Table of Contents

Class Vector3

A 3D vector using floating-point coordinates.

Vector3

Remarks

A 3-element structure that can be used to represent 3D coordinates or any other triplet of numeric values.

It uses floating-point coordinates. By default, these floating-point values use 32-bit precision, unlike float which is always 64-bit. If double precision is needed, compile the engine with the option precision=double.

See Vector3i for its integer counterpart.

Note: In a boolean context, a Vector3 will evaluate to false if it's equal to Vector3(0, 0, 0). Otherwise, a Vector3 will always evaluate to true.

See Also

Math documentation index
Vector math
Advanced vector math
3Blue1Brown Essence of Linear Algebra
Matrix Transform Demo
All 3D Demos

Constructors

Vector3

Constructs a default-initialized Vector3 with all components set to 0.

Vector3 Vector3

Vector3(Vector3)

Constructs a Vector3 as a copy of the given Vector3.

Vector3 Vector3(Vector3 from)

Parameters

from Vector3

Vector3(Vector3i)

Constructs a new Vector3 from Vector3i.

Vector3 Vector3(Vector3i from)

Parameters

from Vector3i

Vector3(float, float, float)

Returns a Vector3 with the given components.

Vector3 Vector3(float x, float y, float z)

Parameters

x float
y float
z float

Fields

ZERO

Zero vector, a vector with all components set to 0.

const ZERO = Vector3(0, 0, 0)

ONE

One vector, a vector with all components set to 1.

const ONE = Vector3(1, 1, 1)

INF

Infinity vector, a vector with all components set to INF.

const INF = Vector3(inf, inf, inf)

LEFT

Left unit vector. Represents the local direction of left, and the global direction of west.

const LEFT = Vector3(-1, 0, 0)

RIGHT

Right unit vector. Represents the local direction of right, and the global direction of east.

const RIGHT = Vector3(1, 0, 0)

UP

Up unit vector.

const UP = Vector3(0, 1, 0)

DOWN

Down unit vector.

const DOWN = Vector3(0, -1, 0)

FORWARD

Forward unit vector. Represents the local direction of forward, and the global direction of north. Keep in mind that the forward direction for lights, cameras, etc is different from 3D assets like characters, which face towards the camera by convention. Use MODEL_FRONT and similar constants when working in 3D asset space.

const FORWARD = Vector3(0, 0, -1)

BACK

Back unit vector. Represents the local direction of back, and the global direction of south.

const BACK = Vector3(0, 0, 1)

MODEL_LEFT

Unit vector pointing towards the left side of imported 3D assets.

const MODEL_LEFT = Vector3(1, 0, 0)

MODEL_RIGHT

Unit vector pointing towards the right side of imported 3D assets.

const MODEL_RIGHT = Vector3(-1, 0, 0)

MODEL_TOP

Unit vector pointing towards the top side (up) of imported 3D assets.

const MODEL_TOP = Vector3(0, 1, 0)

MODEL_BOTTOM

Unit vector pointing towards the bottom side (down) of imported 3D assets.

const MODEL_BOTTOM = Vector3(0, -1, 0)

MODEL_FRONT

Unit vector pointing towards the front side (facing forward) of imported 3D assets.

const MODEL_FRONT = Vector3(0, 0, 1)

MODEL_REAR

Unit vector pointing towards the rear side (back) of imported 3D assets.

const MODEL_REAR = Vector3(0, 0, -1)

Properties

x

The vector's X component. Also accessible by using the index position [0].

var x : float = 0.0

Property Value

float

y

The vector's Y component. Also accessible by using the index position [1].

var y : float = 0.0

Property Value

float

z

The vector's Z component. Also accessible by using the index position [2].

var z : float = 0.0

Property Value

float

Methods

abs

Qualifiers: const

Returns a new vector with all components in absolute values (i.e. positive).

Vector3 abs

angle_to(Vector3)

Qualifiers: const

Returns the unsigned minimum angle to the given vector, in radians.

float angle_to(Vector3 to)

Parameters

to Vector3

bezier_derivative(Vector3, Vector3, Vector3, float)

Qualifiers: const

Returns the derivative at the given t on the Bézier curve defined by this vector and the given control_1, control_2, and end points.

