浮游植物现存量表征指标间相关性研究Ⅰ:叶绿素a与生物量

收集国内、外有关资料,并结合潘家口水库现场围隔实验,主要从实验室内研究水体、野外围隔水体及天然水体三个方面,对浮游植物叶绿素a含量与生物量间的相关性进行探讨。结果表明:在实验室条件下,叶绿素a与生物量一般呈显著正相关关系,但当优势藻种发生明显变更时,二者相关性不明显甚至不相关;现有资料显示,野外围隔实验水中,叶绿素a与生物量一般呈显著正相关。在天然水体中,叶绿素a与生物量可能相关或不相关。叶绿素a与藻密度的关系将在续文中予以讨论。     

On rationally supported surfaces

We analyze the class of surfaces which are equipped with rational support functions. Any rational support function can be decomposed into a symmetric (even) and an antisymmetric (odd) part. We analyze certain geometric properties of surfaces with odd and even rational support functions. In particular it is shown that odd rational support functions correspond to those rational surfaces which can be equipped with a linear field of normal vectors, which were discussed by Sampoli et al. (Sampoli, M.L., Peternell, M., Jüttler, B., 2006. Rational surfaces with linear normals and their convolutions with rational surfaces. Comput. Aided Geom. Design 23, 179–192). As shown recently, this class of surfaces includes non-developable quadratic triangular Bézier surface patches (Lávička, M., Bastl, B., 2007. Rational hypersurfaces with rational convolutions. Comput. Aided Geom. Design 24, 410–426; Peternell, M., Odehnal, B., 2008. Convolution surfaces of quadratic triangular Bézier surfaces. Comput. Aided Geom. Design 25, 116–129).     

Direct 5-axis tool-path generation from point cloud input using 3D biarc fitting

In reverse engineering, geometrical information of a product is obtained directly from a physical shape by a digitizing device. To fabricate the product, manufacturing information (usually tool-path) must be generated from a CAD model. The data digitized must be processed and in most cases, a surface model is constructed from them using some of the surface fitting technologies. However, these technologies are usually complicated and the process for constructing a surface patch from a massive digitizing data is time-consuming. To simplify the process for getting tool-path information, a simple algorithm is proposed in this paper. The algorithm is used to generate a 5-axis machining tool-path. Instead of implementing any complicated surface fitting techniques, a direct method is proposed for constructing three-dimensional (3D) triangular mesh from the digitizing data with the mesh points considered as the tool contact locations. Depending on the locations of the points digitized, a decimation procedure is applied such that some of the digitizing data will be filtered out. Then, the tool axis orientations which must be determined in 5-axis tool-path are calculated and the tool center locations are determined accordingly. A 3D biarc fitting technique is applied for all the tool center locations so that a complete 5-axis tool-path is obtained.     

三角模糊数互补判断矩阵排序的最小方差法

研究偏好信息为三角模糊数互补判断矩阵形式给出的方案排序方法.根据三角模糊数互补判断矩阵完全一致性的概念,建立了一个基于最小方差的非线性规划模型.通过求解该模型,得到三角模糊数互补判断矩阵的权重向量,并利用三角模糊数排序公式对决策方案进行排序.最后通过算例分析表明了所提出的方法是可行而有效的.     

不同算法下生成的数字高程模型对比分析研究

目前数字高程模型的生成在大多数商用地理信息系统软件或遥感图像处理软件中都能实现,但提供的算法有所不同.结合目前常用专业软件提供的不同算法,对同一数据源的高程数据分别生成数字高程模型(DEM),进行对比分析后发现:使用现有专业软件生成的DEM均存在着差异,这些差异主要来源于不同软件采用的算法差别,并且DEM的差异具有空间分布的规律性和负高差多于正高差的特点.由此得出以下结论,TIN算法具有生成的DEM精度高等优点,LRS和Non-LRS算法具有生成的DEM结构简单等优点.若要进行三维显示、土方量计算等,则选择TIN算法生成;若要检查高程数据错误,则选择LRS或Non-LRS算法生成.     

