Class Vector2

A 2D vector using floating-point coordinates.

Vector2

Remarks

A 2-element structure that can be used to represent 2D coordinates or any other pair 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 Vector2i for its integer counterpart.

Note: In a boolean context, a Vector2 will evaluate to false if it's equal to Vector2(0, 0). Otherwise, a Vector2 will always evaluate to true.

See Also

Math documentation index

Vector math

Advanced vector math

3Blue1Brown Essence of Linear Algebra

Matrix Transform Demo

All 2D Demos

Constructors

Vector2

Constructs a default-initialized Vector2 with all components set to 0.

Vector2 Vector2

Vector2(Vector2)

Constructs a Vector2 as a copy of the given Vector2.

Vector2 Vector2(Vector2 from)

Parameters

from Vector2

Vector2(Vector2i)

Constructs a new Vector2 from Vector2i.

Vector2 Vector2(Vector2i from)

Parameters

from Vector2i

Vector2(float, float)

Constructs a new Vector2 from the given x and y.

Vector2 Vector2(float x, float y)

Parameters

x float

y float

Fields

ZERO

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

const ZERO = Vector2(0, 0)

ONE

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

const ONE = Vector2(1, 1)

INF

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

const INF = Vector2(inf, inf)

LEFT

Left unit vector. Represents the direction of left.

const LEFT = Vector2(-1, 0)

RIGHT

Right unit vector. Represents the direction of right.

const RIGHT = Vector2(1, 0)

UP

Up unit vector. Y is down in 2D, so this vector points -Y.

const UP = Vector2(0, -1)

DOWN

Down unit vector. Y is down in 2D, so this vector points +Y.

const DOWN = Vector2(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

Methods

abs

Qualifiers: const

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

Vector2 abs

angle

Qualifiers: const

Returns this vector's angle with respect to the positive X axis, or (1, 0) vector, in radians.

For example, Vector2.RIGHT.angle() will return zero, Vector2.DOWN.angle() will return PI / 2 (a quarter turn, or 90 degrees), and Vector2(1, -1).angle() will return -PI / 4 (a negative eighth turn, or -45 degrees).

\ Illustration of the returned angle.\

Equivalent to the result of @GlobalScope.atan2 when called with the vector's y and x as parameters: atan2(y, x).

float angle

angle_to(Vector2)

Qualifiers: const

Returns the signed angle to the given vector, in radians.

\ Illustration of the returned angle.

float angle_to(Vector2 to)

Parameters

to Vector2

angle_to_point(Vector2)

Qualifiers: const

Returns the angle between the line connecting the two points and the X axis, in radians.

a.angle_to_point(b) is equivalent of doing (b - a).angle().

\ Illustration of the returned angle.

float angle_to_point(Vector2 to)

Parameters

to Vector2

aspect

Qualifiers: const

Returns the aspect ratio of this vector, the ratio of x to y.

float aspect

bezier_derivative(Vector2, Vector2, Vector2, 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.

Vector2 bezier_derivative(Vector2 control_1, Vector2 control_2, Vector2 end, float t)

Parameters

control_1 Vector2

control_2 Vector2

end Vector2

t float

bezier_interpolate(Vector2, Vector2, Vector2, 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.

Vector2 bezier_interpolate(Vector2 control_1, Vector2 control_2, Vector2 end, float t)

Parameters

control_1 Vector2

control_2 Vector2

end Vector2

t float

bounce(Vector2)

Qualifiers: const

Returns the vector "bounced off" from a line defined by the given normal n perpendicular to the line.

Note: Vector2.bounce performs the operation that most engines and frameworks call reflect().

Vector2 bounce(Vector2 n)

Parameters

n Vector2

ceil

Qualifiers: const

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

Vector2 ceil

clamp(Vector2, Vector2)

Qualifiers: const

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

Vector2 clamp(Vector2 min, Vector2 max)

Parameters

min Vector2

max Vector2

clampf(float, float)

Qualifiers: const

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

Vector2 clampf(float min, float max)

Parameters

min float

max float

cross(Vector2)

Qualifiers: const

Returns the 2D analog of the cross product for this vector and with.