Vector3 bezier_derivative(Vector3 control_1, Vector3 control_2, Vector3 end, float t)

Parameters

control_1 Vector3
control_2 Vector3
end Vector3
t float

bezier_interpolate(Vector3, Vector3, Vector3, float)

Qualifiers: const

Returns the point at the given t on the Bézier curve defined by this vector and the given control_1, control_2, and end points.

Vector3 bezier_interpolate(Vector3 control_1, Vector3 control_2, Vector3 end, float t)

Parameters

control_1 Vector3
control_2 Vector3
end Vector3
t float

bounce(Vector3)

Qualifiers: const

Returns the vector "bounced off" from a plane defined by the given normal n.

Note: Vector3.bounce performs the operation that most engines and frameworks call reflect().

Vector3 bounce(Vector3 n)

Parameters

n Vector3

ceil

Qualifiers: const

Returns a new vector with all components rounded up (towards positive infinity).

Vector3 ceil

clamp(Vector3, Vector3)

Qualifiers: const

Returns a new vector with all components clamped between the components of min and max, by running @GlobalScope.clamp on each component.

Vector3 clamp(Vector3 min, Vector3 max)

Parameters

min Vector3
max Vector3

clampf(float, float)

Qualifiers: const

Returns a new vector with all components clamped between min and max, by running @GlobalScope.clamp on each component.

Vector3 clampf(float min, float max)

Parameters

min float
max float

cross(Vector3)

Qualifiers: const

Returns the cross product of this vector and with.

This returns a vector perpendicular to both this and with, which would be the normal vector of the plane defined by the two vectors. As there are two such vectors, in opposite directions, this method returns the vector defined by a right-handed coordinate system. If the two vectors are parallel this returns an empty vector, making it useful for testing if two vectors are parallel.

Vector3 cross(Vector3 with)

Parameters

with Vector3

cubic_interpolate(Vector3, Vector3, Vector3, float)

Qualifiers: const

Performs a cubic interpolation between this vector and b using pre_a and post_b as handles, and returns the result at position weight. weight is on the range of 0.0 to 1.0, representing the amount of interpolation.

Vector3 cubic_interpolate(Vector3 b, Vector3 pre_a, Vector3 post_b, float weight)

Parameters

b Vector3
pre_a Vector3
post_b Vector3
weight float

cubic_interpolate_in_time(Vector3, Vector3, Vector3, float, float, float, float)

Qualifiers: const

Performs a cubic interpolation between this vector and b using pre_a and post_b as handles, and returns the result at position weight. weight is on the range of 0.0 to 1.0, representing the amount of interpolation.

It can perform smoother interpolation than Vector3.cubic_interpolate by the time values.

Vector3 cubic_interpolate_in_time(Vector3 b, Vector3 pre_a, Vector3 post_b, float weight, float b_t, float pre_a_t, float post_b_t)

Parameters

b Vector3
pre_a Vector3
post_b Vector3
weight float
b_t float
pre_a_t float
post_b_t float

direction_to(Vector3)

Qualifiers: const

Returns the normalized vector pointing from this vector to to. This is equivalent to using (b - a).normalized().

Vector3 direction_to(Vector3 to)

Parameters

to Vector3

distance_squared_to(Vector3)

Qualifiers: const

Returns the squared distance between this vector and to.

This method runs faster than Vector3.distance_to, so prefer it if you need to compare vectors or need the squared distance for some formula.

float distance_squared_to(Vector3 to)

Parameters

to Vector3

distance_to(Vector3)

Qualifiers: const

Returns the distance between this vector and to.

float distance_to(Vector3 to)

Parameters

to Vector3

dot(Vector3)

Qualifiers: const

Returns the dot product of this vector and with. This can be used to compare the angle between two vectors. For example, this can be used to determine whether an enemy is facing the player.

The dot product will be 0 for a right angle (90 degrees), greater than 0 for angles narrower than 90 degrees and lower than 0 for angles wider than 90 degrees.

When using unit (normalized) vectors, the result will always be between -1.0 (180 degree angle) when the vectors are facing opposite directions, and 1.0 (0 degree angle) when the vectors are aligned.

Note: a.dot(b) is equivalent to b.dot(a).

float dot(Vector3 with)

Parameters

with Vector3

floor

Qualifiers: const

Returns a new vector with all components rounded down (towards negative infinity).

