基于模板阴影体算法的矢量数据在三维场景中的绘制

提出一种基于模板阴影体算法的矢量数据绘制方法,实现矢量数据在三维场景中的高质量实时叠加显示。南于该方法基于屏幕空间,所以具有像素级的精度,不会出现传统的基于纹理方法所产生的绘制走样现象;而且不受地形几何数据的约束,其执行效率与地形数据的复杂度无关,仅取决于矢量数据本身的复杂度。详细论述基于模板阴影体算法矢量数据绘制的关键技术,并通过试验验证该方法的有效性。     

利用模板阴影体算法实现矢量数据在三维场景中的绘制

提出了一种基于模板阴影体算法的矢量数据绘制方法,实现了矢量数据在三维场景中的高质量实时叠加显示。由于该方法基于屏幕空间,所以具有像素级的精度,不会出现传统的基于纹理方法所产生的绘制走样现象;而且不受地形几何数据的约束,其执行效率与地形数据的复杂度无关,仅取决于矢量数据本身的复杂度。详细论述了基于模板阴影体算法矢量数据绘制的关键技术,并通过试验验证了该方法的有效性。     

正多面体的结晶学分类及等大正二十面体共角顶连接的准晶结构模型

本文将正四面体、正八面体、正六面体归为结晶类,将正二十面体、正十二面体归为准晶类。大小相近的原子倾向于形成正二十面体配位;再将正二十面体看成球体,那末符合m35对称的理想堆垛方式是以等大正二十面体共角顶连接,形成大一级的正二十面体。继续按照这一规律连接将不断形成更大一级的正二十面体,从而获得理想准晶结构模型。此模型很好地解释了Al—Mn准晶体的高分辨结构图及Penrose拼图与准晶体的高分辨结构图的密切关系。     

Bond—Valence Sum and Distortion of Coordination Polyhedra

By using the Lagrange‘s intermediate value theorem,it is derived mathematically that the structur-al distortion of a coordination polyhedron may lead to an increase in bond-valence sum of the cen-tral atom of ion .The applicabilities of the bond-valence model are discussed in the following two cases:the modeling of crystal structure ,and the indication of distortion degree of a coordination polyhedron.Also it is shown that a distorted polyhedron should be in favor of a longer average bond length or a smaller coordination number.     

Mutual Potential of Homogeneous Polyhedra

The mutual gravitational potential between a pair of homogeneous polyhedra is expressed using an infinite series. The nested volume integrals are evaluated analytically and result in simple tensor expressions containing no special functions. However, complexity increases as O(6 ⁿ ), where n is the term degree. An alternate formulation due to Liebenthal is also presented.     

Comprehensive methods for measuring regional multidimensional development and their applications in China

National and international research on regional development has matured from the use of single elements and indicators to the application of comprehensive multi-element and multi-indicator measures. We selected 12 indicators from six dimensions for analysis in this study, including income, consumption, education, population urbanization, traffic, and indoor living facilities. We then proposed the polyhedron method to comprehensively measure levels of regional multidimensional development. We also enhanced the polygon and vector sum methods to render them more suitable for studying the status of regional multidimensional development. Finally, we measured levels of regional multidimensional development at county, city, and provincial scales across China and analyzed spatial differences using the three methods above and the weighted sum method applied widely. The results of this study reveal the presence of remarkable regional differences at the county scale across China in terms of single and multidimensional levels of regional development. Analyses show that values of the regional multidimensional development index (RMDI) are high in eastern coastal areas, intermediate in the midlands and in northern border regions, and low in the southwest and in western border regions. Districts characterized by enhanced and the highest levels of this index are distributed in eastern coastal areas, including cities in central and western regions, as well as areas characterized by the development of energy and mineral resources. The regional distribution of reduced and the lowest levels of this index is consistent with concentrations of areas that have always been impoverished. Correlation analyses of the results generated by the four methods at provincial, city, and county scales show that all are equivalent in practical application and can be used to generate satisfactory measures for regional multidimensional development. Additional correlation analyses between RMDI values calculated using the polyhedron method and per capita gross domestic product (GDP) demonstrate that the latter is not a meaningful proxy for the level of regional multidimensional development.     

