球面三角形

Compilation of the plane trigonometry and spherical trigonometry book, spherical trigonometry to solve some problems in, and first proposed the introduction of auxiliary angle method to solve the triangle .

编撰了有关平面三角学和球面三角学的著作，解决了球面三角学中的若干难题，并首先提出引进辅助角的方法解三角形。

Compilation of the plane trigonometry and spherical trigonometry book, spherical trigonometry to solve some problems in, and first proposed the method to solve the introduction of auxiliary angle triangles .

编撰了有关平面三角学和球面三角学的著作，解决了球面三角学中的若干难题，并首先提出引进辅助角的方法解三角形。

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。

According to the principle of the diameter of a circle corresponding to the right angle and the principle of short side for little angle in right triangle, projecting the initially-chosen point to the hyper-planes of the linear equation group in which every linear equation can be regarded as a hyper-plane and the projection points can be obtained. The initially-chosen point, and one arbitrary projection point, and the solution point are all on the surface of the relative hyper-geometry ball, therein-to, there is a projection point which is nearest to the solution point and it can be regarded as the next iterative initially-chosen point, so the solution problem of the linear equation group can be changed as an iterative problem of approaching the solution on the surface of a hyper-geometry ball.

根据直径对应的圆周角足直角以及直角三角形中短边对小角的原理进一步知道，当将初始点向线性方程组中各个方程所代表的超平面上投影得到投影点时，初始点和其任何一个投影点及方程组的解点都将位于一个相应的超球面上，其中必定存在一个投影点离问题解点的距离最短，即把该点作为下一次迭代的初始点，从而可将线性方程组求解的问题变成球面上逼近解点的迭代问题。

In order to generate spherical equal-area grid,this paper finds the corresponding relationships between unfolded icosahedron and sphere using Snyder equal-area projection.

文中利用Snyder等积多面体投影建立了平面与球面的对应关系，设计了球面等积三角形和四边形离散网格的生成算法。

As we all know,there is one Simson line at any point on the circumference of triangles,but in this paper, LHP theorem shows that the above conclusion is not correct for any quadrilateral pyramid in three-dimensional space and also during proving LHP theorem,fixed value theorem is proved,at the same time,one guess about the point H and point P on circumscribed sphere of tetrahedron has been concluded.

众所周知，三角形的外接圆周上任一点存在一条 simson 线，而 LHP 定理则指出对于正四面体该结论是不能推广到三维空间上的，并且在论证 LHP 定理的过程中得出了定值定理，同时作为一般四面体的外接球球面上的 H 点、P 点的分布，给出了一个猜想。

The results show that the design method which unifies the stereographic projection and the spherical triangle analytic geometry is one kind of both simple and the quick methods.

研究表明，采用极射赤平投影和球面三角形解析几何相结合的设计计算方法，是一种既简便又快捷的定向钻进轨迹设计方法。

Angular exported, but can prove that the proposed formula is applicable to any spherical triangle .

角形导出的，但是能够证明所得公式适用于任何球面三角形。

Second, he made an integrated discussion on the existence and uniqueness of solution for spherical trigonometry.

其二，球面三角形解的存在性和唯一性的讨论。

In chapter 3, the characteristics of relative motion of small satellite based on ground station are firstly analyzed, in which using spherical trigometry, the analytic formulas evaluating the longitude ranges of ascending node which can cover the target are deduced with J2 precession. With the solution, the longitude ranges of ascending node limited by the cross-time can be gained. Secondly, a serious of characteristics of small satellite to space station is studied.

在第3章，首先分析了卫星相对地基的运动特性，在地基的运动特性研究中，重点研究了以升交点地理经度来描述所有能覆盖到目标点的轨道，利用球面三角形方法推导了在考虑地球形状J2项摄动影响时，各种情况下能覆盖目标点的轨道升交点经度范围，得到了完整的解析表达式。

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。