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godot-docs-l10n/classes/zh_CN/class_quaternion.rst
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.. _class_Quaternion:
Quaternion
==========
代表 3D 旋转的单位四元数。
.. rst-class:: classref-introduction-group
描述
----
**Quaternion** 即四元数，是一种内置的 :ref:`Variant<class_Variant>` 类型，这种 4D 数据结构使用\ `哈密顿四元数 <https://zh.wikipedia.org/zh-cn/%E5%9B%9B%E5%85%83%E6%95%B0%E4%B8%8E%E7%A9%BA%E9%97%B4%E6%97%8B%E8%BD%AC>`__\ 来代表旋转。\ :ref:`Basis<class_Basis>` 类型能够同时存储旋转和缩放，而四元数\ *只能*\ 存储旋转。
\ **Quaternion** 由 4 个浮点分量组成：\ :ref:`w<class_Quaternion_property_w>`\ 、\ :ref:`x<class_Quaternion_property_x>`\ 、\ :ref:`y<class_Quaternion_property_y>`\ 、\ :ref:`z<class_Quaternion_property_z>`\ 。这些分量在内存中非常紧凑，因此部分运算更加高效、造成的浮点数误差也更低。\ :ref:`get_angle()<class_Quaternion_method_get_angle>`\ 、\ :ref:`get_axis()<class_Quaternion_method_get_axis>`\ 、\ :ref:`slerp()<class_Quaternion_method_slerp>` 等方法与 :ref:`Basis<class_Basis>` 中的版本相比也更快。
四元数的入门知识请观看 `3Blue1Brown 的这个视频 <https://www.bilibili.com/video/BV1SW411y7W1/>`__\ 。四元数背后的数学原理并不需要理解，因为 Godot 提供了一些辅助方法能够帮你处理相关的情况。其中包含 :ref:`slerp()<class_Quaternion_method_slerp>`\ 、\ :ref:`spherical_cubic_interpolate()<class_Quaternion_method_spherical_cubic_interpolate>` 以及 ``*`` 运算符。
\ **注意：**\ 用于旋转前，必须将四元数归一化（见 :ref:`normalized()<class_Quaternion_method_normalized>`\ ）。
\ **注意：**\ 与 :ref:`Vector2<class_Vector2>` 和 :ref:`Vector3<class_Vector3>` 类似，四元数的分量默认使用的是 32 位精度，而 :ref:`float<class_float>` 则是 64 位。如果需要双精度，请使用 ``precision=double`` 选项编译引擎。
.. note::
通过 C# 使用该 API 时会有显著不同，详见 :ref:`doc_c_sharp_differences`\ 。
.. rst-class:: classref-introduction-group
教程
----
- `3Blue1Brown 关于四元数的视频 <https://www.youtube.com/watch?v=d4EgbgTm0Bg>`__
- `在线四元数可视化 <https://quaternions.online/>`__
- `使用 3D 变换 <../tutorials/3d/using_transforms.html#interpolating-with-quaternions>`__
- `第三人称射击（TPS）演示 <https://godotengine.org/asset-library/asset/2710>`__
- `高级四元数可视化 <https://iwatake2222.github.io/rotation_master/rotation_master.html>`__
.. rst-class:: classref-reftable-group
属性
----
.. table::
:widths: auto
+---------------------------+---------------------------------------+---------+
| :ref:`float<class_float>` | :ref:`w<class_Quaternion_property_w>` | ``1.0`` |
+---------------------------+---------------------------------------+---------+
| :ref:`float<class_float>` | :ref:`x<class_Quaternion_property_x>` | ``0.0`` |
+---------------------------+---------------------------------------+---------+
| :ref:`float<class_float>` | :ref:`y<class_Quaternion_property_y>` | ``0.0`` |
+---------------------------+---------------------------------------+---------+
| :ref:`float<class_float>` | :ref:`z<class_Quaternion_property_z>` | ``0.0`` |
+---------------------------+---------------------------------------+---------+
.. rst-class:: classref-reftable-group
构造函数
--------
.. table::
:widths: auto
+-------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`Quaternion<class_Quaternion_constructor_Quaternion>`\ (\ ) |
+-------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`Quaternion<class_Quaternion_constructor_Quaternion>`\ (\ from\: :ref:`Quaternion<class_Quaternion>`\ ) |