Vector3 floor

inverse

Qualifiers: const

Returns the inverse of the vector. This is the same as Vector3(1.0 / v.x, 1.0 / v.y, 1.0 / v.z).

Vector3 inverse

is_equal_approx(Vector3)

Qualifiers: const

Returns true if this vector and to are approximately equal, by running @GlobalScope.is_equal_approx on each component.

bool is_equal_approx(Vector3 to)

Parameters

to Vector3

is_finite

Qualifiers: const

Returns true if this vector is finite, by calling @GlobalScope.is_finite on each component.

bool is_finite

is_normalized

Qualifiers: const

Returns true if the vector is normalized, i.e. its length is approximately equal to 1.

bool is_normalized

is_zero_approx

Qualifiers: const

Returns true if this vector's values are approximately zero, by running @GlobalScope.is_zero_approx on each component.

This method is faster than using Vector3.is_equal_approx with one value as a zero vector.

bool is_zero_approx

length

Qualifiers: const

Returns the length (magnitude) of this vector.

float length

length_squared

Qualifiers: const

Returns the squared length (squared magnitude) of this vector.

This method runs faster than length, so prefer it if you need to compare vectors or need the squared distance for some formula.

float length_squared

lerp(Vector3, float)

Qualifiers: const

Returns the result of the linear interpolation between this vector and to by amount weight. weight is on the range of 0.0 to 1.0, representing the amount of interpolation.

Vector3 lerp(Vector3 to, float weight)

Parameters

to Vector3
weight float

limit_length(float)

Qualifiers: const

Returns the vector with a maximum length by limiting its length to length. If the vector is non-finite, the result is undefined.

Vector3 limit_length(float length)

Parameters

length float

max(Vector3)

Qualifiers: const

Returns the component-wise maximum of this and with, equivalent to Vector3(maxf(x, with.x), maxf(y, with.y), maxf(z, with.z)).

Vector3 max(Vector3 with)

Parameters

with Vector3

max_axis_index

Qualifiers: const

Returns the axis of the vector's highest value. See AXIS_* constants. If all components are equal, this method returns Vector3.AXIS_X.

int max_axis_index

maxf(float)

Qualifiers: const

Returns the component-wise maximum of this and with, equivalent to Vector3(maxf(x, with), maxf(y, with), maxf(z, with)).

Vector3 maxf(float with)

Parameters

with float

min(Vector3)

Qualifiers: const

Returns the component-wise minimum of this and with, equivalent to Vector3(minf(x, with.x), minf(y, with.y), minf(z, with.z)).

Vector3 min(Vector3 with)

Parameters

with Vector3

min_axis_index

Qualifiers: const

Returns the axis of the vector's lowest value. See AXIS_* constants. If all components are equal, this method returns Vector3.AXIS_Z.

int min_axis_index

minf(float)

Qualifiers: const

Returns the component-wise minimum of this and with, equivalent to Vector3(minf(x, with), minf(y, with), minf(z, with)).

Vector3 minf(float with)

Parameters

with float

move_toward(Vector3, float)

Qualifiers: const

Returns a new vector moved toward to by the fixed delta amount. Will not go past the final value.

Vector3 move_toward(Vector3 to, float delta)

Parameters

to Vector3
delta float

normalized

Qualifiers: const

Returns the result of scaling the vector to unit length. Equivalent to v / v.length(). Returns (0, 0, 0) if v.length() == 0. See also is_normalized.

Note: This function may return incorrect values if the input vector length is near zero.

Vector3 normalized

octahedron_decode(Vector2)

Qualifiers: static

Returns the Vector3 from an octahedral-compressed form created using octahedron_encode (stored as a Vector2).

Vector3 octahedron_decode(Vector2 uv)

Parameters

uv Vector2

octahedron_encode

Qualifiers: const

Returns the octahedral-encoded (oct32) form of this Vector3 as a Vector2. Since a Vector2 occupies 1/3 less memory compared to Vector3, this form of compression can be used to pass greater amounts of normalized Vector3s without increasing storage or memory requirements. See also Vector3.octahedron_decode.

Note: octahedron_encode can only be used for normalized vectors. octahedron_encode does not check whether this Vector3 is normalized, and will return a value that does not decompress to the original value if the Vector3 is not normalized.

