几何基础

It, as a basic step in many algorithms, is also an important part in computational geometry.

它也是计算几何的重要内容之一，是许多其它算法的基础。

By analyzing the characteristics of seismic rupture process and considering the three hypothetical conditions of similarity satisfied by earthquake,i e geometrical, stress environment and dynamic similarities of fault planes, the authous have studied the scaling analysis of similarity between earthquakes with various magnitudes and set up the scaling relation between sou.

本文根据Heaskel二维矩形地震破裂模式，导出了以ω立方的波谱衰减，在分析地震破裂过程特征、考虑三个主要的相似性假定基础上，即假定地震满足断层面几何相似、应力环境相似和动力学相似条件，研究了大小地震相似性问题的标度分析，建立了地震破裂和源参数之间的标定律关系。

Based on differential geometry and spatial engaging theory,a set of formula of conical surface double enveloping worm gearing had been derived and its figures,position and distribution had been depicted by graphs.

以微分几何与空间啮合理论为基础，推导了锥面二次包络圆柱蜗杆传动两次包络过程中的啮合方程和主要啮合性能指标方程，以图直观的表示出其形状、位置和分布状况。

A new method for the generation of curvilinear grid has been proposed. Some curvilinear grid generation examples show that satisfactory grids can be generated for simple-connected regions and connected- regions with complex boundary by using the proposed adjusting factors.

3提出了一种生成边界处正交曲线网格的新方法，收敛速度快，在复杂边界流场区域的数值计算中，有很大的实用价值；为了克服复杂几何边界给数值计算带来的困难，提高通用性以及水流的预测精度，本文采用上述网格生成技术，在直角坐标系三维非恒定明渠紊流的沿层积分数值模型基础上，发展了曲线坐标系下的多层紊流水动力模型。

Firstly, the development of the spherical robot is introduced and according to the knowledge of the research forepassed, the nonholonomy and the nonlinear controllability for a spherical robot based on the principle of angular momentum conservation are discussed with the differential geometric control theory.

首先介绍了球形机器人的发展状况，在了解前人研究领域的基础上，应用微分几何控制理论，对此角动量守恒的球形机器人的非完整性和非线性可控性进行了研究。

On the basis of analyzing the lilnitations of the conventional flow equation for rotameter , ac-cording to principle of mechanical energy conservation and transform for real fluid, a new generalflow equation Q=for rotameter has been developed.This equation includes the rota-form factor β to reflect the influence of rota-form on flowmeasurement.

在分析转子流量计习用流量方程局限性的基础上，根据实际流体机械能守恒与转换原理，定义了反映转子形状特征对流量测定影响的转子几何形状因子β；经过推导，最终获得了转子流量计一种新的普遍流量方程Q＝。

Secondly, based on the research of the fabric"s contexture characteristic, the author puts forward using the convex shape as yarn"s section, builds the yarns dimensional geometry model and axes equation of warp and weft. Establishes the illumination model which is fit for fabric with illumination theory.

在研究织物组织模拟的基础上，提出以凸透镜形作为纱线截面，建立了相应的纱线空间几何模型和经、纬纱轴线方程；利用光照理论，结合织物的特点，建立了适用于织物的光照模型。

On this foundation, the followingfew problems are resolved. Firstly, we have a kinematic density formula for pairs of needles by using thekinematic density formula for pairs of oriented lines. The geometric probability thatthe random pairs of needles intersect at a point in convex body K is considered.

在此基础上，重点解决了以下几个问题：首先利用R~2上有向直线偶的运动不变密度公式，得到了针偶的运动不变密度公式，考虑了针偶与凸体K相交且针偶的交点属于K的这样一个几何概率问题。

In this paper,the methods of distance geometry are used to explore the angles of a simplex ,and the second cosine law of a simplex in another form is obtained.

运用距离几何的研究方法，研究了和单形相关的角，给出了单形第二余弦定理的另一种形式，以此为基础得出了BartO¨s体积公式一种简洁的证法；探讨了单形的几个体积公式之间的联系，并推广了单形的一个体积公式。

Considering the dispersity, covertness and fuzziness of drawing information, we propose a layered interpretation technology for engineering drawing based on geometry complexity. This technology uses layered organization of drawing information and primitive layered recognition based on the integration of drawing information to get the entity.

本文针对图样信息分散性、隐含性、模糊性的特点，引入了图样信息几何复杂度的概念，在此基础上提出了工程图样的层次理解技术，即通过对图样信息的分层组织和基于图样信息集成的基元体分层识别得到图样所表达的形体。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。