godotengine/godot-docs-l10n
1
0
Fork 0
mirror of https://github.com/godotengine/godot-docs-l10n.git synced 2026-01-04 10:09:56 +03:00
Code Issues Packages Projects Releases Wiki Activity
Files
36d0439ca5be178d7e6b4f9b6bffbcf4f90209f5
godot-docs-l10n/classes/zh_CN/class_basis.rst

963 lines
45 KiB
ReStructuredText
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

:github_url: hide
.. DO NOT EDIT THIS FILE!!!
.. Generated automatically from Godot engine sources.
.. Generator: https://github.com/godotengine/godot/tree/master/doc/tools/make_rst.py.
.. XML source: https://github.com/godotengine/godot/tree/master/doc/classes/Basis.xml.
.. _class_Basis:
Basis
=====
用于表示 3D 旋转和缩放的 3×3 矩阵。
.. rst-class:: classref-introduction-group
描述
----
The **Basis** built-in :ref:`Variant<class_Variant>` type is a 3×3 `matrix <https://en.wikipedia.org/wiki/Matrix_(mathematics)>`__ used to represent 3D rotation, scale, and shear. It is frequently used within a :ref:`Transform3D<class_Transform3D>`.
A **Basis** is composed by 3 axis vectors, each representing a column of the matrix: :ref:`x<class_Basis_property_x>`, :ref:`y<class_Basis_property_y>`, and :ref:`z<class_Basis_property_z>`. The length of each axis (:ref:`Vector3.length<class_Vector3_method_length>`) influences the basis's scale, while the direction of all axes influence the rotation. Usually, these axes are perpendicular to one another. However, when you rotate any axis individually, the basis becomes sheared. Applying a sheared basis to a 3D model will make the model appear distorted.
A **Basis** is **orthogonal** if its axes are perpendicular to each other. A basis is **normalized** if the length of every axis is ``1``. A basis is **uniform** if all axes share the same length (see :ref:`get_scale<class_Basis_method_get_scale>`). A basis is **orthonormal** if it is both orthogonal and normalized, which allows it to only represent rotations. A basis is **conformal** if it is both orthogonal and uniform, which ensures it is not distorted.
For a general introduction, see the :doc:`Matrices and transforms <../tutorials/math/matrices_and_transforms>` tutorial.
\ **Note:** Godot uses a `right-handed coordinate system <https://en.wikipedia.org/wiki/Right-hand_rule>`__, which is a common standard. For directions, the convention for built-in types like :ref:`Camera3D<class_Camera3D>` is for -Z to point forward (+X is right, +Y is up, and +Z is back). Other objects may use different direction conventions. For more information, see the `3D asset direction conventions <../tutorials/assets_pipeline/importing_3d_scenes/model_export_considerations.html#d-asset-direction-conventions>`__ tutorial.
\ **Note:** The basis matrices are exposed as `column-major <https://www.mindcontrol.org/~hplus/graphics/matrix-layout.html>`__ order, which is the same as OpenGL. However, they are stored internally in row-major order, which is the same as DirectX.
.. 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
----
- :doc:`数学文档索引 <../tutorials/math/index>`
- :doc:`矩阵与变换 <../tutorials/math/matrices_and_transforms>`
- :doc:`使用 3D 变换 <../tutorials/3d/using_transforms>`
- `矩阵变换演示 <https://godotengine.org/asset-library/asset/2787>`__
- `3D 平台跳跃演示 <https://godotengine.org/asset-library/asset/2748>`__
- `3D 体素演示 <https://godotengine.org/asset-library/asset/2755>`__
- `2.5D 游戏演示 <https://godotengine.org/asset-library/asset/2783>`__
.. rst-class:: classref-reftable-group
属性
----
.. table::
:widths: auto
+-------------------------------+----------------------------------+----------------------+
| :ref:`Vector3<class_Vector3>` | :ref:`x<class_Basis_property_x>` | ``Vector3(1, 0, 0)`` |
+-------------------------------+----------------------------------+----------------------+
| :ref:`Vector3<class_Vector3>` | :ref:`y<class_Basis_property_y>` | ``Vector3(0, 1, 0)`` |
+-------------------------------+----------------------------------+----------------------+
| :ref:`Vector3<class_Vector3>` | :ref:`z<class_Basis_property_z>` | ``Vector3(0, 0, 1)`` |
+-------------------------------+----------------------------------+----------------------+
.. rst-class:: classref-reftable-group
构造函数
--------
.. table::
:widths: auto
