pygame.math — pygame-ce v2.5.3 documentation

pygame.math

pygame module for vector classes

pygame.math.clamp	—	returns value clamped to min and max.
pygame.math.lerp	—	returns value linearly interpolated between a and b
pygame.math.invlerp	—	returns value inverse interpolated between a and b
pygame.math.smoothstep	—	returns value smoothly interpolated between a and b.
pygame.math.remap	—	remaps value from given input range to given output range
pygame.math.Vector2	—	a 2-Dimensional Vector
pygame.math.Vector3	—	a 3-Dimensional Vector

The pygame math module currently provides Vector classes in two and three dimensions, Vector2 and Vector3 respectively.

They support the following numerical operations: vec + vec, vec - vec, vec * number, number * vec, vec / number, vec // number, vec += vec, vec -= vec, vec *= number, vec /= number, vec //= number, round(vec, ndigits=0).

All these operations will be performed elementwise. In addition vec * vec will perform a scalar-product (a.k.a. dot-product). If you want to multiply every element from vector v with every element from vector w you can use the elementwise method: v.elementwise() * w

The coordinates of a vector can be retrieved or set using attributes or subscripts

v = pygame.Vector3()

v.x = 5
v[1] = 2 * v.x
print(v[1]) # 10

v.x == v[0]
v.y == v[1]
v.z == v[2]

Multiple coordinates can be set using slices or swizzling

v = pygame.Vector2()
v.xy = 1, 2
v[:] = 1, 2

New in pygame 1.9.2pre.

Changed in pygame 1.9.4: Removed experimental notice.

Changed in pygame 1.9.4: Allow scalar construction like GLSL Vector2(2) == Vector2(2.0, 2.0)

Changed in pygame 1.9.4: pygame.mathpygame module for vector classes import not required. More convenient pygame.Vector2 and pygame.Vector3.

Changed in pygame-ce 2.1.4: round returns a new vector with components rounded to the specified digits.

pygame.math.clamp()¶: returns value clamped to min and max.

clamp(value, min, max, /) -> float

Clamps a numeric value so that it's no lower than min, and no higher than max.

New in pygame-ce 2.1.3.

pygame.math.lerp()¶

returns value linearly interpolated between a and b

lerp(a, b, value, do_clamp=True, /) -> float

Returns a number which is a linear interpolation between a and b. The third parameter determines how far between a and b the result is going to be. If do_clamp is false, the result can exceed the range 0.0 to 1.0.

The formula is:

a * value + (1 - value) * b.

New in pygame-ce 2.4.0.

pygame.math.invlerp()¶

returns value inverse interpolated between a and b

invlerp(a, b, value, /) -> float

Returns a number which is an inverse interpolation between a and b. The third parameter value is the result of the linear interpolation between a and b with a certain coefficient. In other words, this coefficient will be the result of this function. If b and a are equal, it raises a ValueError.

The formula is:

(v - a)/(b - a).

This is an example explaining what is above :

> a = 10
> b = 20
> pygame.math.invlerp(10, 20, 11.5)
> 0.15
> pygame.math.lerp(10, 20, 0.15)
> 11.5

New in pygame-ce 2.5.0.

pygame.math.smoothstep()¶

returns value smoothly interpolated between a and b.

smoothstep(a, b, value, /) -> float

Returns a number which is a "smooth" interpolation between a and b. This means that the interpolation follows an s-shaped curve, with change happening more slowly near the limits (0.0 and 1.0) and faster in the middle. The third parameter determines how far between a and b the result is going to be.

The formula is:

a * interp + (1 - interp) * b

where:

interp = value * value * (3 - 2 * value)

New in pygame-ce 2.4.0.

pygame.math.remap()¶

remaps value from given input range to given output range

remap(i_min, i_max, o_min, o_max, value, /) -> float

Returns a number which is the value remapped from [i_min, i_max] range to [o_min, o_max] range. If i_min and i_max are equal, it raises a ValueError.

