Struct Transform3D

Namespace

Godot

Assembly

GodotSharp.dll

3×4 matrix (3 rows, 4 columns) used for 3D linear transformations. It can represent transformations such as translation, rotation, or scaling. It consists of a Basis (first 3 columns) and a Vector3 for the origin (last column).

For more information, read this documentation article: https://docs.godotengine.org/en/latest/tutorials/math/matrices_and_transforms.html

public struct Transform3D : IEquatable<Transform3D>

Implements

IEquatable<Transform3D>

Inherited Members

object.GetType()

object.Equals(object, object)

object.ReferenceEquals(object, object)

Constructors

Transform3D(Basis, Vector3)

Constructs a transformation matrix from the given basis and origin vector.

public Transform3D(Basis basis, Vector3 origin)

Parameters

basis Basis

The Basis to create the basis from.

origin Vector3

The origin vector, or column index 3.

Transform3D(Projection)

Constructs a transformation matrix from the given projection by trimming the last row of the projection matrix (projection.X.W, projection.Y.W, projection.Z.W, and projection.W.W are not copied over).

public Transform3D(Projection projection)

Parameters

projection Projection

The Projection to create the transform from.

Transform3D(Vector3, Vector3, Vector3, Vector3)

Constructs a transformation matrix from 4 vectors (matrix columns).

public Transform3D(Vector3 column0, Vector3 column1, Vector3 column2, Vector3 origin)

Parameters

column0 Vector3

The X vector, or column index 0.

column1 Vector3

The Y vector, or column index 1.

column2 Vector3

The Z vector, or column index 2.

origin Vector3

The origin vector, or column index 3.

Transform3D(float, float, float, float, float, float, float, float, float, float, float, float)

Constructs a transformation matrix from the given components. Arguments are named such that xy is equal to calling Basis.X.Y.

public Transform3D(float xx, float yx, float zx, float xy, float yy, float zy, float xz, float yz, float zz, float ox, float oy, float oz)

Parameters

xx float

The X component of the X column vector, accessed via t.Basis.X.X or [0][0].

yx float

The X component of the Y column vector, accessed via t.Basis.Y.X or [1][0].

zx float

The X component of the Z column vector, accessed via t.Basis.Z.X or [2][0].

xy float

The Y component of the X column vector, accessed via t.Basis.X.Y or [0][1].

yy float

The Y component of the Y column vector, accessed via t.Basis.Y.Y or [1][1].

zy float

The Y component of the Z column vector, accessed via t.Basis.Y.Y or [2][1].

xz float

The Z component of the X column vector, accessed via t.Basis.X.Y or [0][2].

yz float

The Z component of the Y column vector, accessed via t.Basis.Y.Y or [1][2].

zz float

The Z component of the Z column vector, accessed via t.Basis.Y.Y or [2][2].

ox float

The X component of the origin vector, accessed via t.Origin.X or [2][0].

oy float

The Y component of the origin vector, accessed via t.Origin.Y or [2][1].

oz float

The Z component of the origin vector, accessed via t.Origin.Z or [2][2].

Fields

Basis

The Basis of this transform. Contains the X, Y, and Z basis vectors (columns 0 to 2) and is responsible for rotation and scale.

public Basis Basis

Field Value

Basis

Origin

The origin vector (column 3, the fourth column). Equivalent to array index [3].

public Vector3 Origin

Field Value

Vector3

Properties

FlipX

The transform that will flip something along the X axis.

public static Transform3D FlipX { get; }

Property Value

Transform3D

Equivalent to new Transform(Vector3.Left, Vector3.Up, Vector3.Back, Vector3.Zero).

FlipY

The transform that will flip something along the Y axis.

public static Transform3D FlipY { get; }

Property Value

Transform3D

Equivalent to new Transform(Vector3.Right, Vector3.Down, Vector3.Back, Vector3.Zero).

FlipZ

The transform that will flip something along the Z axis.

public static Transform3D FlipZ { get; }

Property Value

Transform3D

Equivalent to new Transform(Vector3.Right, Vector3.Up, Vector3.Forward, Vector3.Zero).

Identity

The identity transform, with no translation, rotation, or scaling applied. This is used as a replacement for Transform() in GDScript. Do not use new Transform() with no arguments in C#, because it sets all values to zero.

public static Transform3D Identity { get; }

Property Value

Transform3D

Equivalent to new Transform(Vector3.Right, Vector3.Up, Vector3.Back, Vector3.Zero).

this[int]

Access whole columns in the form of Vector3. The fourth column is the Origin vector.

public Vector3 this[int column] { readonly get; set; }

Parameters

column int

Which column vector.

Property Value

Vector3

Exceptions

ArgumentOutOfRangeException

column is not 0, 1, 2 or 3.

this[int, int]

Access matrix elements in column-major order. The fourth column is the Origin vector.

public float this[int column, int row] { readonly get; set; }

Parameters

column int

Which column, the matrix horizontal position.

row int

Which row, the matrix vertical position.

Property Value

float

Methods

AffineInverse()

Returns the inverse of the transform, under the assumption that the basis is invertible (must have non-zero determinant).

public readonly Transform3D AffineInverse()

Returns

Transform3D

The inverse transformation matrix.