Note: Octahedral compression is lossy, although visual differences are rarely perceptible in real world scenarios.

Vector2 octahedron_encode

outer(Vector3)

Qualifiers: const

Returns the outer product with with.

Basis outer(Vector3 with)

Parameters

with Vector3

posmod(float)

Qualifiers: const

Returns a vector composed of the @GlobalScope.fposmod of this vector's components and mod.

Vector3 posmod(float mod)

Parameters

mod float

posmodv(Vector3)

Qualifiers: const

Returns a vector composed of the @GlobalScope.fposmod of this vector's components and modv's components.

Vector3 posmodv(Vector3 modv)

Parameters

modv Vector3

project(Vector3)

Qualifiers: const

Returns a new vector resulting from projecting this vector onto the given vector b. The resulting new vector is parallel to b. See also Vector3.slide.

Note: If the vector b is a zero vector, the components of the resulting new vector will be NAN.

Vector3 project(Vector3 b)

Parameters

b Vector3

reflect(Vector3)

Qualifiers: const

Returns the result of reflecting the vector through a plane defined by the given normal vector n.

Note: Vector3.reflect differs from what other engines and frameworks call reflect(). In other engines, reflect() returns the result of the vector reflected by the given plane. The reflection thus passes through the given normal. While in Godot the reflection passes through the plane and can be thought of as bouncing off the normal. See also Vector3.bounce which does what most engines call reflect().

Vector3 reflect(Vector3 n)

Parameters

n Vector3

rotated(Vector3, float)

Qualifiers: const

Returns the result of rotating this vector around a given axis by angle (in radians). The axis must be a normalized vector. See also @GlobalScope.deg_to_rad.

Vector3 rotated(Vector3 axis, float angle)

Parameters

axis Vector3
angle float

round

Qualifiers: const

Returns a new vector with all components rounded to the nearest integer, with halfway cases rounded away from zero.

Vector3 round

sign

Qualifiers: const

Returns a new vector with each component set to 1.0 if it's positive, -1.0 if it's negative, and 0.0 if it's zero. The result is identical to calling @GlobalScope.sign on each component.

Vector3 sign

signed_angle_to(Vector3, Vector3)

Qualifiers: const

Returns the signed angle to the given vector, in radians. The sign of the angle is positive in a counter-clockwise direction and negative in a clockwise direction when viewed from the side specified by the axis.

float signed_angle_to(Vector3 to, Vector3 axis)

Parameters

to Vector3
axis Vector3

slerp(Vector3, float)

Qualifiers: const

Returns the result of spherical linear interpolation between this vector and to, by amount weight. weight is on the range of 0.0 to 1.0, representing the amount of interpolation.

This method also handles interpolating the lengths if the input vectors have different lengths. For the special case of one or both input vectors having zero length, this method behaves like Vector3.lerp.

Vector3 slerp(Vector3 to, float weight)

Parameters

to Vector3
weight float

slide(Vector3)

Qualifiers: const

Returns a new vector resulting from sliding this vector along a plane with normal n. The resulting new vector is perpendicular to n, and is equivalent to this vector minus its projection on n. See also Vector3.project.

Note: The vector n must be normalized. See also normalized.

Vector3 slide(Vector3 n)

Parameters

n Vector3

snapped(Vector3)

Qualifiers: const

Returns a new vector with each component snapped to the nearest multiple of the corresponding component in step. This can also be used to round the components to an arbitrary number of decimals.

Vector3 snapped(Vector3 step)

Parameters

step Vector3

snappedf(float)

Qualifiers: const

Returns a new vector with each component snapped to the nearest multiple of step. This can also be used to round the components to an arbitrary number of decimals.

Vector3 snappedf(float step)

Parameters

step float

Operators

!= (Vector3)

Returns true if the vectors are not equal.

Note: Due to floating-point precision errors, consider using Vector3.is_equal_approx instead, which is more reliable.

Note: Vectors with NAN elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.

bool != (Vector3 right)

Parameters

right Vector3

* (Basis)

Inversely transforms (multiplies) the Vector3 by the given Basis matrix, under the assumption that the basis is orthonormal (i.e. rotation/reflection is fine, scaling/skew is not).

vector * basis is equivalent to basis.transposed() * vector. See transposed.

