<?xml version="1.0" encoding="UTF-8" ?>
<class name="Basis" version="3.2">
	<brief_description>
		3×3 matrix datatype.
	</brief_description>
	<description>
		3×3 matrix used for 3D rotation and scale. Almost always used as an orthogonal basis for a Transform.
		Contains 3 vector fields X, Y and Z as its columns, which are typically interpreted as the local basis vectors of a transformation. For such use, it is composed of a scaling and a rotation matrix, in that order (M = R.S).
		Can also be accessed as array of 3D vectors. These vectors are normally orthogonal to each other, but are not necessarily normalized (due to scaling).
		For more information, read the "Matrices and transforms" documentation article.
	</description>
	<tutorials>
		<link>https://docs.godotengine.org/en/latest/tutorials/math/matrices_and_transforms.html</link>
		<link>https://docs.godotengine.org/en/latest/tutorials/3d/using_transforms.html</link>
	</tutorials>
	<methods>
		<method name="Basis">
			<return type="Basis">
			</return>
			<argument index="0" name="from" type="Quat">
			</argument>
			<description>
				Constructs a pure rotation basis matrix from the given quaternion.
			</description>
		</method>
		<method name="Basis">
			<return type="Basis">
			</return>
			<argument index="0" name="from" type="Vector3">
			</argument>
			<description>
				Constructs a pure rotation basis matrix from the given Euler angles (in the YXZ convention: when *composing*, first Y, then X, and Z last), given in the vector format as (X angle, Y angle, Z angle).
				Consider using the [Quat] constructor instead, which uses a quaternion instead of Euler angles.
			</description>
		</method>
		<method name="Basis">
			<return type="Basis">
			</return>
			<argument index="0" name="axis" type="Vector3">
			</argument>
			<argument index="1" name="phi" type="float">
			</argument>
			<description>
				Constructs a pure rotation basis matrix, rotated around the given [code]axis[/code] by [code]phi[/code], in radians. The axis must be a normalized vector.
			</description>
		</method>
		<method name="Basis">
			<return type="Basis">
			</return>
			<argument index="0" name="x_axis" type="Vector3">
			</argument>
			<argument index="1" name="y_axis" type="Vector3">
			</argument>
			<argument index="2" name="z_axis" type="Vector3">
			</argument>
			<description>
				Constructs a basis matrix from 3 axis vectors (matrix columns).
			</description>
		</method>
		<method name="determinant">
			<return type="float">
			</return>
			<description>
				Returns the determinant of the basis matrix. If the basis is uniformly scaled, its determinant is the square of the scale.
				A negative determinant means the basis has a negative scale. A zero determinant means the basis isn't invertible, and is usually considered invalid.
			</description>
		</method>
		<method name="get_euler">
			<return type="Vector3">
			</return>
			<description>
				Returns the basis's rotation in the form of Euler angles (in the YXZ convention: when decomposing, first Z, then X, and Y last). The returned vector contains the rotation angles in the format (X angle, Y angle, Z angle).
				Consider using the [method get_rotation_quat] method instead, which returns a [Quat] quaternion instead of Euler angles.
			</description>
		</method>
		<method name="get_orthogonal_index">
			<return type="int">
			</return>
			<description>
				This function considers a discretization of rotations into 24 points on unit sphere, lying along the vectors (x,y,z) with each component being either -1, 0, or 1, and returns the index of the point best representing the orientation of the object. It is mainly used by the [GridMap] editor. For further details, refer to the Godot source code.
			</description>
		</method>
		<method name="get_rotation_quat">
			<return type="Quat">
			</return>
			<description>
				Returns the basis's rotation in the form of a quaternion. See [method get_euler] if you need Euler angles, but keep in mind quaternions should generally be preferred to Euler angles.
			</description>
		</method>
		<method name="get_scale">
			<return type="Vector3">
			</return>
			<description>
				Assuming that the matrix is the combination of a rotation and scaling, return the absolute value of scaling factors along each axis.
			</description>
		</method>
		<method name="inverse">
			<return type="Basis">
			</return>
			<description>
				Returns the inverse of the matrix.
			</description>
		</method>
		<method name="is_equal_approx">
			<return type="bool">
			</return>
			<argument index="0" name="b" type="Basis">
			</argument>
			<argument index="1" name="epsilon" type="float" default="1e-05">
			</argument>
			<description>
				Returns [code]true[/code] if this basis and [code]b[/code] are approximately equal, by calling [code]is_equal_approx[/code] on each component.