Example:

> value = 50
> pygame.math.remap(0, 100, 0, 200, value)
> 100.0

New in pygame-ce 2.5.0.

pygame.math.Vector2¶

a 2-Dimensional Vector
Vector2() -> Vector2(0, 0)
Vector2(int) -> Vector2
Vector2(float) -> Vector2
Vector2(Vector2) -> Vector2
Vector2(x, y) -> Vector2
Vector2((x, y)) -> Vector2

pygame.math.Vector2.dot	—	calculates the dot- or scalar-product with the other vector
pygame.math.Vector2.cross	—	calculates the cross- or vector-product
pygame.math.Vector2.magnitude	—	returns the Euclidean magnitude of the vector.
pygame.math.Vector2.magnitude_squared	—	returns the squared magnitude of the vector.
pygame.math.Vector2.length	—	returns the Euclidean length of the vector.
pygame.math.Vector2.length_squared	—	returns the squared Euclidean length of the vector.
pygame.math.Vector2.normalize	—	returns a vector with the same direction but length 1.
pygame.math.Vector2.normalize_ip	—	normalizes the vector in place so that its length is 1.
pygame.math.Vector2.is_normalized	—	tests if the vector is normalized i.e. has length == 1.
pygame.math.Vector2.scale_to_length	—	scales the vector to a given length.
pygame.math.Vector2.reflect	—	returns a vector reflected of a given normal.
pygame.math.Vector2.reflect_ip	—	reflect the vector of a given normal in place.
pygame.math.Vector2.distance_to	—	calculates the Euclidean distance to a given vector.
pygame.math.Vector2.distance_squared_to	—	calculates the squared Euclidean distance to a given vector.
pygame.math.Vector2.move_towards	—	returns a vector moved toward the target by a given distance.
pygame.math.Vector2.move_towards_ip	—	moves the vector toward its target at a given distance.
pygame.math.Vector2.lerp	—	returns a linear interpolation to the given vector.
pygame.math.Vector2.slerp	—	returns a spherical interpolation to the given vector.
pygame.math.Vector2.smoothstep	—	returns a smooth interpolation to the given vector.
pygame.math.Vector2.elementwise	—	The next operation will be performed elementwise.
pygame.math.Vector2.rotate	—	rotates a vector by a given angle in degrees.
pygame.math.Vector2.rotate_rad	—	rotates a vector by a given angle in radians.
pygame.math.Vector2.rotate_ip	—	rotates the vector by a given angle in degrees in place.
pygame.math.Vector2.rotate_ip_rad	—	rotates the vector by a given angle in radians in place.
pygame.math.Vector2.rotate_rad_ip	—	rotates the vector by a given angle in radians in place.
pygame.math.Vector2.angle_to	—	calculates the angle to a given vector in degrees.
pygame.math.Vector2.as_polar	—	returns a tuple with radial distance and azimuthal angle.
pygame.math.Vector2.from_polar	—	Sets x and y from a polar coordinates tuple.
pygame.math.Vector2.project	—	projects a vector onto another.
pygame.math.Vector2.copy	—	Returns a copy of itself.
pygame.math.Vector2.clamp_magnitude	—	Returns a copy of a vector with the magnitude clamped between max_length and min_length.
pygame.math.Vector2.clamp_magnitude_ip	—	Clamps the vector's magnitude between max_length and min_length
pygame.math.Vector2.update	—	Sets the coordinates of the vector.
pygame.math.Vector2.epsilon	—	Determines the tolerance of vector calculations.

Some general information about the Vector2 class.

Changed in pygame-ce 2.1.3: Inherited methods of vector subclasses now correctly return an instance of the subclass instead of the superclass

dot()¶: calculates the dot- or scalar-product with the other vector

dot(Vector2, /) -> float

cross()¶: calculates the cross- or vector-product

cross(Vector2, /) -> float

calculates the third component of the cross-product.

magnitude()¶: returns the Euclidean magnitude of the vector.

magnitude() -> float

calculates the magnitude of the vector which follows from the theorem: vec.magnitude() == math.sqrt(vec.x**2 + vec.y**2)

magnitude_squared()¶: returns the squared magnitude of the vector.

magnitude_squared() -> float

calculates the magnitude of the vector which follows from the theorem: vec.magnitude_squared() == vec.x**2 + vec.y**2. This is faster than vec.magnitude() because it avoids the square root.

length()¶: returns the Euclidean length of the vector.

length() -> float

calculates the Euclidean length of the vector which follows from the Pythagorean theorem: vec.length() == math.sqrt(vec.x**2 + vec.y**2)

length_squared()¶: returns the squared Euclidean length of the vector.

length_squared() -> float

calculates the Euclidean length of the vector which follows from the Pythagorean theorem: vec.length_squared() == vec.x**2 + vec.y**2. This is faster than vec.length() because it avoids the square root.

normalize()¶: returns a vector with the same direction but length 1.

