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Basis¶
A 3×3 matrix for representing 3D rotation and scale.
Description¶
A 3×3 matrix used for representing 3D rotation and scale. Usually used as an orthogonal basis for a Transform3D.
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).
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).
For more information, read the "Matrices and transforms" documentation article.
참고
There are notable differences when using this API with C#. See C#과 GDScript의 API 차이점 for more information.
Tutorials¶
Properties¶
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Constructors¶
Basis ( ) |
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Basis ( Quaternion from ) |
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Methods¶
determinant ( ) const |
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from_euler ( Vector3 euler, int order=2 ) static |
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from_scale ( Vector3 scale ) static |
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get_rotation_quaternion ( ) const |
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get_scale ( ) const |
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inverse ( ) const |
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is_conformal ( ) const |
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is_equal_approx ( Basis b ) const |
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is_finite ( ) const |
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looking_at ( Vector3 target, Vector3 up=Vector3(0, 1, 0), bool use_model_front=false ) static |
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orthonormalized ( ) const |
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transposed ( ) const |
Operators¶
operator != ( Basis right ) |
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operator * ( Basis right ) |
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operator * ( Vector3 right ) |
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operator * ( float right ) |
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operator * ( int right ) |
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operator == ( Basis right ) |
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operator [] ( int index ) |
Constants¶
IDENTITY = Basis(1, 0, 0, 0, 1, 0, 0, 0, 1)
The identity basis, with no rotation or scaling applied.
This is identical to creating Basis without any parameters. This constant can be used to make your code clearer, and for consistency with C#.
FLIP_X = 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.
FLIP_Y = 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.
FLIP_Z = 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.
Property Descriptions¶
Vector3 x = Vector3(1, 0, 0)
The basis matrix's X vector (column 0). Equivalent to array index 0.
Vector3 y = Vector3(0, 1, 0)
The basis matrix's Y vector (column 1). Equivalent to array index 1.
Vector3 z = Vector3(0, 0, 1)
The basis matrix's Z vector (column 2). Equivalent to array index 2.
Constructor Descriptions¶
Basis Basis ( )
Constructs a default-initialized Basis set to IDENTITY.
Constructs a Basis as a copy of the given Basis.
Basis Basis ( Vector3 axis, float angle )
Constructs a pure rotation basis matrix, rotated around the given axis by angle (in radians). The axis must be a normalized vector.
Basis Basis ( Quaternion from )
Constructs a pure rotation basis matrix from the given quaternion.
Basis Basis ( Vector3 x_axis, Vector3 y_axis, Vector3 z_axis )
Constructs a basis matrix from 3 axis vectors (matrix columns).
Method Descriptions¶
float determinant ( ) const
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.
Basis from_euler ( Vector3 euler, int order=2 ) static
Constructs a pure rotation Basis matrix from Euler angles in the specified Euler rotation order. By default, use YXZ order (most common). See the EulerOrder enum for possible values.
Basis from_scale ( Vector3 scale ) static
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.
Vector3 get_euler ( int order=2 ) const
Returns the basis's rotation in the form of Euler angles. The Euler order depends on the 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).
Consider using the get_rotation_quaternion method instead, which returns a Quaternion quaternion instead of Euler angles.
Quaternion get_rotation_quaternion ( ) const
Returns the basis's rotation in the form of a quaternion. See get_euler if you need Euler angles, but keep in mind quaternions should generally be preferred to Euler angles.
Vector3 get_scale ( ) const
Assuming that the matrix is the combination of a rotation and scaling, return the absolute value of scaling factors along each axis.
Basis inverse ( ) const
Returns the inverse of the matrix.
bool is_conformal ( ) const
Returns true if the basis is conformal, meaning it preserves angles and distance ratios, and may only be composed of rotation and uniform scale. Returns false if the basis has non-uniform scale or shear/skew. This can be used to validate if the basis is non-distorted, which is important for physics and other use cases.
bool is_equal_approx ( Basis b ) const
Returns true if this basis and b are approximately equal, by calling @GlobalScope.is_equal_approx on all vector components.
bool is_finite ( ) const
Returns true if this