+---------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`Basis<class_Basis_constructor_Basis>`\ (\ ) |
+---------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`Basis<class_Basis_constructor_Basis>`\ (\ from\: :ref:`Basis<class_Basis>`\ ) |
+---------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`Basis<class_Basis_constructor_Basis>`\ (\ axis\: :ref:`Vector3<class_Vector3>`, angle\: :ref:`float<class_float>`\ ) |
+---------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`Basis<class_Basis_constructor_Basis>`\ (\ from\: :ref:`Quaternion<class_Quaternion>`\ ) |
+---------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`Basis<class_Basis_constructor_Basis>`\ (\ x_axis\: :ref:`Vector3<class_Vector3>`, y_axis\: :ref:`Vector3<class_Vector3>`, z_axis\: :ref:`Vector3<class_Vector3>`\ ) |
+---------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
.. rst-class:: classref-reftable-group
方法
----
.. table::
:widths: auto
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`float<class_float>` | :ref:`determinant<class_Basis_method_determinant>`\ (\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`from_euler<class_Basis_method_from_euler>`\ (\ euler\: :ref:`Vector3<class_Vector3>`, order\: :ref:`int<class_int>` = 2\ ) |static| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`from_scale<class_Basis_method_from_scale>`\ (\ scale\: :ref:`Vector3<class_Vector3>`\ ) |static| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Vector3<class_Vector3>` | :ref:`get_euler<class_Basis_method_get_euler>`\ (\ order\: :ref:`int<class_int>` = 2\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Quaternion<class_Quaternion>` | :ref:`get_rotation_quaternion<class_Basis_method_get_rotation_quaternion>`\ (\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Vector3<class_Vector3>` | :ref:`get_scale<class_Basis_method_get_scale>`\ (\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`inverse<class_Basis_method_inverse>`\ (\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>` | :ref:`is_conformal<class_Basis_method_is_conformal>`\ (\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>` | :ref:`is_equal_approx<class_Basis_method_is_equal_approx>`\ (\ b\: :ref:`Basis<class_Basis>`\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>` | :ref:`is_finite<class_Basis_method_is_finite>`\ (\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`looking_at<class_Basis_method_looking_at>`\ (\ target\: :ref:`Vector3<class_Vector3>`, up\: :ref:`Vector3<class_Vector3>` = Vector3(0, 1, 0), use_model_front\: :ref:`bool<class_bool>` = false\ ) |static| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`orthonormalized<class_Basis_method_orthonormalized>`\ (\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`rotated<class_Basis_method_rotated>`\ (\ axis\: :ref:`Vector3<class_Vector3>`, angle\: :ref:`float<class_float>`\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`scaled<class_Basis_method_scaled>`\ (\ scale\: :ref:`Vector3<class_Vector3>`\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`slerp<class_Basis_method_slerp>`\ (\ to\: :ref:`Basis<class_Basis>`, weight\: :ref:`float<class_float>`\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`float<class_float>` | :ref:`tdotx<class_Basis_method_tdotx>`\ (\ with\: :ref:`Vector3<class_Vector3>`\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`float<class_float>` | :ref:`tdoty<class_Basis_method_tdoty>`\ (\ with\: :ref:`Vector3<class_Vector3>`\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`float<class_float>` | :ref:`tdotz<class_Basis_method_tdotz>`\ (\ with\: :ref:`Vector3<class_Vector3>`\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`transposed<class_Basis_method_transposed>`\ (\ ) |const| |
+-------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
.. rst-class:: classref-reftable-group
运算符
------
.. table::
:widths: auto
+-------------------------------+--------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>` | :ref:`operator !=<class_Basis_operator_neq_Basis>`\ (\ right\: :ref:`Basis<class_Basis>`\ ) |
+-------------------------------+--------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`operator *<class_Basis_operator_mul_Basis>`\ (\ right\: :ref:`Basis<class_Basis>`\ ) |