normalize() -> Vector2

Returns a new vector that has length equal to 1 and the same direction as self.

normalize_ip()¶: normalizes the vector in place so that its length is 1.

normalize_ip() -> None

Normalizes the vector so that it has length equal to 1. The direction of the vector is not changed.

is_normalized()¶: tests if the vector is normalized i.e. has length == 1.

is_normalized() -> Bool

Returns True if the vector has length equal to 1. Otherwise it returns False.

scale_to_length()¶: scales the vector to a given length.

scale_to_length(float, /) -> None

Scales the vector so that it has the given length. The direction of the vector is not changed. You can also scale to length 0. If the vector is the zero vector (i.e. has length 0 thus no direction) a ValueError is raised.

reflect()¶: returns a vector reflected of a given normal.

reflect(Vector2, /) -> Vector2

Returns a new vector that points in the direction as if self would bounce of a surface characterized by the given surface normal. The length of the new vector is the same as self's.

reflect_ip()¶: reflect the vector of a given normal in place.

reflect_ip(Vector2, /) -> None

Changes the direction of self as if it would have been reflected of a surface with the given surface normal.

distance_to()¶: calculates the Euclidean distance to a given vector.

distance_to(Vector2, /) -> float

distance_squared_to()¶: calculates the squared Euclidean distance to a given vector.

distance_squared_to(Vector2, /) -> float

move_towards()¶: returns a vector moved toward the target by a given distance.

move_towards(Vector2, float, /) -> Vector2

Returns a Vector which is moved towards the given Vector by a given distance and does not overshoot past its target Vector. The first parameter determines the target Vector, while the second parameter determines the delta distance. If the distance is in the negatives, then it will move away from the target Vector.

New in pygame-ce 2.1.3.

move_towards_ip()¶: moves the vector toward its target at a given distance.

move_towards_ip(Vector2, float, /) -> None

Moves itself toward the given Vector at a given distance and does not overshoot past its target Vector. The first parameter determines the target Vector, while the second parameter determines the delta distance. If the distance is in the negatives, then it will move away from the target Vector.

New in pygame-ce 2.1.3.

lerp()¶: returns a linear interpolation to the given vector.

lerp(Vector2, float, /) -> Vector2

Returns a Vector which is a linear interpolation between self and the given Vector. The second parameter determines how far between self and other the result is going to be. It must be a value between 0 and 1 where 0 means self and 1 means other will be returned.

slerp()¶: returns a spherical interpolation to the given vector.

slerp(Vector2, float, /) -> Vector2

Calculates the spherical interpolation from self to the given Vector. The second argument - often called t - must be in the range [-1, 1]. It parametrizes where - in between the two vectors - the result should be. If a negative value is given the interpolation will not take the complement of the shortest path.

smoothstep()¶

returns a smooth interpolation to the given vector.

smoothstep(Vector2, float, /) -> Vector2

Returns a Vector which is a smooth interpolation between self and the given Vector. This means that the interpolation follows an s-shaped curve, with change happening more slowly near the limits (0.0 and 1.0) and faster in the middle. The third parameter determines how far between the two vectors the result is going to be.

The formula is:

a * interp + (1 - interp) * b

where:

interp = value * value * (3 - 2 * value)

New in pygame-ce 2.4.0.

elementwise()¶: The next operation will be performed elementwise.

elementwise() -> VectorElementwiseProxy

Applies the following operation to each element of the vector.

rotate()¶: rotates a vector by a given angle in degrees.

rotate(angle, /) -> Vector2

Returns a vector which has the same length as self but is rotated counterclockwise by the given angle in degrees. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

rotate_rad()¶: rotates a vector by a given angle in radians.

rotate_rad(angle, /) -> Vector2

Returns a vector which has the same length as self but is rotated counterclockwise by the given angle in radians. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

New in pygame 2.0.0.

rotate_ip()¶: rotates the vector by a given angle in degrees in place.

rotate_ip(angle, /) -> None

Rotates the vector counterclockwise by the given angle in degrees. The length of the vector is not changed. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

rotate_ip_rad()¶: rotates the vector by a given angle in radians in place.

rotate_ip_rad(angle, /) -> None

DEPRECATED: Use rotate_rad_ip() instead.

New in pygame 2.0.0.