+-------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`Quaternion<class_Quaternion_constructor_Quaternion>`\ (\ arc_from\: :ref:`Vector3<class_Vector3>`, arc_to\: :ref:`Vector3<class_Vector3>`\ ) |
+-------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`Quaternion<class_Quaternion_constructor_Quaternion>`\ (\ axis\: :ref:`Vector3<class_Vector3>`, angle\: :ref:`float<class_float>`\ ) |
+-------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`Quaternion<class_Quaternion_constructor_Quaternion>`\ (\ from\: :ref:`Basis<class_Basis>`\ ) |
+-------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`Quaternion<class_Quaternion_constructor_Quaternion>`\ (\ x\: :ref:`float<class_float>`, y\: :ref:`float<class_float>`, z\: :ref:`float<class_float>`, w\: :ref:`float<class_float>`\ ) |
+-------------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
.. rst-class:: classref-reftable-group
方法
----
.. table::
:widths: auto
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`float<class_float>` | :ref:`angle_to<class_Quaternion_method_angle_to>`\ (\ to\: :ref:`Quaternion<class_Quaternion>`\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`float<class_float>` | :ref:`dot<class_Quaternion_method_dot>`\ (\ with\: :ref:`Quaternion<class_Quaternion>`\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`exp<class_Quaternion_method_exp>`\ (\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`from_euler<class_Quaternion_method_from_euler>`\ (\ euler\: :ref:`Vector3<class_Vector3>`\ ) |static| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`float<class_float>` | :ref:`get_angle<class_Quaternion_method_get_angle>`\ (\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Vector3<class_Vector3>` | :ref:`get_axis<class_Quaternion_method_get_axis>`\ (\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Vector3<class_Vector3>` | :ref:`get_euler<class_Quaternion_method_get_euler>`\ (\ order\: :ref:`int<class_int>` = 2\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`inverse<class_Quaternion_method_inverse>`\ (\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>` | :ref:`is_equal_approx<class_Quaternion_method_is_equal_approx>`\ (\ to\: :ref:`Quaternion<class_Quaternion>`\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>` | :ref:`is_finite<class_Quaternion_method_is_finite>`\ (\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>` | :ref:`is_normalized<class_Quaternion_method_is_normalized>`\ (\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`float<class_float>` | :ref:`length<class_Quaternion_method_length>`\ (\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`float<class_float>` | :ref:`length_squared<class_Quaternion_method_length_squared>`\ (\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`log<class_Quaternion_method_log>`\ (\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`normalized<class_Quaternion_method_normalized>`\ (\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`slerp<class_Quaternion_method_slerp>`\ (\ to\: :ref:`Quaternion<class_Quaternion>`, weight\: :ref:`float<class_float>`\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`slerpni<class_Quaternion_method_slerpni>`\ (\ to\: :ref:`Quaternion<class_Quaternion>`, weight\: :ref:`float<class_float>`\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`spherical_cubic_interpolate<class_Quaternion_method_spherical_cubic_interpolate>`\ (\ b\: :ref:`Quaternion<class_Quaternion>`, pre_a\: :ref:`Quaternion<class_Quaternion>`, post_b\: :ref:`Quaternion<class_Quaternion>`, weight\: :ref:`float<class_float>`\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`spherical_cubic_interpolate_in_time<class_Quaternion_method_spherical_cubic_interpolate_in_time>`\ (\ b\: :ref:`Quaternion<class_Quaternion>`, pre_a\: :ref:`Quaternion<class_Quaternion>`, post_b\: :ref:`Quaternion<class_Quaternion>`, weight\: :ref:`float<class_float>`, b_t\: :ref:`float<class_float>`, pre_a_t\: :ref:`float<class_float>`, post_b_t\: :ref:`float<class_float>`\ ) |const| |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
.. rst-class:: classref-reftable-group
运算符
------
.. table::
:widths: auto
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>` | :ref:`operator !=<class_Quaternion_operator_neq_Quaternion>`\ (\ right\: :ref:`Quaternion<class_Quaternion>`\ ) |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`operator *<class_Quaternion_operator_mul_Quaternion>`\ (\ right\: :ref:`Quaternion<class_Quaternion>`\ ) |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------+
| :ref:`Vector3<class_Vector3>` | :ref:`operator *<class_Quaternion_operator_mul_Vector3>`\ (\ right\: :ref:`Vector3<class_Vector3>`\ ) |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`operator *<class_Quaternion_operator_mul_float>`\ (\ right\: :ref:`float<class_float>`\ ) |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`operator *<class_Quaternion_operator_mul_int>`\ (\ right\: :ref:`int<class_int>`\ ) |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`operator +<class_Quaternion_operator_sum_Quaternion>`\ (\ right\: :ref:`Quaternion<class_Quaternion>`\ ) |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`operator -<class_Quaternion_operator_dif_Quaternion>`\ (\ right\: :ref:`Quaternion<class_Quaternion>`\ ) |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`operator /<class_Quaternion_operator_div_float>`\ (\ right\: :ref:`float<class_float>`\ ) |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`operator /<class_Quaternion_operator_div_int>`\ (\ right\: :ref:`int<class_int>`\ ) |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>` | :ref:`operator ==<class_Quaternion_operator_eq_Quaternion>`\ (\ right\: :ref:`Quaternion<class_Quaternion>`\ ) |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------+
| :ref:`float<class_float>` | :ref:`operator []<class_Quaternion_operator_idx_int>`\ (\ index\: :ref:`int<class_int>`\ ) |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`operator unary+<class_Quaternion_operator_unplus>`\ (\ ) |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`operator unary-<class_Quaternion_operator_unminus>`\ (\ ) |
+-------------------------------------+-----------------------------------------------------------------------------------------------------------------+
