`pygame.math`
pygame module for vector classes
 pygame.math.Vector2 — a 2-Dimensional Vector pygame.math.Vector3 — a 3-Dimensional Vector pygame.math.enable_swizzling — globally enables swizzling for vectors. pygame.math.disable_swizzling — globally disables swizzling for vectors.

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. 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: required import. More convenient `pygame.Vector2` and `pygame.Vector3`.

`pygame.math.``Vector2`
a 2-Dimensional Vector
Vector2() -> Vector2
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.lerp — returns a linear interpolation to the given vector. pygame.math.Vector2.slerp — returns a spherical 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.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.update — Sets the coordinates of the vector.

Some general information about the Vector2 class.

`dot`()
calculates the dot- or scalar-product with the other vector
dot(Vector2) -> float
`cross`()
calculates the cross- or vector-product
cross(Vector2) -> Vector2

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 == 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 == 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 == 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) an ZeroDivisionError 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
`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.

`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.

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

Returns a vector which has the same length as self but is rotated counterclockwise by the given angle in radians.

New in pygame 2.0.

`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.

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

Rotates the vector counterclockwise by the given angle in radians. The length of the vector is not changed.

New in pygame 2.0.

`angle_to`()
calculates the angle to a given vector in degrees.
angle_to(Vector2) -> float

Returns the angle between self and the given vector.

`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.

`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.

`pygame.math.``Vector3`
a 3-Dimensional Vector
Vector3() -> Vector3
Vector3(int) -> Vector3
Vector3(float) -> Vector3
Vector3(Vector3) -> Vector3
Vector3(x, y, z) -> Vector3
Vector3((x, y, z)) -> Vector3

Some general information about the Vector3 class.

`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 == 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 == 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 == 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) an ZeroDivisionError 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
`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 an 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.

`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.

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

Returns a vector which has the same length as self but is rotated counterclockwise by the given angle in radians around the given axis.

New in pygame 2.0.

`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.

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

Rotates the vector counterclockwise around the given axis by the given angle in radians. The length of the vector is not changed.

New in pygame 2.0.

`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.

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

Returns a vector which has the same length as self but is rotated counterclockwise around the x-axis by the given angle in radians.

New in pygame 2.0.

`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.

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

Rotates the vector counterclockwise around the x-axis by the given angle in radians. The length of the vector is not changed.

New in pygame 2.0.

`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.

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

Returns a vector which has the same length as self but is rotated counterclockwise around the y-axis by the given angle in radians.

New in pygame 2.0.

`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.

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

Rotates the vector counterclockwise around the y-axis by the given angle in radians. The length of the vector is not changed.

New in pygame 2.0.

`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.

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

Returns a vector which has the same length as self but is rotated counterclockwise around the z-axis by the given angle in radians.

New in pygame 2.0.

`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.

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

Rotates the vector counterclockwise around the z-axis by the given angle in radians. The length of the vector is not changed.

`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.

`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.

`pygame.math.``enable_swizzling`()
globally enables swizzling for vectors.
enable_swizzling() -> None

DEPRECATED: Not needed anymore. Will be removed in a later version.

Enables swizzling for all vectors until `disable_swizzling()` is called. By default swizzling is disabled.

Lets you get or set multiple coordinates as one attribute, eg `vec.xyz = 1, 2, 3`.

`pygame.math.``disable_swizzling`()
globally disables swizzling for vectors.
disable_swizzling() -> None

DEPRECATED: Not needed anymore. Will be removed in a later version.

Disables swizzling for all vectors until `enable_swizzling()` is called. By default swizzling is disabled.

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