Deprecated since pygame 2.1.1.

rotate_rad_ip()¶: rotates the vector by a given angle in radians in place.

rotate_rad_ip(angle, /) -> None

Rotates the vector counterclockwise by the given angle in radians. The length of the vector is not changed. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

New in pygame 2.1.1.

angle_to()¶: calculates the angle to a given vector in degrees.

angle_to(Vector2, /) -> float

Returns the angle from self to the passed Vector2 that would rotate self to be aligned with the passed Vector2 without crossing over the negative x-axis.

Example demonstrating the angle returned¶

as_polar()¶: returns a tuple with radial distance and azimuthal angle.

as_polar() -> (r, phi)

Returns a tuple (r, phi) where r is the radial distance, and phi is the azimuthal angle.

from_polar()¶: Sets x and y from a polar coordinates tuple.

from_polar((r, phi), /) -> None

Sets x and y from a tuple (r, phi) where r is the radial distance, and phi is the azimuthal angle.

project()¶: projects a vector onto another.

project(Vector2, /) -> Vector2

Returns the projected vector. This is useful for collision detection in finding the components in a certain direction (e.g. in direction of the wall). For a more detailed explanation see Wikipedia.

New in pygame 2.0.2.

copy()¶: Returns a copy of itself.

copy() -> Vector2

Returns a new Vector2 having the same dimensions.

New in pygame 2.1.1.

clamp_magnitude()¶

Returns a copy of a vector with the magnitude clamped between max_length and min_length.
clamp_magnitude(max_length, /) -> Vector2
clamp_magnitude(min_length, max_length, /) -> Vector2

Experimental: feature still in development available for testing and feedback. It may change. Please leave clamp_magnitude feedback with authors

Returns a new copy of a vector with the magnitude clamped between max_length and min_length. If only one argument is passed, it is taken to be the max_length

This function raises ValueError if min_length is greater than max_length, or if either of these values are negative.

New in pygame-ce 2.1.3.

Changed in pygame-ce 2.4.0: It is now possible to use clamp_magnitude on a zero-vector as long as min_length is unspecified or 0.

Note

Before pygame-ce 2.4.0, attempting to clamp a zero vector would always raise a ValueError

clamp_magnitude_ip()¶

Clamps the vector's magnitude between max_length and min_length
clamp_magnitude_ip(max_length, /) -> None
clamp_magnitude_ip(min_length, max_length, /) -> None

Clamps the vector's magnitude between max_length and min_length. If only one argument is passed, it is taken to be the max_length

This function raises ValueError if min_length is greater than max_length, or if either of these values are negative.

New in pygame-ce 2.1.3.

Changed in pygame-ce 2.4.0: It is now possible to use clamp_magnitude on a zero-vector as long as min_length is unspecified or 0.

Note

Before pygame-ce 2.4.0, attempting to clamp a zero vector would always raise a ValueError

update()¶: Sets the coordinates of the vector.

update() -> None

update(int) -> None

update(float) -> None

update(Vector2) -> None

update(x, y) -> None

update((x, y)) -> None

Sets coordinates x and y in place.

New in pygame 1.9.5.

epsilon¶

Determines the tolerance of vector calculations.

Both Vector classes have a value named epsilon that defaults to 1e-6. This value acts as a numerical margin in various methods to account for floating point arithmetic errors. Specifically, epsilon is used in the following places:

comparing Vectors (== and !=)

the is_normalized method (if the square of the length is within epsilon of 1, it's normalized)

slerping (a Vector with a length of <epsilon is considered a zero vector, and can't slerp with that)

reflection (can't reflect over the zero vector)

projection (can't project onto the zero vector)

rotation (only used when rotating by a multiple of 90 degrees)

While it's possible to change epsilon for a specific instance of a Vector, all the other Vectors will retain the default value. Changing epsilon on a specific instance however could lead to some asymmetric behavior where symmetry would be expected, such as

u = pygame.Vector2(0, 1)
v = pygame.Vector2(0, 1.2)
u.epsilon = 0.5 # don't set it nearly this large

print(u == v) # >> True
print(v == u) # >> False

You'll probably never have to change epsilon from the default value, but in rare situations you might find that either the margin is too large or too small, in which case changing epsilon slightly might help you out.