+-------------------------------+--------------------------------------------------------------------------------------------------+
| :ref:`Vector3<class_Vector3>` | :ref:`operator *<class_Basis_operator_mul_Vector3>`\ (\ right\: :ref:`Vector3<class_Vector3>`\ ) |
+-------------------------------+--------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`operator *<class_Basis_operator_mul_float>`\ (\ right\: :ref:`float<class_float>`\ ) |
+-------------------------------+--------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`operator *<class_Basis_operator_mul_int>`\ (\ right\: :ref:`int<class_int>`\ ) |
+-------------------------------+--------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`operator /<class_Basis_operator_div_float>`\ (\ right\: :ref:`float<class_float>`\ ) |
+-------------------------------+--------------------------------------------------------------------------------------------------+
| :ref:`Basis<class_Basis>` | :ref:`operator /<class_Basis_operator_div_int>`\ (\ right\: :ref:`int<class_int>`\ ) |
+-------------------------------+--------------------------------------------------------------------------------------------------+
| :ref:`bool<class_bool>` | :ref:`operator ==<class_Basis_operator_eq_Basis>`\ (\ right\: :ref:`Basis<class_Basis>`\ ) |
+-------------------------------+--------------------------------------------------------------------------------------------------+
| :ref:`Vector3<class_Vector3>` | :ref:`operator []<class_Basis_operator_idx_int>`\ (\ index\: :ref:`int<class_int>`\ ) |
+-------------------------------+--------------------------------------------------------------------------------------------------+
.. rst-class:: classref-section-separator
----
.. rst-class:: classref-descriptions-group
常量
----
.. _class_Basis_constant_IDENTITY:
.. rst-class:: classref-constant
**IDENTITY** = ``Basis(1, 0, 0, 0, 1, 0, 0, 0, 1)`` :ref:`🔗<class_Basis_constant_IDENTITY>`
单位基。这是一个没有旋转、没有剪切的基，其缩放为 ``1``\ 。这意味着：
- :ref:`x<class_Basis_property_x>` 指向右侧（\ :ref:`Vector3.RIGHT<class_Vector3_constant_RIGHT>`\ ）；
- :ref:`y<class_Basis_property_y>` 指向上方（\ :ref:`Vector3.UP<class_Vector3_constant_UP>`\ ）；
- :ref:`z<class_Basis_property_z>` 指向后面（\ :ref:`Vector3.BACK<class_Vector3_constant_BACK>`\ ）。
::
var basis := Basis.IDENTITY
print("| X | Y | Z")
print("| %s | %s | %s" % [basis.x.x, basis.y.x, basis.z.x])
print("| %s | %s | %s" % [basis.x.y, basis.y.y, basis.z.y])
print("| %s | %s | %s" % [basis.x.z, basis.y.z, basis.z.z])
# 输出：
# | X | Y | Z
# | 1 | 0 | 0
# | 0 | 1 | 0
# | 0 | 0 | 1
这与创建没有任何参数的 :ref:`Basis<class_Basis_constructor_Basis>` 相同。该常量可用于使你的代码更清晰，并与 C# 保持一致。
.. _class_Basis_constant_FLIP_X:
.. rst-class:: classref-constant
**FLIP_X** = ``Basis(-1, 0, 0, 0, 1, 0, 0, 0, 1)`` :ref:`🔗<class_Basis_constant_FLIP_X>`
当任意基被 :ref:`FLIP_X<class_Basis_constant_FLIP_X>` 相乘时，它会取负 :ref:`x<class_Basis_property_x>` 轴（X 列）的所有分量。
当 :ref:`FLIP_X<class_Basis_constant_FLIP_X>` 被任意基相乘时，它会取负所有轴（X 行）的 :ref:`Vector3.x<class_Vector3_property_x>` 分量。
.. _class_Basis_constant_FLIP_Y:
.. rst-class:: classref-constant
**FLIP_Y** = ``Basis(1, 0, 0, 0, -1, 0, 0, 0, 1)`` :ref:`🔗<class_Basis_constant_FLIP_Y>`
当任意基被 :ref:`FLIP_Y<class_Basis_constant_FLIP_Y>` 相乘时，它会取负 :ref:`y<class_Basis_property_y>` 轴（Y 列）的所有分量。
当 :ref:`FLIP_Y<class_Basis_constant_FLIP_Y>` 被任意基相乘时，它会取负所有轴（Y 行）的 :ref:`Vector3.y<class_Vector3_property_y>` 分量。
.. _class_Basis_constant_FLIP_Z:
.. rst-class:: classref-constant
**FLIP_Z** = ``Basis(1, 0, 0, 0, 1, 0, 0, 0, -1)`` :ref:`🔗<class_Basis_constant_FLIP_Z>`
当任意基被 :ref:`FLIP_Z<class_Basis_constant_FLIP_Z>` 相乘时，它会取负 :ref:`z<class_Basis_property_z>` 轴（Z 列）的所有分量。
当 :ref:`FLIP_Z<class_Basis_constant_FLIP_Z>` 被任意基相乘时，它会取负所有轴（Z 行）的 :ref:`Vector3.z<class_Vector3_property_z>` 分量。
.. rst-class:: classref-section-separator
----
.. rst-class:: classref-descriptions-group
属性说明
--------
.. _class_Basis_property_x:
.. rst-class:: classref-property
:ref:`Vector3<class_Vector3>` **x** = ``Vector3(1, 0, 0)`` :ref:`🔗<class_Basis_property_x>`
该基的 X 轴和矩阵的 ``0`` 列。
在单位基上，该向量指向右侧（\ :ref:`Vector3.RIGHT<class_Vector3_constant_RIGHT>`\ ）。
.. rst-class:: classref-item-separator
----
.. _class_Basis_property_y:
.. rst-class:: classref-property
