A 2×3 matrix (2 rows, 3 columns) used for 2D linear transformations. It can represent transformations such as translation, rotation, and scaling. It consists of three Vector2 values: x, y, and the origin.
For a general introduction, see the Matrices and transforms tutorial.
Constructs a default-initialized Transform2D set to IDENTITY.
Constructs a Transform2D as a copy of the given Transform2D.
Constructs the transform from a given angle (in radians) and position.
Constructs the transform from a given angle (in radians), scale, skew (in radians) and position.
Constructs the transform from 3 Vector2 values representing x, y, and the origin (the three column vectors).
Returns true
if the transforms are not equal.
Note: Due to floating-point precision errors, consider using is_equal_approx instead, which is more reliable.
Transforms (multiplies) each element of the Vector2 array by the given Transform2D matrix.
Transforms (multiplies) the Rect2 by the given Transform2D matrix.
Composes these two transformation matrices by multiplying them together. This has the effect of transforming the second transform (the child) by the first transform (the parent).
Transforms (multiplies) the Vector2 by the given Transform2D matrix.
This operator multiplies all components of the Transform2D, including the origin vector, which scales it uniformly.
This operator multiplies all components of the Transform2D, including the origin vector, which scales it uniformly.
This operator divides all components of the Transform2D, including the origin vector, which inversely scales it uniformly.
This operator divides all components of the Transform2D, including the origin vector, which inversely scales it uniformly.
Returns true
if the transforms are exactly equal.
Note: Due to floating-point precision errors, consider using is_equal_approx instead, which is more reliable.
Access transform components using their index. t[0]
is equivalent to t.x
, t[1]
is equivalent to t.y
, and t[2]
is equivalent to t.origin
.
The origin vector (column 2, the third column). Equivalent to array index 2
. The origin vector represents translation.
The basis matrix's X vector (column 0). Equivalent to array index 0
.
The basis matrix's Y vector (column 1). Equivalent to array index 1
.
Returns the inverse of the transform, under the assumption that the basis is invertible (must have non-zero determinant).
Returns a vector transformed (multiplied) by the basis matrix.
This method does not account for translation (the origin vector).
Returns a vector transformed (multiplied) by the inverse basis matrix, under the assumption that the basis is orthonormal (i.e. rotation/reflection is fine, scaling/skew is not).
This method does not account for translation (the origin vector).
transform.basis_xform_inv(vector)
is equivalent to transform.inverse().basis_xform(vector)
. See inverse.
For non-orthonormal transforms (e.g. with scaling) transform.affine_inverse().basis_xform(vector)
can be used instead. See affine_inverse.
Returns the determinant of the basis matrix. If the basis is uniformly scaled, then its determinant equals the square of the scale factor.
A negative determinant means the basis was flipped, so one part of the scale is negative. A zero determinant means the basis isn't invertible, and is usually considered invalid.
Returns the transform's origin (translation).
Returns the transform's rotation (in radians).
Returns the scale.
Returns the transform's skew (in radians).
Returns a transform interpolated between this transform and another by a given weight
(on the range of 0.0 to 1.0).
Returns the inverse of the transform, under the assumption that the transformation basis is orthonormal (i.e. rotation/reflection is fine, scaling/skew is not). Use affine_inverse for non-orthonormal transforms (e.g. with scaling).
Returns true
if the transform's basis is conformal, meaning it preserves angles and distance ratios, and may only be composed of rotation and uniform scale. Returns false
if the transform's basis has non-uniform scale or shear/skew. This can be used to validate if the transform is non-distorted, which is important for physics and other use cases.
Returns true
if this transform and xform
are approximately equal, by running @GlobalScope.is_equal_approx on each component.
Returns true
if this transform is finite, by calling @GlobalScope.is_finite on each component.
Returns a copy of the transform rotated such that the rotated X-axis points towards the target
position.
Operations take place in global space.
Returns the transform with the basis orthogonal (90 degrees), and normalized axis vectors (scale of 1 or -1).
Returns a copy of the transform rotated by the given angle
(in radians).
This method is an optimized version of multiplying the given transform X
with a corresponding rotation transform R
from the left, i.e., R * X
.
This can be seen as transforming with respect to the global/parent frame.
Returns a copy of the transform rotated by the given angle
(in radians).
This method is an optimized version of multiplying the given transform X
with a corresponding rotation transform R
from the right, i.e., X * R
.
This can be seen as transforming with respect to the local frame.
Returns a copy of the transform scaled by the given scale
factor.
This method is an optimized version of multiplying the given transform X
with a corresponding scaling transform S
from the left, i.e., S * X
.
This can be seen as transforming with respect to the global/parent frame.
Returns a copy of the transform scaled by the given scale
factor.
This method is an optimized version of multiplying the given transform X
with a corresponding scaling transform S
from the right, i.e., X * S
.
This can be seen as transforming with respect to the local frame.
Returns a copy of the transform translated by the given offset
.
This method is an optimized version of multiplying the given transform X
with a corresponding translation transform T
from the left, i.e., T * X
.
This can be seen as transforming with respect to the global/parent frame.
Returns a copy of the transform translated by the given offset
.
This method is an optimized version of multiplying the given transform X
with a corresponding translation transform T
from the right, i.e., X * T
.
This can be seen as transforming with respect to the local frame.