pygame.math.Vector3¶

a 3-Dimensional Vector
Vector3() -> Vector3(0, 0, 0)
Vector3(int) -> Vector3
Vector3(float) -> Vector3
Vector3(Vector3) -> Vector3
Vector3(x, y, z) -> Vector3
Vector3((x, y, z)) -> Vector3

pygame.math.Vector3.dot	—	calculates the dot- or scalar-product with the other vector
pygame.math.Vector3.cross	—	calculates the cross- or vector-product
pygame.math.Vector3.magnitude	—	returns the Euclidean magnitude of the vector.
pygame.math.Vector3.magnitude_squared	—	returns the squared Euclidean magnitude of the vector.
pygame.math.Vector3.length	—	returns the Euclidean length of the vector.
pygame.math.Vector3.length_squared	—	returns the squared Euclidean length of the vector.
pygame.math.Vector3.normalize	—	returns a vector with the same direction but length 1.
pygame.math.Vector3.normalize_ip	—	normalizes the vector in place so that its length is 1.
pygame.math.Vector3.is_normalized	—	tests if the vector is normalized i.e. has length == 1.
pygame.math.Vector3.scale_to_length	—	scales the vector to a given length.
pygame.math.Vector3.reflect	—	returns a vector reflected of a given normal.
pygame.math.Vector3.reflect_ip	—	reflect the vector of a given normal in place.
pygame.math.Vector3.distance_to	—	calculates the Euclidean distance to a given vector.
pygame.math.Vector3.distance_squared_to	—	calculates the squared Euclidean distance to a given vector.
pygame.math.Vector3.move_towards	—	returns a vector moved toward the target by a given distance.
pygame.math.Vector3.move_towards_ip	—	moves the vector toward its target at a given distance.
pygame.math.Vector3.lerp	—	returns a linear interpolation to the given vector.
pygame.math.Vector3.slerp	—	returns a spherical interpolation to the given vector.
pygame.math.Vector3.smoothstep	—	returns a smooth interpolation to the given vector.
pygame.math.Vector3.elementwise	—	The next operation will be performed elementwise.
pygame.math.Vector3.rotate	—	rotates a vector by a given angle in degrees.
pygame.math.Vector3.rotate_rad	—	rotates a vector by a given angle in radians.
pygame.math.Vector3.rotate_ip	—	rotates the vector by a given angle in degrees in place.
pygame.math.Vector3.rotate_ip_rad	—	rotates the vector by a given angle in radians in place.
pygame.math.Vector3.rotate_rad_ip	—	rotates the vector by a given angle in radians in place.
pygame.math.Vector3.rotate_x	—	rotates a vector around the x-axis by the angle in degrees.
pygame.math.Vector3.rotate_x_rad	—	rotates a vector around the x-axis by the angle in radians.
pygame.math.Vector3.rotate_x_ip	—	rotates the vector around the x-axis by the angle in degrees in place.
pygame.math.Vector3.rotate_x_ip_rad	—	rotates the vector around the x-axis by the angle in radians in place.
pygame.math.Vector3.rotate_x_rad_ip	—	rotates the vector around the x-axis by the angle in radians in place.
pygame.math.Vector3.rotate_y	—	rotates a vector around the y-axis by the angle in degrees.
pygame.math.Vector3.rotate_y_rad	—	rotates a vector around the y-axis by the angle in radians.
pygame.math.Vector3.rotate_y_ip	—	rotates the vector around the y-axis by the angle in degrees in place.
pygame.math.Vector3.rotate_y_ip_rad	—	rotates the vector around the y-axis by the angle in radians in place.
pygame.math.Vector3.rotate_y_rad_ip	—	rotates the vector around the y-axis by the angle in radians in place.
pygame.math.Vector3.rotate_z	—	rotates a vector around the z-axis by the angle in degrees.
pygame.math.Vector3.rotate_z_rad	—	rotates a vector around the z-axis by the angle in radians.
pygame.math.Vector3.rotate_z_ip	—	rotates the vector around the z-axis by the angle in degrees in place.
pygame.math.Vector3.rotate_z_ip_rad	—	rotates the vector around the z-axis by the angle in radians in place.
pygame.math.Vector3.rotate_z_rad_ip	—	rotates the vector around the z-axis by the angle in radians in place.
pygame.math.Vector3.angle_to	—	calculates the angle to a given vector in degrees.
pygame.math.Vector3.as_spherical	—	returns a tuple with radial distance, inclination and azimuthal angle.
pygame.math.Vector3.from_spherical	—	Sets x, y and z from a spherical coordinates 3-tuple.
pygame.math.Vector3.project	—	projects a vector onto another.
pygame.math.Vector3.copy	—	Returns a copy of itself.
pygame.math.Vector3.clamp_magnitude	—	Returns a copy of a vector with the magnitude clamped between max_length and min_length.
pygame.math.Vector3.clamp_magnitude_ip	—	Clamps the vector's magnitude between max_length and min_length
pygame.math.Vector3.update	—	Sets the coordinates of the vector.
pygame.math.Vector3.epsilon	—	Determines the tolerance of vector calculations.