:ref:`Vector3<class_Vector3>` **y** = ``Vector3(0, 1, 0)`` :ref:`🔗<class_Basis_property_y>`
该基的 Y 轴和矩阵的第 ``1`` 列。
在单位基上，该向量指向上方（\ :ref:`Vector3.UP<class_Vector3_constant_UP>`\ ）。
.. rst-class:: classref-item-separator
----
.. _class_Basis_property_z:
.. rst-class:: classref-property
:ref:`Vector3<class_Vector3>` **z** = ``Vector3(0, 0, 1)`` :ref:`🔗<class_Basis_property_z>`
该基的 Z 轴和矩阵的第 ``2`` 列。
在单位基上，该向量指向后面（\ :ref:`Vector3.BACK<class_Vector3_constant_BACK>`\ ）。
.. rst-class:: classref-section-separator
----
.. rst-class:: classref-descriptions-group
构造函数说明
------------
.. _class_Basis_constructor_Basis:
.. rst-class:: classref-constructor
:ref:`Basis<class_Basis>` **Basis**\ (\ ) :ref:`🔗<class_Basis_constructor_Basis>`
构造一个与 :ref:`IDENTITY<class_Basis_constant_IDENTITY>` 相同的 **Basis**\ 。
.. rst-class:: classref-item-separator
----
.. rst-class:: classref-constructor
:ref:`Basis<class_Basis>` **Basis**\ (\ from\: :ref:`Basis<class_Basis>`\ )
构造给定 **Basis** 的副本。
.. rst-class:: classref-item-separator
----
.. rst-class:: classref-constructor
:ref:`Basis<class_Basis>` **Basis**\ (\ axis\: :ref:`Vector3<class_Vector3>`, angle\: :ref:`float<class_float>`\ )
构造仅表示旋转的 **Basis**\ ，给定的 ``angle`` 以弧度为单位，表示围绕 ``axis`` 轴的旋转量。这个轴必须是归一化的向量。
\ **注意：**\ 与对 :ref:`IDENTITY<class_Basis_constant_IDENTITY>` 基使用 :ref:`rotated<class_Basis_method_rotated>` 一致。多角度旋转请改用 :ref:`from_euler<class_Basis_method_from_euler>`\ 。
.. rst-class:: classref-item-separator
----
.. rst-class:: classref-constructor
:ref:`Basis<class_Basis>` **Basis**\ (\ from\: :ref:`Quaternion<class_Quaternion>`\ )
根据给定的 :ref:`Quaternion<class_Quaternion>` 构造仅表示旋转的 **Basis**\ 。
\ **注意：**\ 四元数\ *仅*\ 存储旋转，不会存储缩放。因此，\ **Basis** 到 :ref:`Quaternion<class_Quaternion>` 的转换并不一定可逆。
.. rst-class:: classref-item-separator
----
.. rst-class:: classref-constructor
:ref:`Basis<class_Basis>` **Basis**\ (\ x_axis\: :ref:`Vector3<class_Vector3>`, y_axis\: :ref:`Vector3<class_Vector3>`, z_axis\: :ref:`Vector3<class_Vector3>`\ )
根据 3 个轴向量构造 **Basis**\ 。这些是基矩阵的列向量。
.. rst-class:: classref-section-separator
----
.. rst-class:: classref-descriptions-group
方法说明
--------
.. _class_Basis_method_determinant:
.. rst-class:: classref-method
:ref:`float<class_float>` **determinant**\ (\ ) |const| :ref:`🔗<class_Basis_method_determinant>`
返回基矩阵的\ `行列式 <https://zh.wikipedia.org/wiki/%E8%A1%8C%E5%88%97%E5%BC%8F>`__\ 。在高等数学中，这个数可以用来确定一些性质：
- 如果行列式为 ``0``\ ，则基不可逆（见 :ref:`inverse<class_Basis_method_inverse>`\ ）。
- 如果行列式为负数，则基表示负缩放。
\ **注意：**\ 如果基的每个轴缩放都相同，那么这个行列式始终为 2 的该缩放次幂。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_from_euler:
.. rst-class:: classref-method
:ref:`Basis<class_Basis>` **from_euler**\ (\ euler\: :ref:`Vector3<class_Vector3>`, order\: :ref:`int<class_int>` = 2\ ) |static| :ref:`🔗<class_Basis_method_from_euler>`
根据给定的 :ref:`Vector3<class_Vector3>` 构造 **Basis**\ ，这个向量为 `欧拉角 <https://zh.wikipedia.org/zh-cn/%E6%AC%A7%E6%8B%89%E8%A7%92>`__\ ，单位为弧度。
- :ref:`Vector3.x<class_Vector3_property_x>` 应包含围绕 :ref:`x<class_Basis_property_x>` 轴的角度（俯仰）。
- :ref:`Vector3.y<class_Vector3_property_y>` 应包含围绕 :ref:`y<class_Basis_property_y>` 轴的角度（偏摆）。
- :ref:`Vector3.z<class_Vector3_property_z>` 应包含围绕 :ref:`z<class_Basis_property_z>` 轴的角度（翻滚）。
.. tabs::
.. code-tab:: gdscript
# 创建 Z 轴向下的 Basis。
var my_basis = Basis.from_euler(Vector3(TAU / 4, 0, 0))
print(my_basis.z) # 输出 (0, -1, 0)。
.. code-tab:: csharp
// 创建 Z 轴向下的 Basis。
var myBasis = Basis.FromEuler(new Vector3(Mathf.Tau / 4.0f, 0.0f, 0.0f));
GD.Print(myBasis.Z); // 输出 (0, -1, 0)。
连续旋转的顺序可以通过 ``order`` 修改（见 :ref:`EulerOrder<enum_@GlobalScope_EulerOrder>` 常量）。默认使用 YXZ 约定（\ :ref:`@GlobalScope.EULER_ORDER_YXZ<class_@GlobalScope_constant_EULER_ORDER_YXZ>`\ ）：基首先围绕 Y 轴旋转（偏摆），然后围绕 X 轴旋转（俯仰），最后围绕 Z 轴旋转（翻滚）。这个顺序在相对的函数 :ref:`get_euler<class_Basis_method_get_euler>` 中是相反的。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_from_scale:
.. rst-class:: classref-method
:ref:`Basis<class_Basis>` **from_scale**\ (\ scale\: :ref:`Vector3<class_Vector3>`\ ) |static| :ref:`🔗<class_Basis_method_from_scale>`
根据给定的 ``scale`` 向量构造仅表示缩放的 **Basis**\ ，不包含旋转和切变。
.. tabs::
.. code-tab:: gdscript
var my_basis = Basis.from_scale(Vector3(2, 4, 8))
print(my_basis.x) # 输出 (2, 0, 0).
print(my_basis.y) # 输出 (0, 4, 0).
print(my_basis.z) # 输出 (0, 0, 8).
