blocks|key|732864|text|在文章中解释了为什么使用四元数更好。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|732865|四元数表示法比|732866|表示法更紧凑，更不容易产生舍入误差|unordered-list-item|732867|四元数元素在R4中的单位球面上连续变化(表示为S3)，以避免不连续的跳跃(三维参数化所固有的)，这通常称为DCM的万向基准数表示法在四元数参数方面不涉及三角函数|732868|使用四元数积|732869|组合表示为四元数的两个单独旋转非常简单|732870|entityMap^0|0|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|O|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|P|8|@]|9|@]|A|$]]|$1|D|3|E|5|F|7|Q|8|@]|9|@]|A|$]]|$1|G|3|H|5|F|7|R|8|@]|9|@]|A|$]]|$1|I|3|J|5|F|7|S|8|@]|9|@]|A|$]]|$1|K|3|L|5|6|7|T|8|@]|9|@]|A|$]]|$1|M|3|-4|5|6|7|U|8|@]|9|@]|A|$]]]|N|$]]

Why it is better to use quaternions is explained in the article.

<ul>
<li>More compact than the DCM representation and less susceptible to round-off errors</li>
<li>The quaternion elements vary continuously over the unit sphere in R4, (denoted by S3) as the orientation changes, avoiding discontinuous jumps (inherent to three-dimensional parameterizations), this is often referred to as gimbal lock.</li>
<li>Expression of the DCM in terms of quaternion parameters involves no trigonometric functions</li>
<li>It is simple to combine two individual rotations represented as quaternions using a quaternion product</li>
</ul>

blocks|key|1933086|text|与欧拉角不同，四元数不会受到gimbal+lock的影响。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|1933087|entityMap|0|LINK|mutability|MUTABLE|url|http://en.wikipedia.org/wiki/Gimbal_lock^0|E|B|0|0^^$0|@$1|2|3|4|5|6|7|L|8|@]|9|@$A|M|B|N|1|O]]|C|$]]|$1|D|3|-4|5|6|7|P|8|@]|9|@]|C|$]]]|E|$F|$5|G|H|I|C|$J|K]]]]

Unlike Euler angles, quaternions don't suffer from <a href="http://en.wikipedia.org/wiki/Gimbal_lock" rel="nofollow noreferrer">gimbal lock</a>.

blocks|key|1933128|text|我不同意四元数更容易可视化的说法，但使用它们的主要原因是，它很容易在没有“矩阵爬行”的情况下连接旋转。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1933129|entityMap^0|0^^$0|@$1|2|3|4|5|6|7|D|8|@]|9|@]|A|$]]|$1|B|3|-4|5|6|7|E|8|@]|9|@]|A|$]]]|C|$]]

I disagree that quaternions are easier to visualize, but the main reason for using them is that it's easy to concatenate rotations without "matrix creep".

blocks|key|1933072|text|四元数通常用于简化计算-当使用四元数时，做像合成变换这样的事情要容易得多(也更快)。引用你链接的维基百科页面，|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1933073|1933074|将两个连续的旋转组合在一起，每个旋转都由欧拉轴和角度表示，这并不简单，实际上也不满足矢量相加定律，这表明有限旋转根本不是真正的矢量。最好使用方向余弦矩阵(DCM)、张量或四元数表示法，计算乘积，然后转换回Euler轴和角度。|blockquote|1933075|1933076|1933077|它们也不存在与轴/角度形式gimbal+lock相同的问题。|offset|length|1933078|entityMap|0|LINK|mutability|MUTABLE|url|http://en.wikipedia.org/wiki/Gimbal_lock^0|0|0|0|0|0|D|B|0|0^^$0|@$1|2|3|4|5|6|7|T|8|@]|9|@]|A|$]]|$1|B|3|-4|5|6|7|U|8|@]|9|@]|A|$]]|$1|C|3|D|5|E|7|V|8|@]|9|@]|A|$]]|$1|F|3|-4|5|6|7|W|8|@]|9|@]|A|$]]|$1|G|3|-4|5|6|7|X|8|@]|9|@]|A|$]]|$1|H|3|I|5|6|7|Y|8|@]|9|@$J|Z|K|10|1|11]]|A|$]]|$1|L|3|-4|5|6|7|12|8|@]|9|@]|A|$]]]|M|$N|$5|O|P|Q|A|$R|S]]]]

Quaternions are generally used for calculative simplicity - it's a lot easier (and faster) to do things like composing transformations when using quaternions. To quote the Wikipedia page you linked,

<blockquote>
 Combining two successive rotations,
 each represented by an Euler axis and
 angle, is not straightforward, and in
 fact does not satisfy the law of
 vector addition, which shows that
 finite rotations are not really
 vectors at all. It is best to employ
 the direction cosine matrix (DCM), or
 tensor, or quaternion notation,
 calculate the product, and then
 convert back to Euler axis and angle.
</blockquote>

They also do not suffer from a problem common to axis/angle form, <a href="http://en.wikipedia.org/wiki/Gimbal_lock" rel="nofollow noreferrer">gimbal lock</a>.

blocks|key|2141503|text|四元数更易于可视化、管理和创建，在您希望围绕可轻松计算的特定轴旋转的场景中。确定单个旋转角度要比将旋转分解为多个角度容易得多。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|2141504|对OP的更正:向量表示旋转轴，而不是方向，并且旋转分量是半角度的余弦，而不是角度本身。|2141505|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|F|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|G|8|@]|9|@]|A|$]]|$1|D|3|-4|5|6|7|H|8|@]|9|@]|A|$]]]|E|$]]

Quaternions are easier to visualize, manage and create in scenarios where you want to rotate about a particular axis that can be easily calculated. Determining a single rotation angle is much easier than decomposing a rotation into multiple angles.