Some general information about the Vector3 class.

Changed in pygame-ce 2.1.3: Inherited methods of vector subclasses now correctly return an instance of the subclass instead of the superclass

dot()¶: calculates the dot- or scalar-product with the other vector

dot(Vector3, /) -> float

cross()¶: calculates the cross- or vector-product

cross(Vector3, /) -> Vector3

calculates the cross-product.

magnitude()¶: returns the Euclidean magnitude of the vector.

magnitude() -> float

calculates the magnitude of the vector which follows from the theorem: vec.magnitude() == math.sqrt(vec.x**2 + vec.y**2 + vec.z**2)

magnitude_squared()¶: returns the squared Euclidean magnitude of the vector.

magnitude_squared() -> float

calculates the magnitude of the vector which follows from the theorem: vec.magnitude_squared() == vec.x**2 + vec.y**2 + vec.z**2. This is faster than vec.magnitude() because it avoids the square root.

length()¶: returns the Euclidean length of the vector.

length() -> float

calculates the Euclidean length of the vector which follows from the Pythagorean theorem: vec.length() == math.sqrt(vec.x**2 + vec.y**2 + vec.z**2)

length_squared()¶: returns the squared Euclidean length of the vector.

length_squared() -> float

calculates the Euclidean length of the vector which follows from the Pythagorean theorem: vec.length_squared() == vec.x**2 + vec.y**2 + vec.z**2. This is faster than vec.length() because it avoids the square root.

normalize()¶: returns a vector with the same direction but length 1.

normalize() -> Vector3

Returns a new vector that has length equal to 1 and the same direction as self.

normalize_ip()¶: normalizes the vector in place so that its length is 1.

normalize_ip() -> None

Normalizes the vector so that it has length equal to 1. The direction of the vector is not changed.

is_normalized()¶: tests if the vector is normalized i.e. has length == 1.

is_normalized() -> Bool

Returns True if the vector has length equal to 1. Otherwise it returns False.

scale_to_length()¶: scales the vector to a given length.

scale_to_length(float, /) -> None

Scales the vector so that it has the given length. The direction of the vector is not changed. You can also scale to length 0. If the vector is the zero vector (i.e. has length 0 thus no direction) a ValueError is raised.

reflect()¶: returns a vector reflected of a given normal.

reflect(Vector3, /) -> Vector3

Returns a new vector that points in the direction as if self would bounce of a surface characterized by the given surface normal. The length of the new vector is the same as self's.

reflect_ip()¶: reflect the vector of a given normal in place.

reflect_ip(Vector3, /) -> None

Changes the direction of self as if it would have been reflected of a surface with the given surface normal.

distance_to()¶: calculates the Euclidean distance to a given vector.

distance_to(Vector3, /) -> float

distance_squared_to()¶: calculates the squared Euclidean distance to a given vector.

distance_squared_to(Vector3, /) -> float

move_towards()¶: returns a vector moved toward the target by a given distance.

move_towards(Vector3, float, /) -> Vector3

Returns a Vector which is moved towards the given Vector by a given distance and does not overshoot past its target Vector. The first parameter determines the target Vector, while the second parameter determines the delta distance. If the distance is in the negatives, then it will move away from the target Vector.

New in pygame-ce 2.1.3.

move_towards_ip()¶: moves the vector toward its target at a given distance.

move_towards_ip(Vector3, float, /) -> None

Moves itself toward the given Vector at a given distance and does not overshoot past its target Vector. The first parameter determines the target Vector, while the second parameter determines the delta distance. If the distance is in the negatives, then it will move away from the target Vector.

