四元数和归一化 [英] Quaternion and normalization

问题描述

我知道如果我想旋转一个向量，需要对四元数进行归一化.

I know that quaternions need to be normalized if I want to rotate a vector.

但是有什么理由不自动规范化四元数吗?如果有，哪些四元数运算会导致非标准化四元数?

But are there any reasons to not automatically normalize a quaternion? And if there are, what quaternion operations do result in non-normalized quaternions?

• 两个四元数相乘?
• 点积?

对不起，如果这个问题有点模糊.我仍在尝试围绕四元数.

Sorry, if this question is a little bit fuzzy. I'm still trying wrap my head around quaternions.

推荐答案

任何产生四元数的操作都需要归一化，因为浮点进动错误会导致它不是单位长度.

Any operation that produces a quaternion will need to be normalized because floating-point precession errors will cause it to not be unit length.

出于性能原因，我建议不要使用标准例程自动执行规范化.任何有能力的程序员都应该意识到精度问题，并能够在必要时对数量进行归一化 - 而且并不总是需要单位长度的四元数.

I would advise against standard routines performing normalization automatically for performance reasons. Any competent programmer should be aware of the precision issues and be able to normalize the quantities when necessary - and it is not always necessary to have a unit length quaternion.

向量运算也是如此.

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