.. rst-class:: classref-section-separator
----
.. rst-class:: classref-descriptions-group
常量
----
.. _class_Quaternion_constant_IDENTITY:
.. rst-class:: classref-constant
**IDENTITY** = ``Quaternion(0, 0, 0, 1)`` :ref:`🔗<class_Quaternion_constant_IDENTITY>`
单位四元数，代表无旋转。这与 :ref:`Basis.IDENTITY<class_Basis_constant_IDENTITY>` 具有相同的旋转。
如果一个 :ref:`Vector3<class_Vector3>` 被该四元数旋转（乘以），则它不会改变。
\ **注意：**\ 在 GDScript 中，该常量等价于不带任何参数创建 :ref:`Quaternion<class_Quaternion_constructor_Quaternion>`\ 。可以用来让代码更加清晰，并且与 C# 保持一致。
.. rst-class:: classref-section-separator
----
.. rst-class:: classref-descriptions-group
属性说明
--------
.. _class_Quaternion_property_w:
.. rst-class:: classref-property
:ref:`float<class_float>` **w** = ``1.0`` :ref:`🔗<class_Quaternion_property_w>`
四元数的 W 分量。这是“实数”的部分。
\ **注意：**\ 四元数分量通常不应被直接操作。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_property_x:
.. rst-class:: classref-property
:ref:`float<class_float>` **x** = ``0.0`` :ref:`🔗<class_Quaternion_property_x>`
四元数的 X 分量。这是沿“虚数” ``i`` 轴的值。
\ **注意：**\ 四元数分量通常不应被直接操作。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_property_y:
.. rst-class:: classref-property
:ref:`float<class_float>` **y** = ``0.0`` :ref:`🔗<class_Quaternion_property_y>`
四元数的 Y 分量。这是沿“虚数” ``j`` 轴的值。
\ **注意：**\ 四元数分量通常不应被直接操作。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_property_z:
.. rst-class:: classref-property
:ref:`float<class_float>` **z** = ``0.0`` :ref:`🔗<class_Quaternion_property_z>`
四元数的 Z 分量。这是沿“虚数” ``k`` 轴的值。
\ **注意：**\ 四元数分量通常不应被直接操作。
.. rst-class:: classref-section-separator
----
.. rst-class:: classref-descriptions-group
构造函数说明
------------
.. _class_Quaternion_constructor_Quaternion:
.. rst-class:: classref-constructor
:ref:`Quaternion<class_Quaternion>` **Quaternion**\ (\ ) :ref:`🔗<class_Quaternion_constructor_Quaternion>`
构造与 :ref:`IDENTITY<class_Quaternion_constant_IDENTITY>` 相同的 **Quaternion**\ 。
\ **注意：**\ 在 C# 中构造的 **Quaternion** 的所有分量都为 ``0.0``\ 。
.. rst-class:: classref-item-separator
----
.. rst-class:: classref-constructor
:ref:`Quaternion<class_Quaternion>` **Quaternion**\ (\ from\: :ref:`Quaternion<class_Quaternion>`\ )
构造给定 **Quaternion** 的副本。
.. rst-class:: classref-item-separator
----
.. rst-class:: classref-constructor
:ref:`Quaternion<class_Quaternion>` **Quaternion**\ (\ arc_from\: :ref:`Vector3<class_Vector3>`, arc_to\: :ref:`Vector3<class_Vector3>`\ )
构造一个表示 ``arc_from`` 和 ``arc_to`` 之间最短弧的 **Quaternion**\ 。这些可以想象为与球体表面相交的两个点，球面半径为 ``1.0``\ 。
.. rst-class:: classref-item-separator
----
.. rst-class:: classref-constructor
:ref:`Quaternion<class_Quaternion>` **Quaternion**\ (\ axis\: :ref:`Vector3<class_Vector3>`, angle\: :ref:`float<class_float>`\ )
构造一个 **Quaternion**\ ，表示围绕 ``axis`` 旋转给定的 ``angle`` 弧度。该轴必须是一个归一化向量。
.. rst-class:: classref-item-separator
----
.. rst-class:: classref-constructor
:ref:`Quaternion<class_Quaternion>` **Quaternion**\ (\ from\: :ref:`Basis<class_Basis>`\ )
根据给定的旋转 :ref:`Basis<class_Basis>` 构造一个 **Quaternion**\ 。
该构造函数比 :ref:`Basis.get_rotation_quaternion()<class_Basis_method_get_rotation_quaternion>` 更快，但给定的基必须是\ *正交归一化的*\ （请参阅 :ref:`Basis.orthonormalized()<class_Basis_method_orthonormalized>`\ ）。否则，构造函数将失败并返回 :ref:`IDENTITY<class_Quaternion_constant_IDENTITY>`\ 。