.. code-tab:: csharp
var myBasis = Basis.FromScale(new Vector3(2.0f, 4.0f, 8.0f));
GD.Print(myBasis.X); // 输出 (2, 0, 0).
GD.Print(myBasis.Y); // 输出 (0, 4, 0).
GD.Print(myBasis.Z); // 输出 (0, 0, 8).
\ **注意：**\ 在线性代数中，这种基矩阵也被称作\ `对角矩阵 <https://zh.wikipedia.org/zh-cn/%E5%B0%8D%E8%A7%92%E7%9F%A9%E9%99%A3>`__\ 。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_get_euler:
.. rst-class:: classref-method
:ref:`Vector3<class_Vector3>` **get_euler**\ (\ order\: :ref:`int<class_int>` = 2\ ) |const| :ref:`🔗<class_Basis_method_get_euler>`
以 :ref:`Vector3<class_Vector3>` 的形式返回基的旋转，这个向量为 `欧拉角 <https://zh.wikipedia.org/zh-cn/%E6%AC%A7%E6%8B%89%E8%A7%92>`__\ ，单位为弧度。
- :ref:`Vector3.x<class_Vector3_property_x>` 包含围绕 :ref:`x<class_Basis_property_x>` 轴的角度（俯仰）。
- :ref:`Vector3.y<class_Vector3_property_y>` 包含围绕 :ref:`y<class_Basis_property_y>` 轴的角度（偏摆）。
- :ref:`Vector3.z<class_Vector3_property_z>` 包含围绕 :ref:`z<class_Basis_property_z>` 轴的角度（翻滚）。
连续旋转的顺序可以通过 ``order`` 修改（见 :ref:`EulerOrder<enum_@GlobalScope_EulerOrder>` 常量）。默认使用 YXZ 约定（\ :ref:`@GlobalScope.EULER_ORDER_YXZ<class_@GlobalScope_constant_EULER_ORDER_YXZ>`\ ）：首先计算围绕 Z 轴的旋转（翻滚），然后计算围绕 X 轴的旋转（俯仰），最后计算围绕 Y 轴旋转（偏摆）。这个顺序在相对的函数 :ref:`from_euler<class_Basis_method_from_euler>` 中是相反的。
\ **注意：**\ 欧拉角更符合直觉，但是并不适合 3D 数学。因此请考虑改用返回 :ref:`Quaternion<class_Quaternion>` 的 :ref:`get_rotation_quaternion<class_Basis_method_get_rotation_quaternion>`\ 。
\ **注意：**\ 在检查器面板中，基的旋转通常是以欧拉角的形式显示的（单位为度），与 :ref:`Node3D.rotation<class_Node3D_property_rotation>` 属性相同。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_get_rotation_quaternion:
.. rst-class:: classref-method
:ref:`Quaternion<class_Quaternion>` **get_rotation_quaternion**\ (\ ) |const| :ref:`🔗<class_Basis_method_get_rotation_quaternion>`
以 :ref:`Quaternion<class_Quaternion>` 的形式返回基的旋转。
\ **注意：**\ 四元数更适合 3D 数学，但是并不那么符合直觉。用户界面相关的场合请考虑使用返回欧拉角的 :ref:`get_euler<class_Basis_method_get_euler>` 方法。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_get_scale:
.. rst-class:: classref-method
:ref:`Vector3<class_Vector3>` **get_scale**\ (\ ) |const| :ref:`🔗<class_Basis_method_get_scale>`
返回该基的每个轴的长度，作为一个 :ref:`Vector3<class_Vector3>`\ 。如果该基没有被剪切，这就是缩放系数。它不受旋转的影响。
.. tabs::
.. code-tab:: gdscript
var my_basis = Basis(
Vector3(2, 0, 0),
Vector3(0, 4, 0),
Vector3(0, 0, 8)
)
# 以任何方式旋转基都会保持其缩放。
my_basis = my_basis.rotated(Vector3.UP, TAU / 2)
my_basis = my_basis.rotated(Vector3.RIGHT, TAU / 4)
print(my_basis.get_scale()) # 输出 (2, 4, 8)。
.. code-tab:: csharp
var myBasis = new Basis(
Vector3(2.0f, 0.0f, 0.0f),
Vector3(0.0f, 4.0f, 0.0f),
Vector3(0.0f, 0.0f, 8.0f)
);
// 以任何方式旋转基都会保持其缩放。
myBasis = myBasis.Rotated(Vector3.Up, Mathf.Tau / 2.0f);
myBasis = myBasis.Rotated(Vector3.Right, Mathf.Tau / 4.0f);
GD.Print(myBasis.Scale); // 输出 (2, 4, 8)。
\ **注意：**\ 如果 :ref:`determinant<class_Basis_method_determinant>` 返回的值为负数，则缩放也为负数。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_inverse:
.. rst-class:: classref-method
:ref:`Basis<class_Basis>` **inverse**\ (\ ) |const| :ref:`🔗<class_Basis_method_inverse>`
返回 `该基矩阵的逆矩阵 <https://en.wikipedia.org/wiki/Invertible_matrix>`__\ 。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_is_conformal:
.. rst-class:: classref-method
:ref:`bool<class_bool>` **is_conformal**\ (\ ) |const| :ref:`🔗<class_Basis_method_is_conformal>`
如果该基是共形的，则返回 ``true``\ 。共形的基既是\ *正交的*\ （轴彼此垂直）又是\ *均匀的*\ （轴共享相同长度）。该方法在物理计算过程中特别有用。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_is_equal_approx:
.. rst-class:: classref-method