New in pygame-ce 2.1.3.

lerp()¶: returns a linear interpolation to the given vector.

lerp(Vector3, float, /) -> Vector3

Returns a Vector which is a linear interpolation between self and the given Vector. The second parameter determines how far between self an other the result is going to be. It must be a value between 0 and 1, where 0 means self and 1 means other will be returned.

slerp()¶: returns a spherical interpolation to the given vector.

slerp(Vector3, float, /) -> Vector3

Calculates the spherical interpolation from self to the given Vector. The second argument - often called t - must be in the range [-1, 1]. It parametrizes where - in between the two vectors - the result should be. If a negative value is given the interpolation will not take the complement of the shortest path.

smoothstep()¶

returns a smooth interpolation to the given vector.

smoothstep(Vector3, float, /) -> Vector3

The formula is:

a * interp + (1 - interp) * b

where:

interp = value * value * (3 - 2 * value)

New in pygame-ce 2.4.0.

elementwise()¶: The next operation will be performed elementwise.

elementwise() -> VectorElementwiseProxy

Applies the following operation to each element of the vector.

rotate()¶: rotates a vector by a given angle in degrees.

rotate(angle, Vector3, /) -> Vector3

Returns a vector which has the same length as self but is rotated counterclockwise by the given angle in degrees around the given axis. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

rotate_rad()¶: rotates a vector by a given angle in radians.

rotate_rad(angle, Vector3, /) -> Vector3

Returns a vector which has the same length as self but is rotated counterclockwise by the given angle in radians around the given axis. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

New in pygame 2.0.0.

rotate_ip()¶: rotates the vector by a given angle in degrees in place.

rotate_ip(angle, Vector3, /) -> None

Rotates the vector counterclockwise around the given axis by the given angle in degrees. The length of the vector is not changed. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

rotate_ip_rad()¶: rotates the vector by a given angle in radians in place.

rotate_ip_rad(angle, Vector3, /) -> None

DEPRECATED: Use rotate_rad_ip() instead.

New in pygame 2.0.0.

Deprecated since pygame 2.1.1.

rotate_rad_ip()¶: rotates the vector by a given angle in radians in place.

rotate_rad_ip(angle, Vector3, /) -> None

Rotates the vector counterclockwise around the given axis by the given angle in radians. The length of the vector is not changed. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

New in pygame 2.1.1.

rotate_x()¶: rotates a vector around the x-axis by the angle in degrees.

rotate_x(angle, /) -> Vector3

Returns a vector which has the same length as self but is rotated counterclockwise around the x-axis by the given angle in degrees. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

rotate_x_rad()¶: rotates a vector around the x-axis by the angle in radians.

rotate_x_rad(angle, /) -> Vector3

Returns a vector which has the same length as self but is rotated counterclockwise around the x-axis by the given angle in radians. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

New in pygame 2.0.0.

rotate_x_ip()¶: rotates the vector around the x-axis by the angle in degrees in place.

rotate_x_ip(angle, /) -> None

Rotates the vector counterclockwise around the x-axis by the given angle in degrees. The length of the vector is not changed. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

rotate_x_ip_rad()¶: rotates the vector around the x-axis by the angle in radians in place.

rotate_x_ip_rad(angle, /) -> None

DEPRECATED: Use rotate_x_rad_ip() instead.

New in pygame 2.0.0.

Deprecated since pygame 2.1.1.

rotate_x_rad_ip()¶: rotates the vector around the x-axis by the angle in radians in place.

rotate_x_rad_ip(angle, /) -> None

Rotates the vector counterclockwise around the x-axis by the given angle in radians. The length of the vector is not changed. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

New in pygame 2.1.1.

rotate_y()¶: rotates a vector around the y-axis by the angle in degrees.

rotate_y(angle, /) -> Vector3

Returns a vector which has the same length as self but is rotated counterclockwise around the y-axis by the given angle in degrees. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

rotate_y_rad()¶: rotates a vector around the y-axis by the angle in radians.

rotate_y_rad(angle, /) -> Vector3

Returns a vector which has the same length as self but is rotated counterclockwise around the y-axis by the given angle in radians. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

New in pygame 2.0.0.

rotate_y_ip()¶: rotates the vector around the y-axis by the angle in degrees in place.

rotate_y_ip(angle, /) -> None

Rotates the vector counterclockwise around the y-axis by the given angle in degrees. The length of the vector is not changed. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

rotate_y_ip_rad()¶: rotates the vector around the y-axis by the angle in radians in place.

rotate_y_ip_rad(angle, /) -> None

DEPRECATED: Use rotate_y_rad_ip() instead.

New in pygame 2.0.0.

