voronoi图的算法,并通过数据实验分析与对比,结果表明:该算法易于理解,程序设计简单易行,提高了运行效率,有效支持地理空间应用与几何学与拓扑邻近查询,满足实际应用的需要。     

地图专题信息量的测量方法研究

对已有的地图信息量测量法进行介绍,针对已有的专题信息量测量方法单方面关注符号类型数量或拓扑邻接性,缺乏对影响专题信息量主要因素的分析提取的问题,分析提出影响专题信息的主要因素——符号类型数量、混合度和每种类型占比,在此基础上提出基于拓扑中心符号的专题信息量测量法、基于全局的专题信息量测量法和基于特征的专题信息测量法。实验表明,以上改进方法对地图符号专题信息量的计算结果更加有效,能够更好地符合人的空间认知特性。     

空间数据的零初始化与障碍空间下的最小生成树实现方法

介绍了障碍空间下的最小生成树实现方法。首先采用零初始化的思想,初始化"位"数据;然后在构建障碍空间下实体点的Voronoi图的基础上,通过障碍空间下的回溯算法得到实体点间的最近连通图,也即障碍空间下实体点之间的Delaunay图;最后根据连通图,采用贪婪策略来得到最小生成树。     

Upper‐amphibolite facies partial melting of paragneisses from the Epupa Complex,NW Namibia,and relations to Mesoproterozoic anorthosite magmatism

The evolution of the mineral assemblages and P–T conditions during partial melting of upper‐amphibolite facies paragneisses in the Orue Unit, Epupa Complex, NW Namibia, is modelled with calculated P–T–X phase diagrams in the Na₂O–CaO–K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O system. The close concordance of predictions from the phase diagrams to petrographic observations and thermobarometric results documents that quantitative phase diagrams are suitable to explain the phase relationships in migmatitic upper‐amphibolite facies low‐ and medium‐pressure metapelites, which occur in many high‐grade metamorphic terranes worldwide. Different mineral assemblages in the migmatitic metapelites of the Orue Unit reflect regional discrepancies in the metamorphic grade: in a Northern Zone, early biotite–sillimanite–quartz assemblages were replaced via melt‐producing reactions by cordierite‐bearing assemblages. In a Southern Zone, they were replaced via melt‐producing reactions by garnet‐bearing assemblages while cordierite is restricted to rare metapelitic granofelses, which preserve Grt–Sil–Crd–Bt peak assemblages. Peak‐metamorphic conditions of 700–750 °C at 5.5–6.7 kbar in the Southern Zone and of ～750 °C at 4.5 kbar in the Northern Zone are estimated by integrating thermobarometric calculations with data from calculated mineral composition isopleths. Retrograde back‐reactions between restite and crystallizing melt are recorded by the replacement of garnet by biotite–sillimanite and/or biotite–muscovite intergrowths. Upper‐amphibolite facies metamorphism and partial melting (c. 1340–1320 Ma) in the rocks of the Southern Zone of the Orue Unit, which underwent probably near‐isobaric heating–cooling paths, are attributed to contact metamorphism induced by the coeval (c. 1385–1319 Ma) emplacement of the Kunene Intrusive Complex, a huge massif‐type anorthosite body. The lower‐pressure metapelites of the Northern Zone are interpreted to record contact metamorphism at an upper crustal level.     

一种用于界定经济客体空间影响范围的方法——Voronoi图

经济客体的空间影响范围界定十分复杂,但在区域规划和城市规划中有着重要的理论和实际意义。该文提出可采用Voronoi图方法用于经济客体的空间影响范围界定,介绍了Voronoi图的基本原理和其若干扩展,编写了生成Voronoi图的程序,最后以城市为例探讨了Voronoi图在经济客体空间影响范围界定中的应用。     

岩土工程数值计算中的无网格方法及其全自动布点技术

自然单元法采用无网格的思想全域构造插值函数,它的求解精度高,计算时间少,可准确地施加边界条件,兼具有无网格法和有限单元法的优点和特点,是一种理想的用于岩土及地下工程分析计算的数值方法。文中简要地介绍了自然单元法的基本理论,并针对岩土及地下工程问题特点,给出了一种无网格离散点的全自动布置方法。     

基于溃变理论的沙尘大风天气预测研究

依据溃变理论和溃变V-3θ结构图的信息数字化,预测天气的转折性变化取得了应用的有效性突破。文中针对沙尘大风天气的预测分析,利用单站探空资料的特性层资料,通过V-3θ图直观反映大气层结的滚流方向、稳定度和水汽含量等信息,以此判断大风、沙尘天气的转折性变化。结果表明,沙尘大风发生前,V-3θ图中位温(θ)、露点温度的假相当位温(θsed)曲线非常靠近,θ曲线左倾明显,整层大气存在顺滚流,且对流层上层存在"超低温"现象;当θsed曲线数值增大,明显靠右,则表明沙尘大风天气将结束。溃变图方法显示了简捷、直观和应用有效的特征。