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Possibly the use of a triangular mesh would have made the description simpler: that is to say, it might be that we could describe the surface more accurately with a coarse triangular mesh than with a fine square mesh, and so on.

也许用三角形格子的网会使描述更为简单：也就是说，用较稀的三角形网格也许比用较密的四方形网格能够更精确地描述这个表面，如此等等。

So this paper proposes a new method for automatic coarse registration of triangular meshes, which is used to approximately align the 3D measured data (represented in the form of triangular mesh) and the tessellated mesh of NURBS surface (instead of using NURBS surface itself to reduce computation) from larger initial pose difference.

为此本文提出了一种全新的三角网格面自动粗略配准方法，用来大致对齐相对位姿偏差较大的三维测量数据与NURBS曲面的离散网格（为减小计算量起见，此处不使用NURBS曲面本身）。

In addition, by utilizing Jacobi two square numbers theorem and Lagrange four square numbers theorem and some theta function identities, we also prove the known results of number theory: two triangular number theorem, four triangular number theorem, and the number of representations of a positive integer by various quadratic forms in terms of divisor functions

包括Jacobi二平方数定理，Lagrange四平方数定理等，然后利用这些结果结合几个theta函数恒等式，我们获得了把任意一个正整数表示成两个三角数或四个三角数的和以及其他的二次形式的方法数，这些方法数都是用因子函数来表示的。

Furthermore, the triangular systems in the normal decomposition still keep the triangular form for the specializations of the parameters.

进一步，对于给定的参数值，正规分解中得到三角形式仍然保持，通过求解三角形式的方程组从而得出原参数方程组的解。

In this paper, the theoretical analysis of matrix's triangular decomposition is mainly discussed, including such as the necessary and sufficient condition of uniqueness of existence in matrix's triangular decomposition,the necessary and sufficient condition of existence and so on.

本文主要对矩阵的三角分解理论分析作了比较全面的统述，它包括矩阵三角分解存在唯一性的充要条件、存在性的充要条件、存在性的充分条件等。

To one quaternion matrix, according to its normal form, into which a quaternion matrix is transformed after decomposed, the types of decomposition of a quaternion matrix are divided into three large classes: diagonalized decomposition, triangular decomposition and triangular-diagonalized decomposition.

对单个四元数矩阵，以分解后的四元数矩阵的标准型作为分类的标准，将四元数矩阵的分解分为三大类：对角化分解、三角化分解、三角一对角化分解。

The calculation of wavelet and scalar function coefficients at the process of decomposition of triangular mesh, the choice of wavelet coefficient threshold and the calculation of scalar function coefficient at the reconstruction process are introduced in this dissertation. The multiresolution decomposition, compression and reconstruction of triangular mesh with subdivision connectivity are realized.

关于细分连续三角网格的多分辨分解、压缩与重构，本文介绍了细分连续三角网格分解过程中小波系数及尺度函数系数的计算、小波系数的阈值选取和重构过程中尺度函数系数的计算，并给予了实现，获得较好的压缩性能和质量。

ABSTRACT This paper summarizes our researches on two key techniques in curve and surface modeling-the geometric approximation techniques and the geometric interpolation techniques. The former includes three types of geometric approximation techniques: Hybrid polynomial approximation to rational curves and surfaces, offset curves and surfaces approximation, interval Bézier curves and surfaces approximation. The latter includes a series of algorithms for shape blending modeling: the MSI algorithm for shape blending between space polylines or trees, the MSI algorithm for shape blending between triangular meshes, and skeleton-based shape blending algorithms using triangular decomposition and star-shape decomposition.

本文是作者对曲线曲面造型中两类核心技术几何逼近技术和几何插值技术的研究成果的总结，其中前者包括有理曲线曲面的Hybrid多项式逼近、等距曲线曲面逼近和区间曲线曲面逼近等三类几何逼近方法；后者包括用于形状混合造型的几何插值方法的一系列算法：空间多边形形状混合的MSI插值算法、三角网格形状混合的MSI插值算法、树的形状混合的MSI插值算法以及基于骨架树形状混合的三角剖分算法和星形剖分算法。

Because the error of normal vector will affect Delaunay triangular technique and the form of global triangular meshes directly, it is a key step to ensure normal vector .

由于法矢的错误将直接影响Delaunay三角剖分的结果进而影响整体三角网格的形成，所以法矢的确定是生成局部逼近平面的关键步骤。

According to the experiential data of the DRASTIC index, the standard values of 10 classes for 7 indexes are proposed in the form of triangular fuzzy numbers, and similarly the weights of indexes are expressed in the form of triangular fuzzy numbers.

参照DRASTIC方法的经验性数据，给出了10个级别7项指标以三角模糊数表示的标准特征值，给出了三角模糊数表示的指标权重。

A backer of an Afghan law that critics say legalizes marital rape has rejected the international outcry as foreign meddling.

饱受批评的一项法律的拥护者说合法化的婚内暴力不会受国际舆论的干涉。

Years ago, a ancient Egyptian fleet went to the Land of punt for seeking a kind of flavor named "myrrh", and aromatic plants which has dense exotic style for the queen Hatshepsut.

3500年前的一个古埃及的舰队到&彭特之地&寻找一种叫没药的香料。