Symbolic computation of the Birkhoff normal form in the problem of stability of the triangular libration points

The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. A software package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is designed so that normalization problems of high analytical complexity could be solved. It is used to obtain the Birkhoff normal form of the Hamiltonian in the given problem. The normalization is carried out up to the 6th order of expansion of the Hamiltonian in the coordinates and momenta. Analytical expressions for the coefficients of the normal form of the 6th order are derived. Though intermediary expressions occupy gigabytes of the computer memory, the obtained coefficients of the normal form are compact enough for presentation in typographic format. The analogue of the Deprit formula for the stability criterion is derived in the 6th order of normalization. The obtained floating-point numerical values for the normal form coefficients and the stability criterion confirm the results by Markeev (1969) and Coppola and Rand (1989), while the obtained analytical and exact numeric expressions confirm the results by Meyer and Schmidt (1986) and Schmidt (1989). The given computational problem is solved without constructing a specialized algebraic processor, i.e., the designed computer algebra package has a broad field of applicability.     

基于图像建模的多视图模型合并

通过基于单幅图像的建模方法或者基于立体像对的建模方法,可以重建图像序列中每一幅图像或者立体图像对对应的模型。但所得的是局部模型,并非物体的完整模型。针对这一问题,提出了一种基于序列图像建模的多视图模型合并方法。基于已重建出的同一物体不同角度的三角形网格模型,在统一坐标系下,对相邻角度下的三角形网格模型求取其重合区域,记录刚好包围重合区域的原始网格区域,对该区域重新进行网格划分,最后得到物体完整的三角网格模型。实验结果表明,该方法是可行的、有效的。     

Adaptive triangular-mesh reconstruction by mean-curvature-based refinement from point clouds using a moving parabolic approximation

We use a moving parabolic approximation (MPA) to reconstruct a triangular mesh that approximates the underlying surface of a point cloud from closed objects. First, an efficient strategy is presented for constructing a hierarchical grid with adaptive resolution and generating an initial mesh from point clouds. By implementing the MPA algorithm, we can estimate the differential quantities of the underlying surface, and subsequently, we can obtain the local quadratic approximants of the squared distance function for any point in the vicinity of the target shape. Thus, second, we adapt the mesh to the target shape by an optimization procedure that minimizes a quadratic function at each step. With the objective of determining the geometrical features of the target surface, we refine the approximating mesh selectively for the non-flat regions by comparing the estimated curvature from the point clouds and the estimated curvatures computed from the current mesh. Finally, we present various examples that demonstrate the robustness of our method and show that the resulting reconstructions preserve geometric details.     

t-Norm based cuts of intuitionistic fuzzy sets

We consider the system of intuitionistic fuzzy sets (IF-sets) in a universe X and study the cuts of an IF-set. Suppose a left continuous triangular norm is given. The t-norm based cut (level set) of an IF-set is defined in a way that binds the membership and nonmembership functions via the triangular norm. This is an extension of usual cuts of IF-sets. We show that the system of these cuts fulfils analogical properties as usual systems of cuts. However, it is not possible to reconstruct an IF-set from the system of t-norm based cuts.     

The triangular pyramid: Routing and topological properties

In this paper, a new topology for multicomputer interconnection networks, based on triangular mesh, is proposed. The new network, referred to as the triangular pyramid (or tripy for short), has L levels of triangular mesh. We study some basic important properties of the proposed network as well as introduce a routing algorithm for the tripy network based on the routing of triangular meshes. We prove that this form of pyramidal network is Hamiltonian, Hamiltonian-connected, and pancyclic. We also prove that the proposed network is 6-colorable and conduct a brief comparison of the tripy and its traditional pyramid counterpart. Our results show that the proposed network has higher scalability, connectivity, and total network bandwidth while preserving the important properties of the traditional pyramid network.