See Also

Inverse()

Equals(Transform3D)

Returns true if the transforms are exactly equal. Note: Due to floating-point precision errors, consider using IsEqualApprox(Transform3D) instead, which is more reliable.

public readonly bool Equals(Transform3D other)

Parameters

other Transform3D

The other transform to compare.

Returns

bool

Whether or not the matrices are exactly equal.

Equals(object?)

Returns true if the transform is exactly equal to the given object (obj). Note: Due to floating-point precision errors, consider using IsEqualApprox(Transform3D) instead, which is more reliable.

public override readonly bool Equals(object? obj)

Parameters

obj object

The object to compare with.

Returns

bool

Whether or not the transform and the object are exactly equal.

GetHashCode()

Serves as the hash function for Transform3D.

public override readonly int GetHashCode()

Returns

int

A hash code for this transform.

InterpolateWith(Transform3D, float)

Returns a transform interpolated between this transform and another transform by a given weight (on the range of 0.0 to 1.0).

public readonly Transform3D InterpolateWith(Transform3D transform, float weight)

Parameters

transform Transform3D

The other transform.

weight float

A value on the range of 0.0 to 1.0, representing the amount of interpolation.

Returns

Transform3D

The interpolated transform.

Inverse()

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 AffineInverse() for non-orthonormal transforms (e.g. with scaling).

public readonly Transform3D Inverse()

Returns

Transform3D

The inverse matrix.

IsEqualApprox(Transform3D)

Returns true if this transform and other are approximately equal, by running IsEqualApprox(Vector3) on each component.

public readonly bool IsEqualApprox(Transform3D other)

Parameters

other Transform3D

The other transform to compare.

Returns

bool

Whether or not the matrices are approximately equal.

IsFinite()

Returns true if this transform is finite, by calling IsFinite(float) on each component.

public readonly bool IsFinite()

Returns

bool

Whether this vector is finite or not.

LookingAt(Vector3, Vector3?, bool)

Returns a copy of the transform rotated such that the forward axis (-Z) points towards the target position. The up axis (+Y) points as close to the up vector as possible while staying perpendicular to the forward axis. The resulting transform is orthonormalized. The existing rotation, scale, and skew information from the original transform is discarded. The target and up vectors cannot be zero, cannot be parallel to each other, and are defined in global/parent space.

public readonly Transform3D LookingAt(Vector3 target, Vector3? up = null, bool useModelFront = false)

Parameters

target Vector3

The object to look at.

up Vector3?

The relative up direction.

useModelFront bool

If true, then the model is oriented in reverse, towards the model front axis (+Z, Vector3.ModelFront), which is more useful for orienting 3D models.

Returns

Transform3D

The resulting transform.

Orthonormalized()

Returns the transform with the basis orthogonal (90 degrees), and normalized axis vectors (scale of 1 or -1).

public readonly Transform3D Orthonormalized()

Returns

Transform3D

The orthonormalized transform.

Rotated(Vector3, float)

Rotates the transform around the given axis by angle (in radians). The axis must be a normalized vector. The operation is done in the parent/global frame, equivalent to multiplying the matrix from the left.

public readonly Transform3D Rotated(Vector3 axis, float angle)

Parameters

axis Vector3

The axis to rotate around. Must be normalized.

angle float

The angle to rotate, in radians.

Returns

Transform3D

The rotated transformation matrix.

RotatedLocal(Vector3, float)

Rotates the transform around the given axis by angle (in radians). The axis must be a normalized vector. The operation is done in the local frame, equivalent to multiplying the matrix from the right.

public readonly Transform3D RotatedLocal(Vector3 axis, float angle)

Parameters

axis Vector3

The axis to rotate around. Must be normalized.

angle float

The angle to rotate, in radians.

Returns

Transform3D

The rotated transformation matrix.

Scaled(Vector3)

Scales the transform by the given 3D scale factor. The operation is done in the parent/global frame, equivalent to multiplying the matrix from the left.

public readonly Transform3D Scaled(Vector3 scale)

Parameters

scale Vector3

The scale to introduce.

Returns

Transform3D

The scaled transformation matrix.

ScaledLocal(Vector3)

Scales the transform by the given 3D scale factor. The operation is done in the local frame, equivalent to multiplying the matrix from the right.

public readonly Transform3D ScaledLocal(Vector3 scale)

Parameters

scale Vector3

The scale to introduce.

Returns

Transform3D

The scaled transformation matrix.

ToString()

Converts this Transform3D to a string.

public override readonly string ToString()

Returns

string

A string representation of this transform.

ToString(string?)

Converts this Transform3D to a string with the given format.

public readonly string ToString(string? format)

Parameters

format string

Returns

string

A string representation of this transform.

Translated(Vector3)

Translates the transform by the given offset. The operation is done in the parent/global frame, equivalent to multiplying the matrix from the left.

public readonly Transform3D Translated(Vector3 offset)

Parameters

offset Vector3

The offset to translate by.

Returns

Transform3D

The translated matrix.

