Transform2D

代表 2D 变换的 2×3 矩阵。

描述

The Transform2D built-in Variant type is a 2×3 matrix) representing a transformation in 2D space. It contains three Vector2 values: x, y, and origin. Together, they can represent translation, rotation, scale, and skew.

The x and y axes form a 2×2 matrix, known as the transform’s basis. The length of each axis (Vector2.length) influences the transform’s scale, while the direction of all axes influence the rotation. Usually, both axes are perpendicular to one another. However, when you rotate one axis individually, the transform becomes skewed. Applying a skewed transform to a 2D sprite will make the sprite appear distorted.

For a general introduction, see the Matrices and transforms tutorial.

Note: Unlike Transform3D, there is no 2D equivalent to the Basis type. All mentions of “basis” refer to the x and y components of Transform2D.

备注

通过 C# 使用该 API 时会有显著不同，详见 C# API 与 GDScript 的差异。

教程

• 数学文档索引

• 矩阵与变换

• 矩阵变换演示

• 2.5D 游戏演示

属性

构造函数

方法

运算符

常量

IDENTITY = Transform2D(1, 0, 0, 1, 0, 0) 🔗

The identity Transform2D. A transform with no translation, no rotation, and its scale being 1. When multiplied by another Variant such as Rect2 or another Transform2D, no transformation occurs. This means that:

• The x points right (Vector2.RIGHT);

• The y points up (Vector2.UP).

var transform = Transform2D.IDENTITY
print("| X | Y | Origin")
print("| %s | %s | %s" % [transform.x.x, transform.y.x, transform.origin.x])
print("| %s | %s | %s" % [transform.x.y, transform.y.y, transform.origin.y])
# Prints:
# | X | Y | Origin
# | 1 | 0 | 0
# | 0 | 1 | 0

This is identical to creating Transform2D without any parameters. This constant can be used to make your code clearer, and for consistency with C#.

FLIP_X = Transform2D(-1, 0, 0, 1, 0, 0) 🔗

When any transform is multiplied by FLIP_X, it negates all components of the x axis (the X column).

When FLIP_X is multiplied by any basis, it negates the Vector2.x component of all axes (the X row).

FLIP_Y = Transform2D(1, 0, 0, -1, 0, 0) 🔗

When any transform is multiplied by FLIP_Y, it negates all components of the y axis (the Y column).

When FLIP_Y is multiplied by any basis, it negates the Vector2.y component of all axes (the Y row).

属性说明

Vector2 origin = Vector2(0, 0) 🔗

The translation offset of this transform, and the column 2 of the matrix. In 2D space, this can be seen as the position.

Vector2 x = Vector2(1, 0) 🔗

The transform basis’s X axis, and the column 0 of the matrix. Combined with y, this represents the transform’s rotation, scale, and skew.

On the identity transform, this vector points right (Vector2.RIGHT).

Vector2 y = Vector2(0, 1) 🔗

The transform basis’s Y axis, and the column 1 of the matrix. Combined with x, this represents the transform’s rotation, scale, and skew.

On the identity transform, this vector points up (Vector2.UP).

构造函数说明

Transform2D Transform2D() 🔗

Constructs a Transform2D identical to IDENTITY.

Transform2D Transform2D(from: Transform2D)

构造给定 Transform2D 的副本。

Transform2D Transform2D(rotation: float, position: Vector2)

Constructs a Transform2D from a given angle (in radians) and position.

Transform2D Transform2D(rotation: float, scale: Vector2, skew: float, position: Vector2)

Constructs a Transform2D from a given angle (in radians), scale, skew (in radians), and position.

Transform2D Transform2D(x_axis: Vector2, y_axis: Vector2, origin: Vector2)

Constructs a Transform2D from 3 Vector2 values representing x, y, and the origin (the three matrix columns).