.. rst-class:: classref-item-separator
----
.. rst-class:: classref-constructor
:ref:`Quaternion<class_Quaternion>` **Quaternion**\ (\ x\: :ref:`float<class_float>`, y\: :ref:`float<class_float>`, z\: :ref:`float<class_float>`, w\: :ref:`float<class_float>`\ )
构造一个由给定值定义的 **Quaternion**\ 。
\ **注意：**\ 只有归一化的四元数才表示旋转；如果这些值没有归一化，则新的 **Quaternion** 将不是有效的旋转。
.. rst-class:: classref-section-separator
----
.. rst-class:: classref-descriptions-group
方法说明
--------
.. _class_Quaternion_method_angle_to:
.. rst-class:: classref-method
:ref:`float<class_float>` **angle_to**\ (\ to\: :ref:`Quaternion<class_Quaternion>`\ ) |const| :ref:`🔗<class_Quaternion_method_angle_to>`
返回这个四元数与 ``to`` 之间的角度。这是从一个旋转到另一个旋转所需的角度大小。
\ **注意：**\ 该方法的浮点数误差异常地高，因此 ``is_zero_approx`` 等方法的结果不可靠。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_dot:
.. rst-class:: classref-method
:ref:`float<class_float>` **dot**\ (\ with\: :ref:`Quaternion<class_Quaternion>`\ ) |const| :ref:`🔗<class_Quaternion_method_dot>`
返回该四元数与 ``with`` 的点积。
等价于 ``(quat.x * with.x) + (quat.y * with.y) + (quat.z * with.z) + (quat.w * with.w)``\ 。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_exp:
.. rst-class:: classref-method
:ref:`Quaternion<class_Quaternion>` **exp**\ (\ ) |const| :ref:`🔗<class_Quaternion_method_exp>`
返回该四元数的指数。该结果的旋转轴是该四元数的归一化旋转轴，该结果的角度是该四元数的向量部分的长度。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_from_euler:
.. rst-class:: classref-method
:ref:`Quaternion<class_Quaternion>` **from_euler**\ (\ euler\: :ref:`Vector3<class_Vector3>`\ ) |static| :ref:`🔗<class_Quaternion_method_from_euler>`
从给定的 `欧拉角 <https://en.wikipedia.org/wiki/Euler_angles>`__\ 的 :ref:`Vector3<class_Vector3>` 弧度角构造一个新的 **Quaternion**\ 。该方法始终使用 YXZ 约定（\ :ref:`@GlobalScope.EULER_ORDER_YXZ<class_@GlobalScope_constant_EULER_ORDER_YXZ>`\ ）。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_get_angle:
.. rst-class:: classref-method
:ref:`float<class_float>` **get_angle**\ (\ ) |const| :ref:`🔗<class_Quaternion_method_get_angle>`
返回该四元数表示的旋转角度。
\ **注意：**\ 该四元数必须被归一化。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_get_axis:
.. rst-class:: classref-method
:ref:`Vector3<class_Vector3>` **get_axis**\ (\ ) |const| :ref:`🔗<class_Quaternion_method_get_axis>`
返回该四元数表示的旋转的旋转轴。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_get_euler:
.. rst-class:: classref-method
:ref:`Vector3<class_Vector3>` **get_euler**\ (\ order\: :ref:`int<class_int>` = 2\ ) |const| :ref:`🔗<class_Quaternion_method_get_euler>`
返回该四元数的旋转作为\ `欧拉角 <https://en.wikipedia.org/wiki/Euler_angles>`__\ 弧度角的 :ref:`Vector3<class_Vector3>`\ 。
每个连续旋转的顺序可以使用 ``order`` 更改（请参阅 :ref:`EulerOrder<enum_@GlobalScope_EulerOrder>` 常量）。默认情况下，使用 YXZ 约定（\ :ref:`@GlobalScope.EULER_ORDER_YXZ<class_@GlobalScope_constant_EULER_ORDER_YXZ>`\ ）：首先计算 Z（翻滚），然后计算 X（俯仰），最后计算 Y（偏航）。当使用相反的方法 :ref:`from_euler()<class_Quaternion_method_from_euler>` 时，该顺序相反。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_inverse:
.. rst-class:: classref-method
:ref:`Quaternion<class_Quaternion>` **inverse**\ (\ ) |const| :ref:`🔗<class_Quaternion_method_inverse>`