This is the signed area of the parallelogram formed by the two vectors. If the second vector is clockwise from the first vector, then the cross product is the positive area. If counter-clockwise, the cross product is the negative area. If the two vectors are parallel this returns zero, making it useful for testing if two vectors are parallel.

Note: Cross product is not defined in 2D mathematically. This method embeds the 2D vectors in the XY plane of 3D space and uses their cross product's Z component as the analog.

float cross(Vector2 with)

Parameters

with Vector2

cubic_interpolate(Vector2, Vector2, Vector2, 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.

Vector2 cubic_interpolate(Vector2 b, Vector2 pre_a, Vector2 post_b, float weight)

Parameters

b Vector2

pre_a Vector2

post_b Vector2

weight float

cubic_interpolate_in_time(Vector2, Vector2, Vector2, 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 Vector2.cubic_interpolate by the time values.

Vector2 cubic_interpolate_in_time(Vector2 b, Vector2 pre_a, Vector2 post_b, float weight, float b_t, float pre_a_t, float post_b_t)

Parameters

b Vector2

pre_a Vector2

post_b Vector2

weight float

b_t float

pre_a_t float

post_b_t float

direction_to(Vector2)

Qualifiers: const

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

Vector2 direction_to(Vector2 to)

Parameters

to Vector2

distance_squared_to(Vector2)

Qualifiers: const

Returns the squared distance between this vector and to.

This method runs faster than Vector2.distance_to, so prefer it if you need to compare vectors or need the squared distance for some formula.

float distance_squared_to(Vector2 to)

Parameters

to Vector2

distance_to(Vector2)

Qualifiers: const

Returns the distance between this vector and to.

float distance_to(Vector2 to)

Parameters

to Vector2

dot(Vector2)

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(Vector2 with)

Parameters

with Vector2

floor

Qualifiers: const

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

Vector2 floor

from_angle(float)

Qualifiers: static

Creates a unit Vector2 rotated to the given angle in radians. This is equivalent to doing Vector2(cos(angle), sin(angle)) or Vector2.RIGHT.rotated(angle).

print(Vector2.from_angle(0)) # Prints (1.0, 0.0)
print(Vector2(1, 0).angle()) # Prints 0.0, which is the angle used above.
print(Vector2.from_angle(PI / 2)) # Prints (0.0, 1.0)

Vector2 from_angle(float angle)

Parameters

angle float

is_equal_approx(Vector2)

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(Vector2 to)

Parameters

to Vector2

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 Vector2.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(Vector2, 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.

Vector2 lerp(Vector2 to, float weight)

Parameters

to Vector2

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.

Vector2 limit_length(float length)

Parameters

length float

max(Vector2)

Qualifiers: const

Returns the component-wise maximum of this and with, equivalent to Vector2(maxf(x, with.x), maxf(y, with.y)).

Vector2 max(Vector2 with)

Parameters

with Vector2

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 Vector2.AXIS_X.

int max_axis_index

maxf(float)

Qualifiers: const

Returns the component-wise maximum of this and with, equivalent to Vector2(maxf(x, with), maxf(y, with)).

Vector2 maxf(float with)

Parameters

with float

min(Vector2)

Qualifiers: const

Returns the component-wise minimum of this and with, equivalent to Vector2(minf(x, with.x), minf(y, with.y)).

Vector2 min(Vector2 with)

Parameters

with Vector2

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 Vector2.AXIS_Y.

int min_axis_index

minf(float)

Qualifiers: const

Returns the component-wise minimum of this and with, equivalent to Vector2(minf(x, with), minf(y, with)).

Vector2 minf(float with)

Parameters

with float

move_toward(Vector2, float)

Qualifiers: const

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

Vector2 move_toward(Vector2 to, float delta)

Parameters

to Vector2

delta float

normalized

Qualifiers: const

Returns the result of scaling the vector to unit length. Equivalent to v / v.length(). Returns (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.

Vector2 normalized

orthogonal

Qualifiers: const

Returns a perpendicular vector rotated 90 degrees counter-clockwise compared to the original, with the same length.

Vector2 orthogonal

posmod(float)

Qualifiers: const

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

Vector2 posmod(float mod)

Parameters

mod float

posmodv(Vector2)

Qualifiers: const

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

Vector2 posmodv(Vector2 modv)

Parameters

modv Vector2

project(Vector2)

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 Vector2.slide.

