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Vector3

A 3D vector using floating point coordinates.

Description

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.

Tutorials

• Math documentation index

• Vector math

• Advanced vector math

• 3Blue1Brown Essence of Linear Algebra

• Matrix Transform Demo

• All 3D Demos

Properties

Constructors

Methods

Operators

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. 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.

BACK = Vector3(0, 0, 1)

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

MODEL_LEFT = Vector3(1, 0, 0)

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

MODEL_RIGHT = Vector3(-1, 0, 0)

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

MODEL_TOP = Vector3(0, 1, 0)

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

MODEL_BOTTOM = Vector3(0, -1, 0)

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

MODEL_FRONT = Vector3(0, 0, 1)

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

MODEL_REAR = Vector3(0, 0, -1)

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

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, i.e. its length is approximately equal to 1.

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 result of scaling the vector to unit length. Equivalent to v / v.length(). See also is_normalized.

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

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.

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

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.

Note: Vectors with @GDScript.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 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.

Note: Vectors with @GDScript.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 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.

Note: Vectors with @GDScript.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 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.

Note: Vectors with @GDScript.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 operator >= ( Vector3 right )

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 @GDScript.NAN elements don’t behave the same as other vectors. Therefore, the results from this operator may not be accurate if NaNs are included.

float operator [] ( int index )

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.

Vector3 operator unary+ ( )

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

Vector3 operator 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.