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<?xml version="1.0" encoding="UTF-8" ?>
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<class name= "Basis" version= "4.0" xmlns:xsi= "http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation= "../class.xsd" >
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<brief_description >
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A 3× 3 matrix for representing 3D rotation and scale.
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</brief_description>
<description >
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A 3× 3 matrix used for representing 3D rotation and scale. Usually used as an orthogonal basis for a [Transform3D].
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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).
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Basis can also be accessed as an array of 3D vectors. These vectors are usually orthogonal to each other, but are not necessarily normalized (due to scaling).
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For more information, read the "Matrices and transforms" documentation article.
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</description>
<tutorials >
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<link title= "Math documentation index" > $DOCS_URL/tutorials/math/index.html</link>
<link title= "Matrices and transforms" > $DOCS_URL/tutorials/math/matrices_and_transforms.html</link>
<link title= "Using 3D transforms" > $DOCS_URL/tutorials/3d/using_transforms.html</link>
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<link title= "Matrix Transform Demo" > https://godotengine.org/asset-library/asset/584</link>
<link title= "3D Platformer Demo" > https://godotengine.org/asset-library/asset/125</link>
<link title= "3D Voxel Demo" > https://godotengine.org/asset-library/asset/676</link>
<link title= "2.5D Demo" > https://godotengine.org/asset-library/asset/583</link>
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</tutorials>
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<constructors >
<constructor name= "Basis" >
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<return type= "Basis" />
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<description >
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Constructs a default-initialized [Basis] set to [constant IDENTITY].
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</description>
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</constructor>
<constructor name= "Basis" >
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<return type= "Basis" />
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<param index= "0" name= "from" type= "Basis" />
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<description >
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Constructs a [Basis] as a copy of the given [Basis].
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</description>
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</constructor>
<constructor name= "Basis" >
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<return type= "Basis" />
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<param index= "0" name= "axis" type= "Vector3" />
<param index= "1" name= "angle" type= "float" />
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<description >
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Constructs a pure rotation basis matrix, rotated around the given [param axis] by [param angle] (in radians). The axis must be a normalized vector.
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</description>
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</constructor>
<constructor name= "Basis" >
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<return type= "Basis" />
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<param index= "0" name= "from" type= "Quaternion" />
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<description >
Constructs a pure rotation basis matrix from the given quaternion.
</description>
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</constructor>
<constructor name= "Basis" >
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<return type= "Basis" />
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<param index= "0" name= "x_axis" type= "Vector3" />
<param index= "1" name= "y_axis" type= "Vector3" />
<param index= "2" name= "z_axis" type= "Vector3" />
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<description >
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Constructs a basis matrix from 3 axis vectors (matrix columns).
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</description>
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</constructor>
</constructors>
<methods >
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<method name= "determinant" qualifiers= "const" >
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<return type= "float" />
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<description >
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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.
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</description>
</method>
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<method name= "from_euler" qualifiers= "static" >
<return type= "Basis" />
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<param index= "0" name= "euler" type= "Vector3" />
<param index= "1" name= "order" type= "int" default= "2" />
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<description >
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Constructs a pure rotation Basis matrix from Euler angles in the specified Euler rotation order. By default, use YXZ order (most common). See the [enum EulerOrder] enum for possible values.
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</description>
</method>
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<method name= "from_scale" qualifiers= "static" >
<return type= "Basis" />
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<param index= "0" name= "scale" type= "Vector3" />
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<description >
Constructs a pure scale basis matrix with no rotation or shearing. The scale values are set as the diagonal of the matrix, and the other parts of the matrix are zero.
</description>
</method>
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<method name= "get_euler" qualifiers= "const" >
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<return type= "Vector3" />
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<param index= "0" name= "order" type= "int" default= "2" />
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<description >
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Returns the basis's rotation in the form of Euler angles. The Euler order depends on the [param order] parameter, by default it uses 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).
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Consider using the [method get_rotation_quaternion] method instead, which returns a [Quaternion] quaternion instead of Euler angles.
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</description>
</method>
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<method name= "get_rotation_quaternion" qualifiers= "const" >
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<return type= "Quaternion" />
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<description >
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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.
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</description>
</method>
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<method name= "get_scale" qualifiers= "const" >
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<return type= "Vector3" />
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<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>
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<method name= "inverse" qualifiers= "const" >
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<return type= "Basis" />
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<description >
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Returns the inverse of the matrix.
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</description>
</method>
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<method name= "is_equal_approx" qualifiers= "const" >
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<return type= "bool" />
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<param index= "0" name= "b" type= "Basis" />
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<description >
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Returns [code]true[/code] if this basis and [param b] are approximately equal, by calling [method @GlobalScope.is_equal_approx] on all vector components.
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</description>
</method>
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<method name= "is_finite" qualifiers= "const" >
<return type= "bool" />
<description >
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Returns [code]true[/code] if this basis is finite, by calling [method @GlobalScope.is_finite] on all vector components.
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</description>
</method>
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<method name= "looking_at" qualifiers= "static" >
<return type= "Basis" />
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<param index= "0" name= "target" type= "Vector3" />
<param index= "1" name= "up" type= "Vector3" default= "Vector3(0, 1, 0)" />
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<description >
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Creates a Basis with a rotation such that the forward axis (-Z) points towards the [param target] position.
The up axis (+Y) points as close to the [param up] vector as possible while staying perpendicular to the forward axis. The resulting Basis is orthonormalized. The [param target] and [param up] vectors cannot be zero, and cannot be parallel to each other.