TranslatedLocal(Vector3)

Translates the transform by the given offset. The operation is done in the local frame, equivalent to multiplying the matrix from the right.

public readonly Transform3D TranslatedLocal(Vector3 offset)

Parameters

offset Vector3

The offset to translate by.

Returns

Transform3D

The translated matrix.

Operators

operator ==(Transform3D, Transform3D)

Returns true if the transforms are exactly equal. Note: Due to floating-point precision errors, consider using IsEqualApprox(Transform3D) instead, which is more reliable.

public static bool operator ==(Transform3D left, Transform3D right)

Parameters

left Transform3D

The left transform.

right Transform3D

The right transform.

Returns

bool

Whether or not the transforms are exactly equal.

operator !=(Transform3D, Transform3D)

Returns true if the transforms are not equal. Note: Due to floating-point precision errors, consider using IsEqualApprox(Transform3D) instead, which is more reliable.

public static bool operator !=(Transform3D left, Transform3D right)

Parameters

left Transform3D

The left transform.

right Transform3D

The right transform.

Returns

bool

Whether or not the transforms are not equal.

operator *(Aabb, Transform3D)

Returns an AABB transformed (multiplied) by the inverse transformation matrix, under the assumption that the transformation basis is orthonormal (i.e. rotation/reflection is fine, scaling/skew is not). aabb * transform is equivalent to transform.Inverse() * aabb. See Inverse(). For transforming by inverse of an affine transformation (e.g. with scaling) transform.AffineInverse() * aabb can be used instead. See AffineInverse().

public static Aabb operator *(Aabb aabb, Transform3D transform)

Parameters

aabb Aabb

An AABB to inversely transform.

transform Transform3D

The transformation to apply.

Returns

Aabb

The inversely transformed AABB.

operator *(Plane, Transform3D)

Returns a Plane transformed (multiplied) by the inverse transformation matrix. plane * transform is equivalent to transform.AffineInverse() * plane. See AffineInverse().

public static Plane operator *(Plane plane, Transform3D transform)

Parameters

plane Plane

A Plane to inversely transform.

transform Transform3D

The transformation to apply.

Returns

Plane

The inversely transformed Plane.

operator *(Transform3D, Aabb)

Returns an AABB transformed (multiplied) by the transformation matrix.

public static Aabb operator *(Transform3D transform, Aabb aabb)

Parameters

transform Transform3D

The transformation to apply.

aabb Aabb

An AABB to transform.

Returns

Aabb

The transformed AABB.

operator *(Transform3D, Plane)

Returns a Plane transformed (multiplied) by the transformation matrix.

public static Plane operator *(Transform3D transform, Plane plane)

Parameters

transform Transform3D

The transformation to apply.

plane Plane

A Plane to transform.

Returns

Plane

The transformed Plane.

operator *(Transform3D, Transform3D)

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).

public static Transform3D operator *(Transform3D left, Transform3D right)

Parameters

left Transform3D

The parent transform.

right Transform3D

The child transform.

Returns

Transform3D

The composed transform.

operator *(Transform3D, Vector3)

Returns a Vector3 transformed (multiplied) by the transformation matrix.

public static Vector3 operator *(Transform3D transform, Vector3 vector)

Parameters

transform Transform3D

The transformation to apply.

vector Vector3

A Vector3 to transform.

Returns

Vector3

The transformed Vector3.

operator *(Transform3D, Vector3[])

Returns a copy of the given Vector3[] transformed (multiplied) by the transformation matrix.

public static Vector3[] operator *(Transform3D transform, Vector3[] array)

Parameters

transform Transform3D

The transformation to apply.

array Vector3[]

A Vector3[] to transform.

Returns

Vector3[]

The transformed copy of the Vector3[].

operator *(Vector3, Transform3D)

Returns a Vector3 transformed (multiplied) by the inverse transformation matrix, under the assumption that the transformation basis is orthonormal (i.e. rotation/reflection is fine, scaling/skew is not). vector * transform is equivalent to transform.Inverse() * vector. See Inverse(). For transforming by inverse of an affine transformation (e.g. with scaling) transform.AffineInverse() * vector can be used instead. See AffineInverse().

public static Vector3 operator *(Vector3 vector, Transform3D transform)

Parameters

vector Vector3

A Vector3 to inversely transform.

transform Transform3D

The transformation to apply.

Returns

Vector3

The inversely transformed Vector3.

operator *(Vector3[], Transform3D)

Returns a copy of the given Vector3[] transformed (multiplied) by the inverse transformation matrix, under the assumption that the transformation basis is orthonormal (i.e. rotation/reflection is fine, scaling/skew is not). array * transform is equivalent to transform.Inverse() * array. See Inverse(). For transforming by inverse of an affine transformation (e.g. with scaling) transform.AffineInverse() * array can be used instead. See AffineInverse().

public static Vector3[] operator *(Vector3[] array, Transform3D transform)

Parameters

array Vector3[]

A Vector3[] to inversely transform.

transform Transform3D

The transformation to apply.

Returns

Vector3[]

The inversely transformed copy of the Vector3[].