返回该四元数的逆版本，反转除 :ref:`w<class_Quaternion_property_w>` 之外的每个分量的符号。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_is_equal_approx:
.. rst-class:: classref-method
:ref:`bool<class_bool>` **is_equal_approx**\ (\ to\: :ref:`Quaternion<class_Quaternion>`\ ) |const| :ref:`🔗<class_Quaternion_method_is_equal_approx>`
如果该四元数和 ``to`` 近似相等，则返回 ``true``\ ，判断方法是通过对每个分量调用 :ref:`@GlobalScope.is_equal_approx()<class_@GlobalScope_method_is_equal_approx>`\ 。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_is_finite:
.. rst-class:: classref-method
:ref:`bool<class_bool>` **is_finite**\ (\ ) |const| :ref:`🔗<class_Quaternion_method_is_finite>`
如果该四元数是有限的，则返回 ``true``\ ，判断方法是在每个分量上调用 :ref:`@GlobalScope.is_finite()<class_@GlobalScope_method_is_finite>`\ 。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_is_normalized:
.. rst-class:: classref-method
:ref:`bool<class_bool>` **is_normalized**\ (\ ) |const| :ref:`🔗<class_Quaternion_method_is_normalized>`
如果该四元数已被归一化，则返回 ``true``\ 。另见 :ref:`normalized()<class_Quaternion_method_normalized>`\ 。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_length:
.. rst-class:: classref-method
:ref:`float<class_float>` **length**\ (\ ) |const| :ref:`🔗<class_Quaternion_method_length>`
返回该四元数的长度，也被称为幅度。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_length_squared:
.. rst-class:: classref-method
:ref:`float<class_float>` **length_squared**\ (\ ) |const| :ref:`🔗<class_Quaternion_method_length_squared>`
返回该四元数的长度的平方。
\ **注意：**\ 该方法比 :ref:`length()<class_Quaternion_method_length>` 更快，因此如果你只需要比较四元数的长度，则优先使用它。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_log:
.. rst-class:: classref-method
:ref:`Quaternion<class_Quaternion>` **log**\ (\ ) |const| :ref:`🔗<class_Quaternion_method_log>`
返回该四元数的对数。将该四元数的旋转轴乘以它的旋转角度，并将结果存储在返回的四元数的向量部分（\ :ref:`x<class_Quaternion_property_x>`\ 、\ :ref:`y<class_Quaternion_property_y>` 和 :ref:`z<class_Quaternion_property_z>`\ ）中。返回的四元数的实数部分（\ :ref:`w<class_Quaternion_property_w>`\ ）始终为 ``0.0``\ 。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_normalized:
.. rst-class:: classref-method
:ref:`Quaternion<class_Quaternion>` **normalized**\ (\ ) |const| :ref:`🔗<class_Quaternion_method_normalized>`
返回该四元数的副本，已归一化，因此其长度为 ``1.0``\ 。另见 :ref:`is_normalized()<class_Quaternion_method_is_normalized>`\ 。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_slerp:
.. rst-class:: classref-method
:ref:`Quaternion<class_Quaternion>` **slerp**\ (\ to\: :ref:`Quaternion<class_Quaternion>`, weight\: :ref:`float<class_float>`\ ) |const| :ref:`🔗<class_Quaternion_method_slerp>`
使用 ``to`` 四元数，在给定 ``weight`` 下执行球面线性插值并返回结果。该四元数和 ``to`` 都必须已归一化。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_slerpni:
.. rst-class:: classref-method
:ref:`Quaternion<class_Quaternion>` **slerpni**\ (\ to\: :ref:`Quaternion<class_Quaternion>`, weight\: :ref:`float<class_float>`\ ) |const| :ref:`🔗<class_Quaternion_method_slerpni>`
在给定 ``weight`` 的情况下，使用 ``to`` 四元数执行球面线性插值并返回结果。与 :ref:`slerp()<class_Quaternion_method_slerp>` 不同，该方法不检查旋转路径是否小于 90 度。该四元数和 ``to`` 都必须是归一化的。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_spherical_cubic_interpolate:
