近似逆三角函数 [英] Approximating inverse trigonometric functions

问题描述

我必须在只有以下数学工具的环境中实现asin，acos和atan:

I have to implement asin, acos and atan in environment where I have only following math tools:

• 正弦波
• 余弦
• 基本定点算法(不提供浮点数)

我也已经具有相当好的平方根函数.

I also already have reasonably good square root function.

我可以使用它们来实现合理有效的逆三角函数吗?

我不需要太大的精度(无论如何，浮点数的精度都非常有限)，基本近似就可以了.

I don't need too big precision (the floating point numbers have very limited precision anyways), basic approximation will do.

我已经半数决定使用表查找，但是我想知道是否有一些更整洁的选择(不需要花几百行代码即可实现基本数学).

I'm already half decided to go with table lookup, but I would like to know if there is some neater option (that doesn't need several hundred lines of code just to implement basic math).

要清除这些问题:我需要以每秒35帧的速度每帧运行数百次该功能.

To clear things up: I need to run the function hundreds of times per frame at 35 frames per second.

推荐答案

arcsin(x)函数是否需要较大的精度?如果否，则可以在N个节点中计算arcsin，并将值保留在内存中.我建议使用行近似.如果x = A*x_(N) + (1-A)*x_(N+1)，则x = A*arcsin(x_(N)) + (1-A)*arcsin(x_(N+1))其中arcsin(x_(N))是已知的.

Do you need a large precision for arcsin(x) function? If no you may calculate arcsin in N nodes, and keep values in memory. I suggest using line aproximation. if x = A*x_(N) + (1-A)*x_(N+1) then x = A*arcsin(x_(N)) + (1-A)*arcsin(x_(N+1)) where arcsin(x_(N)) is known.

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