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</description>
</method>
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<method name= "orthonormalized" qualifiers= "const" >
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<return type= "Basis" />
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<description >
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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.
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</description>
</method>
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<method name= "rotated" qualifiers= "const" >
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<return type= "Basis" />
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<param index= "0" name= "axis" type= "Vector3" />
<param index= "1" name= "angle" type= "float" />
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<description >
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Introduce an additional rotation around the given axis by [param angle] (in radians). The axis must be a normalized vector.
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</description>
</method>
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<method name= "scaled" qualifiers= "const" >
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<return type= "Basis" />
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<param index= "0" name= "scale" type= "Vector3" />
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<description >
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Introduce an additional scaling specified by the given 3D scaling factor.
</description>
</method>
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<method name= "slerp" qualifiers= "const" >
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<return type= "Basis" />
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<param index= "0" name= "to" type= "Basis" />
<param index= "1" name= "weight" type= "float" />
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<description >
Assuming that the matrix is a proper rotation matrix, slerp performs a spherical-linear interpolation with another rotation matrix.
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</description>
</method>
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<method name= "tdotx" qualifiers= "const" >
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<return type= "float" />
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<param index= "0" name= "with" type= "Vector3" />
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<description >
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Transposed dot product with the X axis of the matrix.
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</description>
</method>
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<method name= "tdoty" qualifiers= "const" >
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<return type= "float" />
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<param index= "0" name= "with" type= "Vector3" />
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<description >
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Transposed dot product with the Y axis of the matrix.
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</description>
</method>
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<method name= "tdotz" qualifiers= "const" >
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<return type= "float" />
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<param index= "0" name= "with" type= "Vector3" />
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<description >
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Transposed dot product with the Z axis of the matrix.
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</description>
</method>
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<method name= "transposed" qualifiers= "const" >
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<return type= "Basis" />
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<description >
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Returns the transposed version of the matrix.
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</description>
</method>
</methods>
<members >
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<member name= "x" type= "Vector3" setter= "" getter= "" default= "Vector3(1, 0, 0)" >
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The basis matrix's X vector (column 0). Equivalent to array index [code]0[/code].
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</member>
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<member name= "y" type= "Vector3" setter= "" getter= "" default= "Vector3(0, 1, 0)" >
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The basis matrix's Y vector (column 1). Equivalent to array index [code]1[/code].
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</member>
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<member name= "z" type= "Vector3" setter= "" getter= "" default= "Vector3(0, 0, 1)" >
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The basis matrix's Z vector (column 2). Equivalent to array index [code]2[/code].
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</member>
</members>
<constants >
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<constant name= "IDENTITY" value= "Basis(1, 0, 0, 0, 1, 0, 0, 0, 1)" >
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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#.
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</constant>
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<constant name= "FLIP_X" value= "Basis(-1, 0, 0, 0, 1, 0, 0, 0, 1)" >
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The basis that will flip something along the X axis when used in a transformation.
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</constant>
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<constant name= "FLIP_Y" value= "Basis(1, 0, 0, 0, -1, 0, 0, 0, 1)" >
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The basis that will flip something along the Y axis when used in a transformation.
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</constant>
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<constant name= "FLIP_Z" value= "Basis(1, 0, 0, 0, 1, 0, 0, 0, -1)" >
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The basis that will flip something along the Z axis when used in a transformation.
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</constant>
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</constants>
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<operators >
<operator name= "operator !=" >
<return type= "bool" />
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<param index= "0" name= "right" type= "Basis" />
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<description >
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Returns [code]true[/code] if the [Basis] matrices are not equal.
[b]Note:[/b] Due to floating-point precision errors, consider using [method is_equal_approx] instead, which is more reliable.
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</description>
</operator>
<operator name= "operator *" >
<return type= "Basis" />
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<param index= "0" name= "right" type= "Basis" />
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<description >
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Composes these two basis matrices by multiplying them together. This has the effect of transforming the second basis (the child) by the first basis (the parent).
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</description>
</operator>
<operator name= "operator *" >
<return type= "Vector3" />
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<param index= "0" name= "right" type= "Vector3" />
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<description >
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Transforms (multiplies) the [Vector3] by the given [Basis] matrix.
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</description>
</operator>
<operator name= "operator *" >
<return type= "Basis" />
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<param index= "0" name= "right" type= "float" />
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<description >
This operator multiplies all components of the [Basis], which scales it uniformly.
</description>
</operator>
<operator name= "operator *" >
<return type= "Basis" />
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<param index= "0" name= "right" type= "int" />
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<description >
This operator multiplies all components of the [Basis], which scales it uniformly.
</description>
</operator>
<operator name= "operator ==" >
<return type= "bool" />
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<param index= "0" name= "right" type= "Basis" />
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<description >
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Returns [code]true[/code] if the [Basis] matrices are exactly equal.
[b]Note:[/b] Due to floating-point precision errors, consider using [method is_equal_approx] instead, which is more reliable.
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</description>
</operator>
<operator name= "operator []" >
<return type= "Vector3" />
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<param index= "0" name= "index" type= "int" />
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<description >
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Access basis components using their index. [code]b[0][/code] is equivalent to [code]b.x[/code], [code]b[1][/code] is equivalent to [code]b.y[/code], and [code]b[2][/code] is equivalent to [code]b.z[/code].
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</description>
</operator>
</operators>
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</class>