:ref:`bool<class_bool>` **is_equal_approx**\ (\ b\: :ref:`Basis<class_Basis>`\ ) |const| :ref:`🔗<class_Basis_method_is_equal_approx>`
如果该基和 ``b`` 近似相等，则返回 ``true``\ ，判断方法是在每个向量分量上调用 :ref:`@GlobalScope.is_equal_approx<class_@GlobalScope_method_is_equal_approx>`\ 。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_is_finite:
.. rst-class:: classref-method
:ref:`bool<class_bool>` **is_finite**\ (\ ) |const| :ref:`🔗<class_Basis_method_is_finite>`
如果该基是有限的，则返回 ``true``\ ，判断方法是在每个向量分量上调用 :ref:`@GlobalScope.is_finite<class_@GlobalScope_method_is_finite>`\ 。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_looking_at:
.. rst-class:: classref-method
:ref:`Basis<class_Basis>` **looking_at**\ (\ target\: :ref:`Vector3<class_Vector3>`, up\: :ref:`Vector3<class_Vector3>` = Vector3(0, 1, 0), use_model_front\: :ref:`bool<class_bool>` = false\ ) |static| :ref:`🔗<class_Basis_method_looking_at>`
创建一个带有旋转的新 **Basis**\ ，使向前轴（-Z）指向 ``target`` 的位置。
默认情况下，-Z 轴（相机向前）被视为向前（意味着 +X 位于右侧）。如果 ``use_model_front`` 为 ``true``\ ，则 +Z 轴（资产正面）被视为向前（意味着 +X 位于左侧）并指向 ``target`` 的位置。
向上轴（+Y）尽可能靠近 ``up`` 向量，同时保持垂直于向前轴。返回的基是正交归一化的（参见 :ref:`orthonormalized<class_Basis_method_orthonormalized>`\ ）。\ ``target`` 和 ``up`` 向量不能是 :ref:`Vector3.ZERO<class_Vector3_constant_ZERO>`\ ，并且不能彼此平行。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_orthonormalized:
.. rst-class:: classref-method
:ref:`Basis<class_Basis>` **orthonormalized**\ (\ ) |const| :ref:`🔗<class_Basis_method_orthonormalized>`
返回该基的正交归一化版本。正交归一化基既是\ *正交的*\ （轴彼此垂直）又是\ *归一化的*\ （轴长度为 ``1``\ ），这也意味着它只能代表旋转。
调用该方法通常很有用，以避免旋转基上的舍入错误：
.. tabs::
.. code-tab:: gdscript
# 每帧旋转该 Node3D。
func _process(delta):
basis = basis.rotated(Vector3.UP, TAU * delta)
basis = basis.rotated(Vector3.RIGHT, TAU * delta)
basis = basis.orthonormalized()
.. code-tab:: csharp
// 每帧旋转该 Node3D。
public override void _Process(double delta)
{
Basis = Basis.Rotated(Vector3.Up, Mathf.Tau * (float)delta)
.Rotated(Vector3.Right, Mathf.Tau * (float)delta)
.Orthonormalized();
}
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_rotated:
.. rst-class:: classref-method
:ref:`Basis<class_Basis>` **rotated**\ (\ axis\: :ref:`Vector3<class_Vector3>`, angle\: :ref:`float<class_float>`\ ) |const| :ref:`🔗<class_Basis_method_rotated>`
返回围绕给定 ``axis`` 旋转 ``angle``\ （单位为弧度）的基。\ ``axis`` 必须是归一化的向量（请参阅 :ref:`Vector3.normalized<class_Vector3_method_normalized>`\ ）。
正值绕该轴顺时针旋转该基，而负值则逆时针旋转该基。
.. tabs::
.. code-tab:: gdscript
var my_basis = Basis.IDENTITY
var angle = TAU / 2
my_basis = my_basis.rotated(Vector3.UP, angle) # 绕向上轴旋转（偏航）。
my_basis = my_basis.rotated(Vector3.RIGHT, angle) # 绕向右轴旋转（俯仰）。
my_basis = my_basis.rotated(Vector3.BACK, angle) # 绕向后轴旋转（滚动）。
.. code-tab:: csharp
var myBasis = Basis.Identity;
var angle = Mathf.Tau / 2.0f;
myBasis = myBasis.Rotated(Vector3.Up, angle); // 绕向上轴旋转（偏航）。
myBasis = myBasis.Rotated(Vector3.Right, angle); // 绕向右轴旋转（俯仰）。
myBasis = myBasis.Rotated(Vector3.Back, angle); // 绕向后轴旋转（滚动）。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_scaled:
.. rst-class:: classref-method
:ref:`Basis<class_Basis>` **scaled**\ (\ scale\: :ref:`Vector3<class_Vector3>`\ ) |const| :ref:`🔗<class_Basis_method_scaled>`
返回该基，其中每个轴的分量都按给定的 ``scale`` 的分量缩放。
该基矩阵的行乘以 ``scale`` 的分量。该操作是全局缩放（相对于父级）。
.. tabs::
.. code-tab:: gdscript
var my_basis = Basis(
Vector3(1, 1, 1),
Vector3(2, 2, 2),
Vector3(3, 3, 3)
)
my_basis = my_basis.scaled(Vector3(0, 2, -2))
print(my_basis.x) # 输出 (0, 2, -2).
print(my_basis.y) # 输出 (0, 4, -4).
print(my_basis.z) # 输出 (0, 6, -6).
