三角

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。

Triangular norms are a common form of conjunction operator to a real number based representation of the true value of a compound fuzzy proposition.

对基于单一数值表达的模糊命题间的合取、析取关系的最一般运算形式是三角范数和三角余范数。

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。

The weight vector of triangular fuzzy complementary judgement matrix is obtained by solving the model.

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，并利用已有的三角模糊数排序公式求得决策方案的排序。

In the second chapter, firstly, the definition of triangular matrix rings Γ, which is of order 3, is introduced.

在第二章中，我们首先引入了三级三角矩阵环Γ的定义，给出了三级三角矩阵环是左阿丁环、右阿丁环、阿丁R-代数的充分必要条件。

When it approaches the triangular limit ,the non-diagonal reflection matrix of triangular statistical model is obtained.

本文得到了ZnBelavin模型反射矩阵的矩阵元表达式，在退化到三角极限后，得到了非对角的三角统计模型的反射矩阵。

Based on the conventional ranking method of triangular fuzzy number complementary judge matrix and integrated with the conception of the mean value of triangular fuzzy number, an improved ranking method is proposed.

在传统的三角模糊数互补判断矩阵排序方法的基础上，结合三角模糊数均值的概念，提出了一种改进的排序方法。

The experiment results on remote sensing image segmentation show that the improved method effectively increases the speed of image segmentation based on the texture,and keeps the accurateness of the fractal dimension with the triangular prism method.

利用此法对遥感图像进行分割，结果表明：改进后的三角棱柱面法提高了基于遥感图像纹理特征的图像分割方法的计算速度，同时保留了三角棱柱面法对于分形维数计算的准确性。

The calculated results show: the ground state structures of PtNi5, Pt2Ni4 and Pt3Ni3 clusters are quadrangular bi-pyramid, and Pt4Ni2 and Pt5Ni clusters are triangular bi-pyramid with hat and triangular pyramid with quadrilateral, respectively. From the point of view of thermodynamics, PtnNim clusters are stable because of the negative enthalpy of formation; the positive NICS of PtNi5 clusters show anti-aromaticity, The negative NICS of Pt2Ni4 and Pt5Ni clusters show aromaticity. The number of the IR absorption peak of Pt3Ni3 is the most. The IR and raman absorption peak of PtNi5 , IR of Pt2Ni4, Raman of Pt3Ni3 and Pt4Ni2 have only one. The absorption peak of Pt5Ni appears in the bigger frequencies only, and is zero almost in the small frequencies.

研究结果表明：PtNi5、、Pt2Ni4、Pt3Ni3团簇的基态结构都为四角双锥结构，Pt4Ni2 和Pt5Ni团簇的基态结构分别是戴帽三角双锥和三角锥戴四边形结构；PtnNim团簇的生成焓都为负值，表明团簇在热力学上是稳定的；由NICS值可得，PtNi5团簇具有反芳香性，Pt2Ni4和Pt5Ni团簇具有芳香性；从光谱分析来看，Pt3Ni3团簇的IR较强吸收峰的个数最多，PtNi5团簇的IR和Raman、Pt2Ni4团簇的IR、Pt3Ni3和Pt4Ni2团簇的Raman只有一个强吸收峰值，Pt5Ni团簇的峰值只出现在频率较大的位置，频率小的位置几乎为零。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。