球面坐标

Firstly, a spherical mesh with regular subdivision connectivity is constructed to partition the spherical domain into some small regions. Then the region, which contains the query point p, is found according to the position of p and selected as the search area for locating p. During the point location, the barycentric coordinates are used to extract local heuristic information about the location of p so as to find the shortest path from the start triangle to the target one containing p.

通过构造规则子分网格将原始球面网格区域划分成若干具有子分层次关系的查询小块；在进行查询前，根据查询点p的位置找到它所在的小块作为搜索区域，从而极大地缩小了查询范围；在查询过程中，根据重心坐标所包含的启发信息，选择一条从初始搜索三角形到目标三角形的最短查询路径。

Based on the theories of Differential Geometry and Geodesy,algorithms and formulas for direct and inverse solution of geodetic problem in the new form of geodetic coordinate system on the ellipsoidal surface are deduced in this paper.

基于地球椭球面上所构建的新型大地坐标系，推导出用新大地纵横坐标表述的大地主题解算公式，并研制了相应的正反解算法。

By constructing a sphere hexagonal grid system based on the Truncated Icosahedrons Projection, this paper focuses on the study of the address coding mechanism of the sphere hexagonal grids, including the hierarchy coding schemes, the study of the positional relations among the grid units and the mutual conversion between the address codes of the grid units and the geographical coordinates.

本文通过构建基于截顶正二十面体投影的球面六边形网格系统，对球面六边形网格的地址编码机制进行了重点研究，包括网格的层次编码方案、网格单元位置关系研究和网格单元地址码与地理坐标之间的相互转换。

The determination of projective coordinates in different reference ellipsoid ,which is with the transform between Ellipsoid elements in different reference ellipsoid ,gets the Coordinates in corresponding new Ellipsoid,and finally projects to horizontal coordinates.

位于不同参考椭球面下投影面坐标的求解，是通过不同参考椭球间椭球元素的转换，求得对应的新椭球体上的大地坐标，最后投影至平面坐标。

The formula for area of ellipsoidal triangle on earth ellipsoid by means of geodesic coordinate is derived in this paper. It is showed that the primary term is identical with the formula for area of plane triangle by planimetric rectangular coordinate in three angular point, while the expression of remainder terms has also regularity of its form. The presented formula can be applicable also to convex polygon on earth ellipsoid.

本文推导出用三顶点的测地坐标计算地球椭球面上三角形面积的公式，公式表明，其主项的表示式与按平面坐标求面积的计算式完全一致，而附加项的表示式亦有规律可循，因此该公式的适用范围可由椭球面三角形推广至椭球面上任意凸多边形。

This is the will of local coordinates into spherical coordinates, very practical.

这是将局部坐标系的坐标转化为球面坐标系的坐标，非常实用。

The use of spherical coordinates brings new certain difficuhy of numerical simulation, since partial differential equations might possess singularity at the center of ball.

然而，球面坐标的引入也给我们带来了新的困难，特别是偏微分方程在球的中心处会出现形式上的奇异性。

An initial spherical parameterization is firstly constructed by lifting planar parameterization to the sphere through the stereographic projection. Then we introduce an efficient approach based on bary centric coordinate to improve the initial spherical parameterization. At last, a uniform spherical parameterization is generated by a Moebius transformation.

通过立体投影将现有的平面参数化方法推广到球面上，得到一个初始的球面参数化；为了减小变形，引入质心坐标进行全局优化；最后用Moebius变换均匀化最终的球面网格。

As the most important factor in the proposed calibration methods, vanishing point are addressed through the whole paper.

该方法既不需要将直线投影到球面坐标，也不需要对大量直线作统计特性分析，当存在大量多余直线观测时，这种平差方法可快速、准确地计算出灭点的最优位置。

The paper discusses the position relationship between the litter circles of torus and the section circle of sphere figured out the intersection of torus and sphere when the central axis of torus and sphere center in XOZ coordinate plane through coordinate transformation.

利用坐标变换使圆环中心轴与球心同在XOZ平面内，讨论了在该平面内圆环截圆与球圆的位置不相交、相切和相交时圆环面和球面的相交情况，并给出了判别圆环面、球面相交情况的流程图以及圆环面和球面相交实例。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。