# Vector3¶

Vector used for 3D math using floating point coordinates.

## Description¶

3-element structure that can be used to represent positions in 3D space 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`.

## Properties¶

 float x `0.0` float y `0.0` float z `0.0`

## Constructors¶

 Vector3 Vector3 ( ) Vector3 Vector3 ( Vector3 from ) Vector3 Vector3 ( Vector3i from ) Vector3 Vector3 ( float x, float y, float z )

## Methods¶

 Vector3 abs ( ) const float angle_to ( Vector3 to ) const Vector3 bezier_derivative ( Vector3 control_1, Vector3 control_2, Vector3 end, float t ) const Vector3 bezier_interpolate ( Vector3 control_1, Vector3 control_2, Vector3 end, float t ) const Vector3 bounce ( Vector3 n ) const Vector3 ceil ( ) const Vector3 clamp ( Vector3 min, Vector3 max ) const Vector3 cross ( Vector3 with ) const Vector3 cubic_interpolate ( Vector3 b, Vector3 pre_a, Vector3 post_b, float weight ) const 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 ) const Vector3 direction_to ( Vector3 to ) const float distance_squared_to ( Vector3 to ) const float distance_to ( Vector3 to ) const float dot ( Vector3 with ) const Vector3 floor ( ) const Vector3 inverse ( ) const bool is_equal_approx ( Vector3 to ) const bool is_finite ( ) const bool is_normalized ( ) const bool is_zero_approx ( ) const float length ( ) const float length_squared ( ) const Vector3 lerp ( Vector3 to, float weight ) const Vector3 limit_length ( float length=1.0 ) const int max_axis_index ( ) const int min_axis_index ( ) const Vector3 move_toward ( Vector3 to, float delta ) const Vector3 normalized ( ) const Vector3 octahedron_decode ( Vector2 uv ) static Vector2 octahedron_encode ( ) const Basis outer ( Vector3 with ) const Vector3 posmod ( float mod ) const Vector3 posmodv ( Vector3 modv ) const Vector3 project ( Vector3 b ) const Vector3 reflect ( Vector3 n ) const Vector3 rotated ( Vector3 axis, float angle ) const Vector3 round ( ) const Vector3 sign ( ) const float signed_angle_to ( Vector3 to, Vector3 axis ) const Vector3 slerp ( Vector3 to, float weight ) const Vector3 slide ( Vector3 n ) const Vector3 snapped ( Vector3 step ) const

## Operators¶

 bool operator != ( Vector3 right ) Vector3 operator * ( Basis right ) Vector3 operator * ( Quaternion right ) Vector3 operator * ( Transform3D right ) Vector3 operator * ( Vector3 right ) Vector3 operator * ( float right ) Vector3 operator * ( int right ) Vector3 operator + ( Vector3 right ) Vector3 operator - ( Vector3 right ) Vector3 operator / ( Vector3 right ) Vector3 operator / ( float right ) Vector3 operator / ( int right ) bool operator < ( Vector3 right ) bool operator <= ( Vector3 right ) bool operator == ( Vector3 right ) bool operator > ( Vector3 right ) bool operator >= ( Vector3 right ) float operator [] ( int index ) Vector3 Vector3

## Constants¶

AXIS_X = `0`

Enumerated value for the X axis. Returned by max_axis_index and min_axis_index.

AXIS_Y = `1`

Enumerated value for the Y axis. Returned by max_axis_index and min_axis_index.

AXIS_Z = `2`

Enumerated value for the Z axis. Returned by max_axis_index and min_axis_index.

ZERO = `Vector3(0, 0, 0)`

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

ONE = `Vector3(1, 1, 1)`

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

INF = `Vector3(inf, inf, inf)`

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

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

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

RIGHT = `Vector3(1, 0, 0)`

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

UP = `Vector3(0, 1, 0)`

Up unit vector.

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

Down unit vector.

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

Forward unit vector. Represents the local direction of forward, and the global direction of north.

BACK = `Vector3(0, 0, 1)`

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

## Property Descriptions¶

float x = `0.0`

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

float y = `0.0`

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

float z = `0.0`

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

## Constructor Descriptions¶

Vector3 Vector3 ( )

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

Vector3 Vector3 ( Vector3 from )

Constructs a Vector3 as a copy of the given Vector3.

Vector3 Vector3 ( Vector3i from )

Constructs a new Vector3 from Vector3i.

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

Returns a Vector3 with the given components.