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

Vector2 project(Vector2 b)

Parameters

b Vector2

reflect(Vector2)

Qualifiers: const

Returns the result of reflecting the vector from a line defined by the given direction vector line.

Note: Vector2.reflect differs from what other engines and frameworks call reflect(). In other engines, reflect() takes a normal direction which is a direction perpendicular to the line. In Godot, you specify the direction of the line directly. See also Vector2.bounce which does what most engines call reflect().

Vector2 reflect(Vector2 line)

Parameters

line Vector2

rotated(float)

Qualifiers: const

Returns the result of rotating this vector by angle (in radians). See also @GlobalScope.deg_to_rad.

Vector2 rotated(float angle)

Parameters

angle float

round

Qualifiers: const

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

Vector2 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.

Vector2 sign

slerp(Vector2, 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 Vector2.lerp.

Vector2 slerp(Vector2 to, float weight)

Parameters

to Vector2

weight float

slide(Vector2)

Qualifiers: const

Returns a new vector resulting from sliding this vector along a line with normal n. The resulting new vector is perpendicular to n, and is equivalent to this vector minus its projection on n. See also Vector2.project.

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

Vector2 slide(Vector2 n)

Parameters

n Vector2

snapped(Vector2)

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.

Vector2 snapped(Vector2 step)

Parameters

step Vector2

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.

Vector2 snappedf(float step)

Parameters

step float

Operators

!= (Vector2)

Returns true if the vectors are not equal.

Note: Due to floating-point precision errors, consider using Vector2.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 != (Vector2 right)

Parameters

right Vector2

* (Transform2D)

Inversely transforms (multiplies) the Vector2 by the given Transform2D 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.

Vector2 * (Transform2D right)

Parameters

right Transform2D

* (Vector2)

Multiplies each component of the Vector2 by the components of the given Vector2.

print(Vector2(10, 20) * Vector2(3, 4)) # Prints (30.0, 80.0)

Vector2 * (Vector2 right)

Parameters

right Vector2

* (float)

Multiplies each component of the Vector2 by the given float.

Vector2 * (float right)

Parameters

right float

* (int)

Multiplies each component of the Vector2 by the given int.

Vector2 * (int right)

Parameters

right int

+ (Vector2)

Adds each component of the Vector2 by the components of the given Vector2.

print(Vector2(10, 20) + Vector2(3, 4)) # Prints (13.0, 24.0)

Vector2 + (Vector2 right)

Parameters

right Vector2

- (Vector2)

Subtracts each component of the Vector2 by the components of the given Vector2.

print(Vector2(10, 20) - Vector2(3, 4)) # Prints (7.0, 16.0)

Vector2 - (Vector2 right)

Parameters

right Vector2

/ (Vector2)

Divides each component of the Vector2 by the components of the given Vector2.

print(Vector2(10, 20) / Vector2(2, 5)) # Prints (5.0, 4.0)

Vector2 / (Vector2 right)

Parameters

right Vector2

/ (float)

Divides each component of the Vector2 by the given float.

Vector2 / (float right)

Parameters

right float

/ (int)

Divides each component of the Vector2 by the given int.

Vector2 / (int right)

Parameters

right int

< (Vector2)

Compares two Vector2 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. 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 < (Vector2 right)

Parameters

right Vector2

<= (Vector2)

Compares two Vector2 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. 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 <= (Vector2 right)

Parameters

right Vector2

== (Vector2)

Returns true if the vectors are exactly equal.

Note: Due to floating-point precision errors, consider using Vector2.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 == (Vector2 right)

Parameters

right Vector2

> (Vector2)

Compares two Vector2 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. 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 > (Vector2 right)

Parameters

right Vector2

>= (Vector2)

Compares two Vector2 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. 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 >= (Vector2 right)

Parameters

right Vector2

[] (int)

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

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.

Vector2 unary+

unary-

Returns the negative value of the Vector2. This is the same as writing Vector2(-v.x, -v.y). This operation flips the direction of the vector while keeping the same magnitude. With floats, the number zero can be either positive or negative.

Vector2 unary-