方法说明

Transform2D affine_inverse() const 🔗

Returns the inverted version of this transform. Unlike inverse, this method works with almost any basis, including non-uniform ones, but is slower. See also inverse.

Note: For this method to return correctly, the transform’s basis needs to have a determinant that is not exactly 0 (see determinant).

Vector2 basis_xform(v: Vector2) const 🔗

Returns a copy of the v vector, transformed (multiplied) by the transform basis’s matrix. Unlike the multiplication operator (*), this method ignores the origin.

Vector2 basis_xform_inv(v: Vector2) const 🔗

Returns a copy of the v vector, transformed (multiplied) by the inverse transform basis’s matrix (see inverse). This method ignores the origin.

Note: This method assumes that this transform’s basis is orthonormal (see orthonormalized). If the basis is not orthonormal, transform.affine_inverse().basis_xform(vector) should be used instead (see affine_inverse).

float determinant() const 🔗

Returns the determinant of this transform basis’s matrix. For advanced math, this number can be used to determine a few attributes:

• If the determinant is exactly 0, the basis is not invertible (see inverse).

• If the determinant is a negative number, the basis represents a negative scale.

Note: If the basis’s scale is the same for every axis, its determinant is always that scale by the power of 2.

Vector2 get_origin() const 🔗

Returns this transform’s translation. Equivalent to origin.

float get_rotation() const 🔗

Returns this transform’s rotation (in radians). This is equivalent to x‘s angle (see Vector2.angle).

Vector2 get_scale() const 🔗

Returns the length of both x and y, as a Vector2. If this transform’s basis is not skewed, this value is the scaling factor. It is not affected by rotation.

GDScriptC#

var my_transform = Transform2D(
    Vector2(2, 0),
    Vector2(0, 4),
    Vector2(0, 0)
)
# Rotating the Transform2D in any way preserves its scale.
my_transform = my_transform.rotated(TAU / 2)
print(my_transform.get_scale()) # Prints (2, 4).

var myTransform = new Transform2D(
    Vector3(2.0f, 0.0f),
    Vector3(0.0f, 4.0f),
    Vector3(0.0f, 0.0f)
);
// Rotating the Transform2D in any way preserves its scale.
myTransform = myTransform.Rotated(Mathf.Tau / 2.0f);
GD.Print(myTransform.GetScale()); // Prints (2, 4, 8).

Note: If the value returned by determinant is negative, the scale is also negative.

float get_skew() const 🔗

Returns this transform’s skew (in radians).

Transform2D interpolate_with(xform: Transform2D, weight: float) const 🔗

返回将该变换和 xform 按照给定的权重 weight 进行线性插值结果。

weight 应该在 0.0 到 1.0（闭区间）的范围内。允许使用超出这个范围的值，表示进行外插。

Transform2D inverse() const 🔗

Returns the inverted version of this transform.

Note: For this method to return correctly, the transform’s basis needs to be orthonormal (see orthonormalized). That means, the basis should only represent a rotation. If it does not, use affine_inverse instead.

bool is_conformal() const 🔗

Returns true if this transform’s basis is conformal. A conformal basis is both orthogonal (the axes are perpendicular to each other) and uniform (the axes share the same length). This method can be especially useful during physics calculations.

bool is_equal_approx(xform: Transform2D) const 🔗

如果通过在每个分量上运行 @GlobalScope.is_equal_approx，该变换和 xform 近似相等，则返回 true。

bool is_finite() const 🔗

如果该变换是有限的，则返回 true，判断方法是在每个分量上调用 @GlobalScope.is_finite。

Transform2D looking_at(target: Vector2 = Vector2(0, 0)) const 🔗

Returns a copy of the transform rotated such that the rotated X-axis points towards the target position, in global space.

Transform2D orthonormalized() const 🔗

Returns a copy of this transform with its basis orthonormalized. An orthonormal basis is both orthogonal (the axes are perpendicular to each other) and normalized (the axes have a length of 1), which also means it can only represent rotation.