## Method Descriptions¶

Vector3 abs ( ) const

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

float angle_to ( Vector3 to ) const

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

Vector3 bezier_derivative ( Vector3 control_1, Vector3 control_2, Vector3 end, float t ) 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_interpolate ( Vector3 control_1, Vector3 control_2, Vector3 end, float t ) 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 bounce ( Vector3 n ) const

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

Vector3 ceil ( ) const

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

Vector3 clamp ( Vector3 min, Vector3 max ) const

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

Vector3 cross ( Vector3 with ) const

Returns the cross product of this vector and `with`.

Vector3 cubic_interpolate ( Vector3 b, Vector3 pre_a, Vector3 post_b, float weight ) 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_in_time ( Vector3 b, Vector3 pre_a, Vector3 post_b, float weight, float b_t, float pre_a_t, float post_b_t ) 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 `cubic_interpolate()` by the time values.

Vector3 direction_to ( Vector3 to ) const

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

float distance_squared_to ( Vector3 to ) const

Returns the squared distance between this vector and `to`.

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

float distance_to ( Vector3 to ) const

Returns the distance between this vector and `to`.

float dot ( Vector3 with ) 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 straight 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)`.

Vector3 floor ( ) const

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

Vector3 inverse ( ) 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)`.

bool is_equal_approx ( Vector3 to ) const

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

bool is_finite ( ) const

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

bool is_normalized ( ) const

Returns `true` if the vector is normalized, `false` otherwise.

bool is_zero_approx ( ) 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 is_equal_approx with one value as a zero vector.

float length ( ) const

Returns the length (magnitude) of this vector.

float length_squared ( ) 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.

Vector3 lerp ( Vector3 to, float weight ) 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 limit_length ( float length=1.0 ) const

Returns the vector with a maximum length by limiting its length to `length`.

int max_axis_index ( ) const

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

int min_axis_index ( ) const

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

Vector3 move_toward ( Vector3 to, float delta ) const

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

Vector3 normalized ( ) const

Returns the vector scaled to unit length. Equivalent to `v / v.length()`. See also is_normalized.

Vector3 octahedron_decode ( Vector2 uv ) static

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

Vector2 octahedron_encode ( ) 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 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.

Basis outer ( Vector3 with ) const

Returns the outer product with `with`.

Vector3 posmod ( float mod ) const

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

Vector3 posmodv ( Vector3 modv ) const

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

Vector3 project ( Vector3 b ) const

Returns the result of projecting the vector onto the given vector `b`.

Vector3 reflect ( Vector3 n ) const

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

Vector3 rotated ( Vector3 axis, float angle ) 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 round ( ) const

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

Vector3 sign ( ) 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.

float signed_angle_to ( Vector3 to, Vector3 axis ) 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`.

Vector3 slerp ( Vector3 to, float weight ) 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 lerp.

Vector3 slide ( Vector3 n ) const

Returns a new vector slid along a plane defined by the given normal.

Vector3 snapped ( Vector3 step ) 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.

## Operator Descriptions¶

bool operator != ( Vector3 right )

Returns `true` if the vectors are not equal.

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

Vector3 operator * ( Basis right )

Inversely transforms (multiplies) the Vector3 by the given Basis matrix.

Vector3 operator * ( Quaternion right )

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

Vector3 operator * ( Transform3D right )

Inversely transforms (multiplies) the Vector3 by the given Transform3D transformation matrix.

Vector3 operator * ( Vector3 right )

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

```print(Vector3(10, 20, 30) * Vector3(3, 4, 5)) # Prints "(30, 80, 150)"
```

Vector3 operator * ( float right )

Multiplies each component of the Vector3 by the given float.

Vector3 operator * ( int right )

Multiplies each component of the Vector3 by the given int.

Vector3 operator + ( Vector3 right )

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

```print(Vector3(10, 20, 30) + Vector3(3, 4, 5)) # Prints "(13, 24, 35)"
```

Vector3 operator - ( Vector3 right )

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

```print(Vector3(10, 20, 30) - Vector3(3, 4, 5)) # Prints "(7, 16, 25)"
```

Vector3 operator / ( Vector3 right )

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

```print(Vector3(10, 20, 30) / Vector3(2, 5, 3)) # Prints "(5, 4, 10)"
```

Vector3 operator / ( float right )

Divides each component of the Vector3 by the given float.

Vector3 operator / ( int right )

Divides each component of the Vector3 by the given int.

bool operator < ( Vector3 right )

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.

bool operator <= ( Vector3 right )

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.

bool operator == ( Vector3 right )

Returns `true` if the vectors are exactly equal.

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

bool operator > ( Vector3 right )

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.

bool operator >= ( Vector3</