.. code-tab:: csharp
var myBasis = new Basis(
new Vector3(1.0f, 1.0f, 1.0f),
new Vector3(2.0f, 2.0f, 2.0f),
new Vector3(3.0f, 3.0f, 3.0f)
);
myBasis = myBasis.Scaled(new Vector3(0.0f, 2.0f, -2.0f));
GD.Print(myBasis.X); // 输出 (0, 2, -2).
GD.Print(myBasis.Y); // 输出 (0, 4, -4).
GD.Print(myBasis.Z); // 输出 (0, 6, -6).
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_slerp:
.. rst-class:: classref-method
:ref:`Basis<class_Basis>` **slerp**\ (\ to\: :ref:`Basis<class_Basis>`, weight\: :ref:`float<class_float>`\ ) |const| :ref:`🔗<class_Basis_method_slerp>`
使用 ``to`` 基在给定 ``weight`` 的情况下执行球面线性插值。该基和 ``to`` 两者都应该代表一个旋转。
\ **示例：**\ 使用 :ref:`Tween<class_Tween>` 随时间平滑地将 :ref:`Node3D<class_Node3D>` 旋转到目标基。
::
var start_basis = Basis.IDENTITY
var target_basis = Basis.IDENTITY.rotated(Vector3.UP, TAU / 2)
func _ready():
create_tween().tween_method(interpolate, 0.0, 1.0, 5.0).set_trans(Tween.TRANS_EXPO)
func interpolate(weight):
basis = start_basis.slerp(target_basis, weight)
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_tdotx:
.. rst-class:: classref-method
:ref:`float<class_float>` **tdotx**\ (\ with\: :ref:`Vector3<class_Vector3>`\ ) |const| :ref:`🔗<class_Basis_method_tdotx>`
返回 ``with`` 和 :ref:`x<class_Basis_property_x>` 轴之间的转置点积（请参阅 :ref:`transposed<class_Basis_method_transposed>`\ ）。
这相当于 ``basis.x.dot(vector)``\ 。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_tdoty:
.. rst-class:: classref-method
:ref:`float<class_float>` **tdoty**\ (\ with\: :ref:`Vector3<class_Vector3>`\ ) |const| :ref:`🔗<class_Basis_method_tdoty>`
返回 ``with`` 和 :ref:`y<class_Basis_property_y>` 轴之间的转置点积（请参阅 :ref:`transposed<class_Basis_method_transposed>`\ ）。
这相当于 ``basis.y.dot(vector)``\ 。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_tdotz:
.. rst-class:: classref-method
:ref:`float<class_float>` **tdotz**\ (\ with\: :ref:`Vector3<class_Vector3>`\ ) |const| :ref:`🔗<class_Basis_method_tdotz>`
返回 ``with`` 和 :ref:`z<class_Basis_property_z>` 轴之间的转置点积（请参阅 :ref:`transposed<class_Basis_method_transposed>`\ ）。
这相当于 ``basis.z.dot(vector)``\ 。
.. rst-class:: classref-item-separator
----
.. _class_Basis_method_transposed:
.. rst-class:: classref-method
:ref:`Basis<class_Basis>` **transposed**\ (\ ) |const| :ref:`🔗<class_Basis_method_transposed>`
返回该基的转置版本。这会将基矩阵的列转换为行，并将其行转换为列。
.. tabs::
.. code-tab:: gdscript
var my_basis = Basis(
Vector3(1, 2, 3),
Vector3(4, 5, 6),
Vector3(7, 8, 9)
)
my_basis = my_basis.transposed()
print(my_basis.x) # 输出 (1, 4, 7).
print(my_basis.y) # 输出 (2, 5, 8).
print(my_basis.z) # 输出 (3, 6, 9).
.. code-tab:: csharp
var myBasis = new Basis(
new Vector3(1.0f, 2.0f, 3.0f),
new Vector3(4.0f, 5.0f, 6.0f),
new Vector3(7.0f, 8.0f, 9.0f)
);
myBasis = myBasis.Transposed();
GD.Print(myBasis.X); // 输出 (1, 4, 7).
GD.Print(myBasis.Y); // 输出 (2, 5, 8).
GD.Print(myBasis.Z); // 输出 (3, 6, 9).