.. rst-class:: classref-method
:ref:`Quaternion<class_Quaternion>` **spherical_cubic_interpolate**\ (\ b\: :ref:`Quaternion<class_Quaternion>`, pre_a\: :ref:`Quaternion<class_Quaternion>`, post_b\: :ref:`Quaternion<class_Quaternion>`, weight\: :ref:`float<class_float>`\ ) |const| :ref:`🔗<class_Quaternion_method_spherical_cubic_interpolate>`
在四元数 ``pre_a``\ 、这个向量、\ ``b`` 以及 ``post_b`` 之间按照给定的 ``weight`` 进行球面三次插值。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_method_spherical_cubic_interpolate_in_time:
.. rst-class:: classref-method
:ref:`Quaternion<class_Quaternion>` **spherical_cubic_interpolate_in_time**\ (\ b\: :ref:`Quaternion<class_Quaternion>`, pre_a\: :ref:`Quaternion<class_Quaternion>`, post_b\: :ref:`Quaternion<class_Quaternion>`, weight\: :ref:`float<class_float>`, b_t\: :ref:`float<class_float>`, pre_a_t\: :ref:`float<class_float>`, post_b_t\: :ref:`float<class_float>`\ ) |const| :ref:`🔗<class_Quaternion_method_spherical_cubic_interpolate_in_time>`
在四元数 ``pre_a``\ 、该向量、\ ``b`` 和 ``post_b`` 之间，按给定量 ``weight`` 执行三次球面插值。
它可以根据时间值执行比 :ref:`spherical_cubic_interpolate()<class_Quaternion_method_spherical_cubic_interpolate>` 更平滑的插值。
.. rst-class:: classref-section-separator
----
.. rst-class:: classref-descriptions-group
运算符说明
----------
.. _class_Quaternion_operator_neq_Quaternion:
.. rst-class:: classref-operator
:ref:`bool<class_bool>` **operator !=**\ (\ right\: :ref:`Quaternion<class_Quaternion>`\ ) :ref:`🔗<class_Quaternion_operator_neq_Quaternion>`
如果两个四元数的分量不完全相等，则返回 ``true``\ 。
\ **注意：**\ 由于浮点精度误差，请考虑改用 :ref:`is_equal_approx()<class_Quaternion_method_is_equal_approx>`\ ，这样更可靠。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_operator_mul_Quaternion:
.. rst-class:: classref-operator
:ref:`Quaternion<class_Quaternion>` **operator ***\ (\ right\: :ref:`Quaternion<class_Quaternion>`\ ) :ref:`🔗<class_Quaternion_operator_mul_Quaternion>`
组合（相乘）两个四元数。这会由该四元数（父项）旋转 ``right`` 四元数（子项）。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_operator_mul_Vector3:
.. rst-class:: classref-operator
:ref:`Vector3<class_Vector3>` **operator ***\ (\ right\: :ref:`Vector3<class_Vector3>`\ ) :ref:`🔗<class_Quaternion_operator_mul_Vector3>`
由该四元数旋转（乘以） ``right`` 向量，返回一个 :ref:`Vector3<class_Vector3>`\ 。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_operator_mul_float:
.. rst-class:: classref-operator
:ref:`Quaternion<class_Quaternion>` **operator ***\ (\ right\: :ref:`float<class_float>`\ ) :ref:`🔗<class_Quaternion_operator_mul_float>`
将该 **Quaternion** 的每个分量乘以右侧的 :ref:`float<class_float>` 值。
该操作本身没有意义，但可以用作更大表达式的一部分。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_operator_mul_int:
.. rst-class:: classref-operator
:ref:`Quaternion<class_Quaternion>` **operator ***\ (\ right\: :ref:`int<class_int>`\ ) :ref:`🔗<class_Quaternion_operator_mul_int>`
将该 **Quaternion** 的每个分量乘以右侧 :ref:`int<class_int>` 值。
该操作本身没有意义，但可以用作更大表达式的一部分。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_operator_sum_Quaternion:
.. rst-class:: classref-operator
:ref:`Quaternion<class_Quaternion>` **operator +**\ (\ right\: :ref:`Quaternion<class_Quaternion>`\ ) :ref:`🔗<class_Quaternion_operator_sum_Quaternion>`