Corrections to the OP: the vector represents the axis of rotation, not a direction, and the rotation component is the cosine of the half-angle, not the angle itself.

blocks|key|632702|text|正如前面提到的，四元数不会受到给定旋转的影响，只有一个标准化的四元数表示。，gimble+lock.|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|632703|For，，|unordered-list-item|632704|，|632705|。可以有几个看似不相关的轴/角值导致相同的rotation.|632706|632707|
+|632708|632709|632710|​|632711|可以轻松组合|632712|四元数旋转。|632713|计算轴/角度符号非常复杂，它是另外两个轴/角度符号的累加|632714|632715|632716|632717|632718|浮点数在表示0.0到1.0之间的值时具有更高的精确度。|632719|632720|简而言之，轴/角度表示法最初看起来似乎是最合理的表示法，但在实践中，四元数缓解了轴/角度表示法带来的许多问题。|632721|entityMap|0|LINK|mutability|MUTABLE|url|http://en.wikipedia.org/wiki/Gimbal_lock^0|12|B|0|0|0|0|0|0|0|0|0|0|0|1|1|0|0|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|1E|8|@]|9|@$A|1F|B|1G|1|1H]]|C|$]]|$1|D|3|E|5|F|7|1I|8|@]|9|@]|C|$]]|$1|G|3|H|5|F|7|1J|8|@]|9|@]|C|$]]|$1|I|3|J|5|F|7|1K|8|@]|9|@]|C|$]]|$1|K|3|-4|5|6|7|1L|8|@]|9|@]|C|$]]|$1|L|3|M|5|6|7|1M|8|@]|9|@]|C|$]]|$1|N|3|-4|5|F|7|1N|8|@]|9|@]|C|$]]|$1|O|3|-4|5|6|7|1O|8|@]|9|@]|C|$]]|$1|P|3|Q|5|6|7|1P|8|@]|9|@]|C|$]]|$1|R|3|S|5|6|7|1Q|8|@]|9|@]|C|$]]|$1|T|3|U|5|F|7|1R|8|@]|9|@]|C|$]]|$1|V|3|W|5|F|7|1S|8|@]|9|@]|C|$]]|$1|X|3|-4|5|6|7|1T|8|@]|9|@]|C|$]]|$1|Y|3|-4|5|6|7|1U|8|@]|9|@]|C|$]]|$1|Z|3|Q|5|6|7|1V|8|@]|9|@]|C|$]]|$1|10|3|-4|5|6|7|1W|8|@]|9|@]|C|$]]|$1|11|3|12|5|F|7|1X|8|@]|9|@]|C|$]]|$1|13|3|-4|5|6|7|1Y|8|@]|9|@]|C|$]]|$1|14|3|15|5|6|7|1Z|8|@]|9|@]|C|$]]|$1|16|3|-4|5|6|7|20|8|@]|9|@]|C|$]]]|17|$18|$5|19|1A|1B|C|$1C|1D]]]]

<ul>
<li>As mentioned, quaternions don't suffer from <a href="http://en.wikipedia.org/wiki/Gimbal_lock" rel="nofollow noreferrer">gimble lock</a>.</li>
<li>For a given rotation, there is exactly one normalized quaternion representation.

<ul>
<li>There can be several seemingly unrelated axis/angle values that result in the same rotation.</li>
</ul></li>
<li>Quaternion rotations can be easily combined.

<ul>
<li>It is extraordinarily complex to calculate an axis/angle notation that is the cumulation of two other axis/angle rotations.</li>
</ul></li>
<li>Floating point numbers have a higher degree of accuracy when representing values between 0.0 and 1.0.</li>
</ul>

The short answer is that axis/angle notation can initially seem like the most reasonable representation, but in practice quaternions alleviate many problems that axis/angle notation presents.

Tell me if I am wrong.

I'm starting using quaternions. Using a rotation matrix 4 x 4 (as used in OpenGL), I can compute model view matrix multiplying the current model view with a rotation matrix. The rotation matrix is derived from the quaternion.

The quaternion is a direction vector (even not normalized) and a rotation angle. Resulted rotation is dependent on the direction vector module and the w quaternion component.

But why I should use quaternions instead of Euler axis/angle notation? The latter is simpler to visualize and to manage...

All information that I found could be synthetized with this beatifull article:

<a href="http://en.wikipedia.org/wiki/Rotation_representation" rel="nofollow noreferrer">http://en.wikipedia.org/wiki/Rotation_representation</a>

Quaternions and Transform Matrices

翻译质量差，导致语言生硬或混乱。

没有提供实际的解决方法或示例。

解答不清晰，无法理解或解决问题。

页面排版不美观，阅读体验差。

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如果我错了，请告诉我。我开始用四元数了。使用旋转矩阵4x4(就像在OpenGL中使用的那样)，我可以计算模型视图矩阵，将当前模型视图乘以旋转矩阵。旋转矩阵是由四元数导出的。四元数是方向向量(即使未规格化)和旋转角度。产生的旋转取决于方向向量模块和w四元数分量。但是为什么我应该使用四元数而不是Euler轴/角度符号呢？后者更易于可视化和管理……我找到的所有信息都可以用这篇漂亮的文章综合起来：

问四元数和变换矩阵
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