块状地质体的多面体表示及交互编辑

针对固体矿产的地质建模问题,中国科技工作者提出了用于人机交互构造块状地质模型的“橡皮膜技术”并在此基础上完成了人机交互计算机辅助勘查系统PandaCAEX。“橡皮膜技术”可以快速地构造出任意形状的块状地质模型,为地质模型的构造提供了极大的方便。但“橡皮膜技术”本身存在着模型表达过于复杂和一些功能上的缺陷。本文针对这些问题提出直接使用多面体模型对块状地质体进行表达,同时给出了模型的交互编辑方法。与“橡皮膜技术”相比,这种技术在保留“橡皮膜技术”优点的同时,使块状地质模型的表达大大简化、功能更加完善。该模型已经成为新的改进系统的核心,证明了模型的实用性。     

Using estimated thermodynamic properties to model accessory phases: the case of tourmaline

Accessory phases and minor components in minerals are commonly ignored in thermodynamic modelling. Such an approach seems unwarranted, as accessory phases can represent a significant element reservoir and minor components can substantially change their host mineral's stability field. However, a lack of thermodynamic data prohibits assessment of these effects. In this contribution, the polyhedron method is used to estimate the thermodynamic properties of tourmaline, a common and widespread accessory phase, stable over a range of P–T–X conditions. The polyhedron method allows Δ H , S , V , C _P and V _m ( T , P ) properties to be estimated from a linear stoichiometric summation over the fractional properties of its polyhedron constituents. To allow for estimates of tourmaline, fractional thermodynamic properties for B^III and B^IV polyhedra were derived. Mixing contributions to molar volume were evaluated and symmetrical mixing parameters derived for Al-Mg, Al-Fe and Al-Li interaction on tourmaline's Y-site and T-site Al-Si interaction. Evaluation of the estimated properties using experimental and natural equilibria between tourmaline and melts, minerals and hydrothermal fluids, shows that reliable semi-quantitative results are obtained. The boron contents in fluids coexisting with tourmaline are calculated to within an order of magnitude of measured content, and where anchor-points are available, agreement improves to within a factor of 2. Including tourmaline in petrogenetic modelling of metamorphic rocks indicates that its presence leads to disappearance of staurolite and garnet, among others, and modifies the X _Mg of coexisting phases, in line with observations on natural rocks.     

A new method to calculate end-member thermodynamic properties of minerals from their constituent polyhedra II: heat capacity, compressibility and thermal expansion

Thermodynamic calculations in petrology are generally performed at pressures and temperatures beyond the standard state conditions. Accurate prediction of mineral equilibria therefore requires knowledge of the heat capacity, thermal expansion and compressibility for the minerals involved. Unfortunately, such data are not always available. In this contribution we present a data set to estimate the heat capacity, thermal expansion and compressibility of mineral end‐members from their constituent polyhedra, based on the premise that the thermodynamic properties of minerals can be described by a linear combination of the fractional properties of their constituents. As such, only the crystallography of the phase of interest needs to be known. This approach is especially powerful for hypothetical mineral end‐members and for minerals, for which the experimental determination of their thermodynamic properties is difficult. The data set consists of the properties for 35 polyhedra in the system K–Na–Ca–Li–Be–Mg–Mn–Fe–Co–Ni–Zn–Al–Ti–Si–H, determined by multiple linear regression analysis on a data set of 111 published end‐member thermodynamic properties. The large number of polyhedra determined allows calculation of a much larger variety of phases than was previously possible, and the choice of constituents together with the large number of thermodynamic input data results in estimates with associated uncertainty of generally <5%. The quality of the data appears to be sufficiently accurate for thermodynamic modelling as demonstrated by modelling the stability of margarite in the CASH system and the position of the talc–staurolite–chloritoid–pyrope absent invariant point in the KMASH system. In both cases, our results overlap within error with published equivalents.     

Functional substitution of coordination polyhedron in crystal structure of silicates

On the bases of the study of comparative crystal chemistry of silicates it has been concluded that the octahedra and square pyramids of Ti-0 and Zr-0 play functional role of tetrahedra of Si-0 in the construction of crystal structures. Therefore, those silicates may be named titano-and zircono-silicates. Because of the functional similarity of coordination polyhedra, the structures of cristobalite and feldspar have been compared with those of perovskite and garnet, respectively. As a new concept, the functional replacement of tetrahedra by octahedra and/or pyramids is defined by the authors of this paper for favorable comparison of relative crystal structures.