如果你知道你所在的高度和周围的位置，原则上就可以确定你在球面上的位置。
If you know how high you are and where you are around, in principle you know where you are on the sphere.
在中国，我们正在使用500米口径球面射电望远镜寻找太空中的星星。
在很多甚至是大多数以太空为主题的电影中，每当地球面临灾难时，解决办法总是乘坐宇宙飞船逃离这个地球。
In many—even most-space—themed films, whenever Earth faces a disaster,the solution is always running away from the planet in spaceships.
他研究的主题的技术术语是非谐性，非球面性，非弹性以及畸形的。
The technical terms for the subjects of his studies are anharmonicity, asphericity, inelasticity, as well as anisotropy.
总是可以找到球面的一部分以它为界。
I can always find a portion of the sphere that's bounded by it.
大圆弧长计算球面两点之间的最短距离。
The great-circle distance calculates the shortest distance between any two points on the surface of a sphere.
这个有裂痕的球面，确实有一个边界是该回路。
But, that spherical thing with a little slit going twisting into it will actually have boundary my loop.
先作出半径为a的球面，再画出给定的向量场。
另外一种想法是从这个点出发，因为在球面上，所以ρ是。
The other way to think about it is at this point, 1 well, rho is equal to one because you are on the sphere.
看一看的话，能看到类似于球面小块的玩意，但是它有厚度。
So anyway, if you look at, now, something that's a bit like that piece of sphere, but with some thickness to it.
例如，对于一个单位球面，仅用x,y,z计算就可以。
For example, if this was the unit sphere then I would just put x, y, z.
球面上的两点确定一条圆弧，因此任意两点可将橙子切成两块。
Two points determine a great circle on a sphere, so for any two points, cut the orange into half.
当然有，你可以做一个球面，或者，只要不是这样的圆盘都行？
Yeah, I can take the sphere, you know, for example, or anything that's just not quite the disk?
空间可以向球面一样有正的曲率，也可以像马鞍面一样有负的曲率。
Space can have positive curvature, like the surface of a sphere, or negative curvature, like the surface of a saddle.
不妨想一想，考虑一个水平面，一个垂直面，或是一个球面时的做法。
That is, for example, what we do when we look at, say, a horizontal plane or a vertical plane or a sphere or a cylinder.
当两点之间的距离相隔很远和要求更高的准确度时，需要使用球面模型。
The spherical model is better-suited when distances are further apart and more accuracy is needed.
它还可以支持各种碰撞原语(例如球面碰撞和平面碰撞)和几个碰撞空间。
It also supports a variety of collision primitives (such as sphere and plane) and several collision Spaces.
我希望大家能够了解，如果我将法向量平移至球面，那么它将以原点为心向外放射。
Hopefully, you can see that if I take a normal vector to the sphere it is actually pointing radially out away from the origin.
在其他情况下使用球面模型，所使用的主要距离计算为大圆弧长(参见参考资料)。
In other cases, a spherical model is used, and the primary distance calculation used is the great-circle distance (see Resources).
只有我们两国的积极合作，才能很好的应对21世纪全球面临的主要挑战。
No major global challenge of the 21st century can be addressed without the active collaboration of our two countries.
splot命令默认使用的是笛卡儿坐标系，不过也可以支持球面或柱面坐标系。
The splot command is Cartesian by default but can also support spherical and cylindrical coordinates.
我们建立有两个变量φ和θ的球面的参数方程,它们恰好是,球坐标系统的一部分。
We are finding a parametric equation for the sphere using two variables phi and theta which happen to be part of the spherical coordinate system.
已知以原点为心，以a为半径的球面，也可以说是半球面或是球面的一部分。
Let's say that I gave you a sphere of radius a centered at the origin, or maybe just half of that sphere or some portion of it.
比如说，我可以选择，一个半球面，或者我可以选一个…，先叫它，诶…，一个尖的曲面。
I could choose, for example, s1 a half sphere if I want or I can choose, let's call that s1, s2 I don't know, a pointy thing, s2.
它垂直于其表面指向外面，但这与球面法向量的指向的方式有点不同，圆柱的边缘是竖直的。
Well, it is sticking straight out, but sticking straight out in a slightly different way from what happens with a sphere. See, the sides of a cylinder are vertical.
全球面临的问题也将不再是艾滋病能否得以根除，而是人们是否做好了支付药价的准备。
The question for the world will no longer be whether it can wipe out the plague, but whether it is prepared to pay the price.
安置单分子并将其呈球面对称放置对于生命来说必不可少，这也能让研究者对两者进行更深入研究。
Placing a molecule that's essential to life within a spherically symmetrical one could let researchers learn more about each.
从这些球面可以看出海平面的高度异常，红色意味着比平均值高，而蓝色则指比平均值低。
The globes show sea surface height anomalies, which means places where the water surface is higher (red) or lower (blue) than average.
从这些球面可以看出海平面的高度异常，红色意味着比平均值高，而蓝色则指比平均值低。
The globes show sea surface height anomalies, which means places where the water surface is higher (red) or lower (blue) than average.
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