			</description>
		</method>
		<method name="orthonormalized">
			<return type="Basis">
			</return>
			<description>
				Returns the orthonormalized version of the matrix (useful to call from time to time to avoid rounding error for orthogonal matrices). This performs a Gram-Schmidt orthonormalization on the basis of the matrix.
			</description>
		</method>
		<method name="rotated">
			<return type="Basis">
			</return>
			<argument index="0" name="axis" type="Vector3">
			</argument>
			<argument index="1" name="phi" type="float">
			</argument>
			<description>
				Introduce an additional rotation around the given axis by phi (radians). The axis must be a normalized vector.
			</description>
		</method>
		<method name="scaled">
			<return type="Basis">
			</return>
			<argument index="0" name="scale" type="Vector3">
			</argument>
			<description>
				Introduce an additional scaling specified by the given 3D scaling factor.
			</description>
		</method>
		<method name="slerp">
			<return type="Basis">
			</return>
			<argument index="0" name="b" type="Basis">
			</argument>
			<argument index="1" name="t" type="float">
			</argument>
			<description>
				Assuming that the matrix is a proper rotation matrix, slerp performs a spherical-linear interpolation with another rotation matrix.
			</description>
		</method>
		<method name="tdotx">
			<return type="float">
			</return>
			<argument index="0" name="with" type="Vector3">
			</argument>
			<description>
				Transposed dot product with the X axis of the matrix.
			</description>
		</method>
		<method name="tdoty">
			<return type="float">
			</return>
			<argument index="0" name="with" type="Vector3">
			</argument>
			<description>
				Transposed dot product with the Y axis of the matrix.
			</description>
		</method>
		<method name="tdotz">
			<return type="float">
			</return>
			<argument index="0" name="with" type="Vector3">
			</argument>
			<description>
				Transposed dot product with the Z axis of the matrix.
			</description>
		</method>
		<method name="transposed">
			<return type="Basis">
			</return>
			<description>
				Returns the transposed version of the matrix.
			</description>
		</method>
		<method name="xform">
			<return type="Vector3">
			</return>
			<argument index="0" name="v" type="Vector3">
			</argument>
			<description>
				Returns a vector transformed (multiplied) by the matrix.
			</description>
		</method>
		<method name="xform_inv">
			<return type="Vector3">
			</return>
			<argument index="0" name="v" type="Vector3">
			</argument>
			<description>
				Returns a vector transformed (multiplied) by the transposed basis matrix.
				[b]Note:[/b] This results in a multiplication by the inverse of the matrix only if it represents a rotation-reflection.
			</description>
		</method>
	</methods>
	<members>
		<member name="x" type="Vector3" setter="" getter="" default="Vector3( 1, 0, 0 )">
			The basis matrix's X vector (column 0). Equivalent to array index [code]0[/code].
		</member>
		<member name="y" type="Vector3" setter="" getter="" default="Vector3( 0, 1, 0 )">
			The basis matrix's Y vector (column 1). Equivalent to array index [code]1[/code].
		</member>
		<member name="z" type="Vector3" setter="" getter="" default="Vector3( 0, 0, 1 )">
			The basis matrix's Z vector (column 2). Equivalent to array index [code]2[/code].
		</member>
	</members>
	<constants>
		<constant name="IDENTITY" value="Basis( 1, 0, 0, 0, 1, 0, 0, 0, 1 )">
			The identity basis, with no rotation or scaling applied.
			This is identical to calling [code]Basis()[/code] without any parameters. This constant can be used to make your code clearer, and for consistency with C#.
		</constant>
		<constant name="FLIP_X" value="Basis( -1, 0, 0, 0, 1, 0, 0, 0, 1 )">
			The basis that will flip something along the X axis when used in a transformation.
		</constant>
		<constant name="FLIP_Y" value="Basis( 1, 0, 0, 0, -1, 0, 0, 0, 1 )">
			The basis that will flip something along the Y axis when used in a transformation.
		</constant>
		<constant name="FLIP_Z" value="Basis( 1, 0, 0, 0, 1, 0, 0, 0, -1 )">
			The basis that will flip something along the Z axis when used in a transformation.
		</constant>
	</constants>
</class>