Deprecated since pygame 2.1.1.

rotate_y_rad_ip()¶: rotates the vector around the y-axis by the angle in radians in place.

rotate_y_rad_ip(angle, /) -> None

Rotates the vector counterclockwise around the y-axis by the given angle in radians. The length of the vector is not changed. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

New in pygame 2.1.1.

rotate_z()¶: rotates a vector around the z-axis by the angle in degrees.

rotate_z(angle, /) -> Vector3

Returns a vector which has the same length as self but is rotated counterclockwise around the z-axis by the given angle in degrees. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

rotate_z_rad()¶: rotates a vector around the z-axis by the angle in radians.

rotate_z_rad(angle, /) -> Vector3

Returns a vector which has the same length as self but is rotated counterclockwise around the z-axis by the given angle in radians. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

New in pygame 2.0.0.

rotate_z_ip()¶: rotates the vector around the z-axis by the angle in degrees in place.

rotate_z_ip(angle, /) -> None

Rotates the vector counterclockwise around the z-axis by the given angle in degrees. The length of the vector is not changed. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

rotate_z_ip_rad()¶: rotates the vector around the z-axis by the angle in radians in place.

rotate_z_ip_rad(angle, /) -> None

DEPRECATED: Use rotate_z_rad_ip() instead.

Deprecated since pygame 2.1.1.

rotate_z_rad_ip()¶: rotates the vector around the z-axis by the angle in radians in place.

rotate_z_rad_ip(angle, /) -> None

Rotates the vector counterclockwise around the z-axis by the given angle in radians. The length of the vector is not changed. (Note that due to pygame's inverted y coordinate system, the rotation will look clockwise if displayed).

New in pygame 2.1.1.

angle_to()¶: calculates the angle to a given vector in degrees.

angle_to(Vector3, /) -> float

Returns the angle between self and the given vector.

as_spherical()¶: returns a tuple with radial distance, inclination and azimuthal angle.

as_spherical() -> (r, theta, phi)

Returns a tuple (r, theta, phi) where r is the radial distance, theta is the inclination angle and phi is the azimuthal angle.

from_spherical()¶: Sets x, y and z from a spherical coordinates 3-tuple.

from_spherical((r, theta, phi), /) -> None

Sets x, y and z from a tuple (r, theta, phi) where r is the radial distance, theta is the inclination angle and phi is the azimuthal angle.

project()¶: projects a vector onto another.

project(Vector3, /) -> Vector3

Returns the projected vector. This is useful for collision detection in finding the components in a certain direction (e.g. in direction of the wall). For a more detailed explanation see Wikipedia.

New in pygame 2.0.2.

copy()¶: Returns a copy of itself.

copy() -> Vector3

Returns a new Vector3 having the same dimensions.

New in pygame 2.1.1.

clamp_magnitude()¶

Returns a copy of a vector with the magnitude clamped between max_length and min_length.
clamp_magnitude(max_length, /) -> Vector3
clamp_magnitude(min_length, max_length, /) -> Vector3

Returns a new copy of a vector with the magnitude clamped between max_length and min_length. If only one argument is passed, it is taken to be the max_length

This function raises ValueError if min_length is greater than max_length, or if either of these values are negative.

New in pygame-ce 2.1.3.

Changed in pygame-ce 2.4.0: It is now possible to use clamp_magnitude on a zero-vector as long as min_length is unspecified or 0.

Note

Before pygame-ce 2.4.0, attempting to clamp a zero vector would always raise a ValueError

clamp_magnitude_ip()¶

Clamps the vector's magnitude between max_length and min_length
clamp_magnitude_ip(max_length, /) -> None
clamp_magnitude_ip(min_length, max_length, /) -> None

Clamps the vector's magnitude between max_length and min_length. If only one argument is passed, it is taken to be the max_length

This function raises ValueError if min_length is greater than max_length, or if either of these values are negative.

New in pygame-ce 2.1.3.

Changed in pygame-ce 2.4.0: It is now possible to use clamp_magnitude on a zero-vector as long as min_length is unspecified or 0.

Note

Before pygame-ce 2.4.0, attempting to clamp a zero vector would always raise a ValueError

update()¶: Sets the coordinates of the vector.

update() -> None

update(int) -> None

update(float) -> None

update(Vector3) -> None

update(x, y, z) -> None

update((x, y, z)) -> None

Sets coordinates x, y, and z in place.

New in pygame 1.9.5.

epsilon¶: Determines the tolerance of vector calculations.

With lengths within this number, vectors are considered equal. For more information see pygame.math.Vector2.epsilonDetermines the tolerance of vector calculations.

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