球面坐标：范围选择 - 最佳实践和方法表现
我正在编写一些处理坐标系、几何和其他类似内容的代码。 我想知道一般来说，关于球坐标的常见计算，哪种是存储球坐标的最常见/实用/有效的方法。 是：
theta - [0, 180)
phi - [0, 360)
还是
theta - [-90, 90)
phi - [-180, 180)
其他什么？
（为了清楚起见，上述坐标以弧度表示，但我通常会将它们保留为弧度以提高速度，因为数学函数通常是针对弧度实现的。）
我知道从数学方面来看，这是完全无关的，但我想知道某个选择是否会导致更容易或更有效的实施。
I am writing some code which deals with coordinate systems, geometry and other similar stuff.
I would like to know which is, in general, the most common/practical/efficient way for storing spherical coordinates, regarding common calculations on them.
Is it:
theta - [0, 180)
phi - [0, 360)
or
theta - [-90, 90)
phi - [-180, 180)
or something other?
(The above coordinates are expressed in radians for clarity, but I would normally keep them in radians to improve speed, since math functions are usually implemented for radians.)
I know that from a mathematical aspect, it is completely irrelevant, but I am wondering if a certain choice would result in an easier or more efficient implementation.
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一些想法：
这些表示在数学上确实是等价的。从一种转换为另一种将花费您几次浮点加法，分别为 pi/2 和 pi。与球体几何算术中常见的三角学、逆三角、乘法/除法和平方根计算相比，在通用硬件上进行这些加法的成本相形见绌。
有大量关于球体几何的算术文本，这些文本是多年来为处理地球导航而开发的。本文经常使用纬度/经度坐标系，分别为-90..+90 和-180..+180。要使用众所周知的公式而不进行转换，您可能需要坚持使用该坐标系。
A couple of thoughts:
The representations are indeed mathematically equivalent. Converting from one to the other will cost you a couple of floating point additions, by pi/2 and pi, respectively. The cost of those additions on common hardware pales in comparison to that of the trigonometry, reverse trig, multiplication/division, and square-root calculations that are common in the arithmetic of sphere geometry.
There is a large body of arithmetic text regarding sphere geometry that was developed over the years for dealing with navigation over the earth. This text often uses the latitude/longitude coordinate system, of -90..+90 and -180..+180, respectively. To use the well known formulas without conversion, you might want to stick with that coordinate system.