.. rst-class:: classref-section-separator
----
.. rst-class:: classref-descriptions-group
运算符说明
----------
.. _class_Basis_operator_neq_Basis:
.. rst-class:: classref-operator
:ref:`bool<class_bool>` **operator !=**\ (\ right\: :ref:`Basis<class_Basis>`\ ) :ref:`🔗<class_Basis_operator_neq_Basis>`
如果两个 **Basis** 矩阵的分量不相等，则返回 ``true``\ 。
\ **注意：**\ 由于浮点精度误差，请考虑改用 :ref:`is_equal_approx<class_Basis_method_is_equal_approx>`\ ，这样更可靠。
.. rst-class:: classref-item-separator
----
.. _class_Basis_operator_mul_Basis:
.. rst-class:: classref-operator
:ref:`Basis<class_Basis>` **operator ***\ (\ right\: :ref:`Basis<class_Basis>`\ ) :ref:`🔗<class_Basis_operator_mul_Basis>`
由该基转换（乘以） ``right`` 基。
这是父级和子级 :ref:`Node3D<class_Node3D>` 之间执行的操作。
.. rst-class:: classref-item-separator
----
.. _class_Basis_operator_mul_Vector3:
.. rst-class:: classref-operator
:ref:`Vector3<class_Vector3>` **operator ***\ (\ right\: :ref:`Vector3<class_Vector3>`\ ) :ref:`🔗<class_Basis_operator_mul_Vector3>`
由该基变换（乘以）\ ``right`` 向量，返回一个 :ref:`Vector3<class_Vector3>`\ 。
.. tabs::
.. code-tab:: gdscript
# 交换 X/Z 轴并使缩放加倍的基。
var my_basis = Basis(Vector3(0, 2, 0), Vector3(2, 0, 0), Vector3(0, 0, 2))
print(my_basis * Vector3(1, 2, 3)) # 输出 (4, 2, 6)
.. code-tab:: csharp
// 交换 X/Z 轴并使缩放加倍的基。
var myBasis = new Basis(new Vector3(0, 2, 0), new Vector3(2, 0, 0), new Vector3(0, 0, 2));
GD.Print(myBasis * new Vector3(1, 2, 3)); // 输出 (4, 2, 6)
.. rst-class:: classref-item-separator
----
.. _class_Basis_operator_mul_float:
.. rst-class:: classref-operator
:ref:`Basis<class_Basis>` **operator ***\ (\ right\: :ref:`float<class_float>`\ ) :ref:`🔗<class_Basis_operator_mul_float>`
将 **Basis** 的所有分量乘以给定的 :ref:`float<class_float>`\ 。这会均匀地影响该基矩阵的缩放，并通过 ``right`` 值调整所有 3 个轴的大小。
.. rst-class:: classref-item-separator
----
.. _class_Basis_operator_mul_int:
.. rst-class:: classref-operator
:ref:`Basis<class_Basis>` **operator ***\ (\ right\: :ref:`int<class_int>`\ ) :ref:`🔗<class_Basis_operator_mul_int>`
将该 **Basis** 的所有分量乘以给定的 :ref:`int<class_int>`\ 。这会均匀地影响该基的缩放，并通过 ``right`` 值调整所有 3 个轴的大小。
.. rst-class:: classref-item-separator
----
.. _class_Basis_operator_div_float:
.. rst-class:: classref-operator
:ref:`Basis<class_Basis>` **operator /**\ (\ right\: :ref:`float<class_float>`\ ) :ref:`🔗<class_Basis_operator_div_float>`
将 **Basis** 的所有分量除以给定的 :ref:`float<class_float>`\ 。这会均匀地影响该基的缩放，并通过 ``right`` 值调整所有 3 个轴的大小。
.. rst-class:: classref-item-separator
----
.. _class_Basis_operator_div_int:
.. rst-class:: classref-operator
:ref:`Basis<class_Basis>` **operator /**\ (\ right\: :ref:`int<class_int>`\ ) :ref:`🔗<class_Basis_operator_div_int>`
将 **Basis** 的所有分量除以给定的 :ref:`int<class_int>`\ 。这会均匀地影响该基的缩放，并通过 ``right`` 值调整所有 3 个轴的大小。
.. rst-class:: classref-item-separator
----
.. _class_Basis_operator_eq_Basis:
.. rst-class:: classref-operator
:ref:`bool<class_bool>` **operator ==**\ (\ right\: :ref:`Basis<class_Basis>`\ ) :ref:`🔗<class_Basis_operator_eq_Basis>`
如果两个 **Basis** 矩阵的分量完全相等，则返回 ``true``\ 。
\ **注意：**\ 由于浮点精度误差，请考虑改用 :ref:`is_equal_approx<class_Basis_method_is_equal_approx>`\ ，这样更可靠。
.. rst-class:: classref-item-separator
----
.. _class_Basis_operator_idx_int:
.. rst-class:: classref-operator
:ref:`Vector3<class_Vector3>` **operator []**\ (\ index\: :ref:`int<class_int>`\ ) :ref:`🔗<class_Basis_operator_idx_int>`
通过索引访问该基的每个轴（列）。索引 ``0`` 与 :ref:`x<class_Basis_property_x>` 相同，索引 ``1`` 与 :ref:`y<class_Basis_property_y>` 相同，索引 ``2`` 与 :ref:`z<class_Basis_property_z>` 相同。
\ **注意：**\ 在 C++ 中，该运算符访问基础矩阵的行，而\ *不*\ 是列。对于与脚本语言相同的行为，请使用 ``set_column`` 和 ``get_column`` 方法。
.. |virtual| replace:: :abbr:`virtual (本方法通常需要用户覆盖才能生效。)`
.. |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。)`
Reference in New Issue View Git Blame Copy Permalink