For transforming by inverse of a non-orthonormal basis (e.g. with scaling) basis.inverse() * vector can be used instead. See inverse.

Vector3 * (Basis right)

Parameters

right Basis

* (Quaternion)

Inversely transforms (multiplies) the Vector3 by the given Quaternion.

vector * quaternion is equivalent to quaternion.inverse() * vector. See inverse.

Vector3 * (Quaternion right)

Parameters

right Quaternion

* (Transform3D)

Inversely transforms (multiplies) the Vector3 by the given Transform3D 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.affine_inverse() * vector can be used instead. See affine_inverse.

Vector3 * (Transform3D right)

Parameters

right Transform3D

* (Vector3)

Multiplies each component of the Vector3 by the components of the given Vector3.

print(Vector3(10, 20, 30) * Vector3(3, 4, 5)) # Prints (30.0, 80.0, 150.0)


Vector3 * (Vector3 right)

Parameters

right Vector3

* (float)

Multiplies each component of the Vector3 by the given float.

Vector3 * (float right)

Parameters

right float

* (int)

Multiplies each component of the Vector3 by the given int.

Vector3 * (int right)

Parameters

right int

+ (Vector3)

Adds each component of the Vector3 by the components of the given Vector3.

print(Vector3(10, 20, 30) + Vector3(3, 4, 5)) # Prints (13.0, 24.0, 35.0)


Vector3 + (Vector3 right)

Parameters

right Vector3

- (Vector3)

Subtracts each component of the Vector3 by the components of the given Vector3.

print(Vector3(10, 20, 30) - Vector3(3, 4, 5)) # Prints (7.0, 16.0, 25.0)


Vector3 - (Vector3 right)

Parameters

right Vector3

/ (Vector3)

Divides each component of the Vector3 by the components of the given Vector3.

print(Vector3(10, 20, 30) / Vector3(2, 5, 3)) # Prints (5.0, 4.0, 10.0)


Vector3 / (Vector3 right)

Parameters

right Vector3

/ (float)

Divides each component of the Vector3 by the given float.

Vector3 / (float right)

Parameters

right float

/ (int)

Divides each component of the Vector3 by the given int.

Vector3 / (int right)

Parameters

right int

< (Vector3)

Compares two Vector3 vectors by first checking if the X value of the left vector is less than the X value of the right vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors, and then with the Z values. This operator is useful for sorting vectors.

Note: Vectors with NAN elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.

bool < (Vector3 right)

Parameters

right Vector3

<= (Vector3)

Compares two Vector3 vectors by first checking if the X value of the left vector is less than or equal to the X value of the right vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors, and then with the Z values. This operator is useful for sorting vectors.

Note: Vectors with NAN elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.

bool <= (Vector3 right)

Parameters

right Vector3

== (Vector3)

Returns true if the vectors are exactly equal.

Note: Due to floating-point precision errors, consider using Vector3.is_equal_approx instead, which is more reliable.

Note: Vectors with NAN elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.

bool == (Vector3 right)

Parameters

right Vector3

> (Vector3)

Compares two Vector3 vectors by first checking if the X value of the left vector is greater than the X value of the right vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors, and then with the Z values. This operator is useful for sorting vectors.

Note: Vectors with NAN elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.

bool > (Vector3 right)

Parameters

right Vector3

>= (Vector3)

Compares two Vector3 vectors by first checking if the X value of the left vector is greater than or equal to the X value of the right vector. If the X values are exactly equal, then it repeats this check with the Y values of the two vectors, and then with the Z values. This operator is useful for sorting vectors.

Note: Vectors with NAN elements don't behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.

bool >= (Vector3 right)

Parameters

right Vector3

[] (int)

Access vector components using their index. v[0] is equivalent to v.x, v[1] is equivalent to v.y, and v[2] is equivalent to v.z.

float [] (int index)

Parameters

index int

unary+

Returns the same value as if the + was not there. Unary + does nothing, but sometimes it can make your code more readable.

Vector3 unary+

unary-

Returns the negative value of the Vector3. This is the same as writing Vector3(-v.x, -v.y, -v.z). This operation flips the direction of the vector while keeping the same magnitude. With floats, the number zero can be either positive or negative.

Vector3 unary-