Transform2D rotated(angle: float) const 🔗

返回该变换的副本，该副本进行了夹角为 angle 的旋转操作（单位为弧度）。

这个方法的结果和让 X 变换与相应的旋转变换 R 从左侧相乘一致，即 R * X，但进行了优化。

可以视作在全局/父级坐标系中的变换。

Transform2D rotated_local(angle: float) const 🔗

返回该变换的副本，该副本进行了夹角为 angle 的旋转操作（单位为弧度）。

这个方法的结果和让 X 变换与相应的旋转变换 R 从右侧相乘一致，即 X * R，但进行了优化。

可以视作在局部坐标系中的变换。

Transform2D scaled(scale: Vector2) const 🔗

返回该变换的副本，该副本进行了系数为 scale 的缩放操作。

这个方法的结果和让 X 变换与相应的缩放变换 S 从左侧相乘一致，即 S * X，但进行了优化。

可以视作在全局/父级坐标系中的变换。

Transform2D scaled_local(scale: Vector2) const 🔗

返回该变换的副本，该副本进行了系数为 scale 的缩放操作。

这个方法的结果和让 X 变换与相应的缩放变换 S 从右侧相乘一致，即 X * S，但进行了优化。

可以视作在局部坐标系中的变换。

Transform2D translated(offset: Vector2) const 🔗

返回该变换的副本，该副本进行了偏移量为 offset 的平移操作。

这个方法的结果和让 X 变换与相应的平移变换 T 从左侧相乘一致，即 T * X，但进行了优化。

可以视作在全局/父级坐标系中的变换。

Transform2D translated_local(offset: Vector2) const 🔗

返回该变换的副本，该副本进行了偏移量为 offset 的平移操作。

这个方法的结果和让 X 变换与相应的平移变换 T 从右侧相乘一致，即 X * T，但进行了优化。

可以视作在局部坐标系中的变换。

运算符说明

bool operator !=(right: Transform2D) 🔗

如果两个变换的分量不相等，则返回 true。

注意：由于浮点精度误差，请考虑改用 is_equal_approx，这样更可靠。

PackedVector2Array operator *(right: PackedVector2Array) 🔗

Transforms (multiplies) every Vector2 element of the given PackedVector2Array by this transformation matrix.

On larger arrays, this operation is much faster than transforming each Vector2 individually.

Rect2 operator *(right: Rect2) 🔗

Transforms (multiplies) the Rect2 by this transformation matrix.

Transform2D operator *(right: Transform2D) 🔗

Transforms (multiplies) this transform by the right transform.

This is the operation performed between parent and child CanvasItem nodes.

Note: If you need to only modify one attribute of this transform, consider using one of the following methods, instead:

• For translation, see translated or translated_local.

• For rotation, see rotated or rotated_local.

• For scale, see scaled or scaled_local.

Vector2 operator *(right: Vector2) 🔗

Transforms (multiplies) the Vector2 by this transformation matrix.

Transform2D operator *(right: float) 🔗

Multiplies all components of the Transform2D by the given float, including the origin. This affects the transform’s scale uniformly.

Transform2D operator *(right: int) 🔗

Multiplies all components of the Transform2D by the given int, including the origin. This affects the transform’s scale uniformly.

Transform2D operator /(right: float) 🔗

Divides all components of the Transform2D by the given float, including the origin. This affects the transform’s scale uniformly.

Transform2D operator /(right: int) 🔗

Divides all components of the Transform2D by the given int, including the origin. This affects the transform’s scale uniformly.

bool operator ==(right: Transform2D) 🔗

如果两个变换的分量完全相等，则返回 true。

注意：由于浮点精度误差，请考虑改用 is_equal_approx，这样更可靠。

Vector2 operator [](index: int) 🔗

Accesses each axis (column) of this transform by their index. Index 0 is the same as x, index 1 is the same as y, and index 2 is the same as origin.