将左侧 **Quaternion** 的每个分量添加到右侧 **Quaternion**\ 。
该操作本身没有意义，但可以用作更大表达式的一部分，例如用于近似两个相邻旋转之间的中间旋转。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_operator_dif_Quaternion:
.. rst-class:: classref-operator
:ref:`Quaternion<class_Quaternion>` **operator -**\ (\ right\: :ref:`Quaternion<class_Quaternion>`\ ) :ref:`🔗<class_Quaternion_operator_dif_Quaternion>`
将左侧 **Quaternion** 的每个分量减去右侧 **Quaternion**\ 。
该操作本身没有意义，但可以用作更大表达式的一部分。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_operator_div_float:
.. rst-class:: classref-operator
:ref:`Quaternion<class_Quaternion>` **operator /**\ (\ right\: :ref:`float<class_float>`\ ) :ref:`🔗<class_Quaternion_operator_div_float>`
将该 **Quaternion** 的每个分量除以右侧 :ref:`float<class_float>` 值。
该操作本身没有意义，但可以用作更大表达式的一部分。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_operator_div_int:
.. rst-class:: classref-operator
:ref:`Quaternion<class_Quaternion>` **operator /**\ (\ right\: :ref:`int<class_int>`\ ) :ref:`🔗<class_Quaternion_operator_div_int>`
将该 **Quaternion** 的每个分量除以右侧的 :ref:`int<class_int>` 值。
该操作本身没有意义，但可以用作更大表达式的一部分。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_operator_eq_Quaternion:
.. rst-class:: classref-operator
:ref:`bool<class_bool>` **operator ==**\ (\ right\: :ref:`Quaternion<class_Quaternion>`\ ) :ref:`🔗<class_Quaternion_operator_eq_Quaternion>`
如果两个四元数的分量完全相等，则返回 ``true``\ 。
\ **注意：**\ 由于浮点精度误差，请考虑改用 :ref:`is_equal_approx()<class_Quaternion_method_is_equal_approx>`\ ，这样更可靠。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_operator_idx_int:
.. rst-class:: classref-operator
:ref:`float<class_float>` **operator []**\ (\ index\: :ref:`int<class_int>`\ ) :ref:`🔗<class_Quaternion_operator_idx_int>`
通过索引访问该四元数的每个分量。
索引 ``0`` 与 :ref:`x<class_Quaternion_property_x>` 相同，索引 ``1`` 与 :ref:`y<class_Quaternion_property_y>` 相同，索引 ``2`` 与 :ref:`z<class_Quaternion_property_z>` 相同，索引 ``3`` 与 :ref:`w<class_Quaternion_property_w>` 相同。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_operator_unplus:
.. rst-class:: classref-operator
:ref:`Quaternion<class_Quaternion>` **operator unary+**\ (\ ) :ref:`🔗<class_Quaternion_operator_unplus>`
返回与 ``+`` 不存在时相同的值。单目 ``+`` 没有作用，但有时可以使你的代码更具可读性。
.. rst-class:: classref-item-separator
----
.. _class_Quaternion_operator_unminus:
.. rst-class:: classref-operator
:ref:`Quaternion<class_Quaternion>` **operator unary-**\ (\ ) :ref:`🔗<class_Quaternion_operator_unminus>`
返回该 **Quaternion** 的负值。这与将所有分量乘以 ``-1`` 相同。这个操作得到的是代表相同旋转的四元数。
.. |virtual| replace:: :abbr:`virtual (本方法通常需要用户覆盖才能生效。)`
.. |required| replace:: :abbr:`required (This method is required to be overridden when extending its base class.)`
.. |const| replace:: :abbr:`const (本方法无副作用，不会修改该实例的任何成员变量。)`
.. |vararg| replace:: :abbr:`vararg (本方法除了能接受在此处描述的参数外，还能够继续接受任意数量的参数。)`
.. |constructor| replace:: :abbr:`constructor (本方法用于构造某个类型。)`
.. |static| replace:: :abbr:`static (调用本方法无需实例，可直接使用类名进行调用。)`
.. |operator| replace:: :abbr:`operator (本方法描述的是使用本类型作为左操作数的有效运算符。)`
.. |bitfield| replace:: :abbr:`BitField (这个值是由下列位标志构成位掩码的整数。)`
.. |void| replace:: :abbr:`void (无返回值。)`
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