`pygame.math`
pygame module for vector classes
 pygame.math.clamp — returns value clamped to min and max. pygame.math.lerp — interpolates between two values by a weight. 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 = 2 * v.x
print(v) # 10

v.x == v
v.y == v
v.z == v
```

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: import not required. More convenient `pygame.Vector2` and `pygame.Vector3`.

Changed in pygame 2.2.0: 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

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

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

New in pygame 2.1.3.

pygame.math.lerp()
interpolates between two values by a weight.
lerp(a, b, weight) -> float

Linearly interpolates between `a` and `b` by `weight` using the formula `a + (b-a) * weight`.

If `weight` is `0.5`, `lerp` will return the value half-way between `a` and `b`. When `a = 10` and `b = 20`, `lerp(a, b, 0.5)` will return `15`. You can think of weight as the percentage of interpolation from `a` to `b`, `0.0` being 0% and `1.0` being 100%.

`lerp` can be used for many things. You could rotate a sprite by a weight with `angle = lerp(0, 360, weight)`. You could even scale an enemy's attack value based on the level you're playing:

```FINAL_LEVEL = 10
current_level = 2

attack = lerp(10, 50, current_level/MAX_LEVEL) # 18
```

If you're on level 0, `attack` will be `10`, if you're on level 10, `attack` will be `50`. If you're on level 5, the result of `current_level/MAX_LEVEL` will be `0.5` which represents 50%, therefore `attack` will be `30`, which is the midpoint of `10` and `50`.

Raises a ValueError if `weight` is outside the range of `[0, 1]`.

New in pygame 2.1.3.

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.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 — Creates a Vector2(x, y) or 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 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

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

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 2.1.3.

move_towards_ip()
moves the vector toward its target at a given distance.
move_towards_ip(Vector2, float) -> None

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

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 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.

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).

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. (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).

rotates the vector by a given angle in radians in place.

New in pygame 2.0.0.

Deprecated since pygame 2.1.1.

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. (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.

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()
Creates a Vector2(x, y) or sets x and y from a polar coordinates tuple.
Vector2.from_polar((r, phi)) -> Vector2
Vector2().from_polar((r, phi)) -> None

If used from the class creates a Vector2(x,y), else sets x and y. The values of x and y are defined 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 2.1.3.

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

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

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 2.1.3.

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

Some general information about the Vector3 class.

Changed in pygame 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

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

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 2.1.3.

move_towards_ip()
moves the vector toward its target at a given distance.
move_towards_ip(Vector3, float) -> None

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

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 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.

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).

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. (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).

rotates the vector by a given angle in radians in place.

New in pygame 2.0.0.

Deprecated since pygame 2.1.1.

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. (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).

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. (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).

rotates the vector around the x-axis by the angle in radians in place.

New in pygame 2.0.0.

Deprecated since pygame 2.1.1.

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. (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).

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. (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).

rotates the vector around the y-axis by the angle in radians in place.

New in pygame 2.0.0.

Deprecated since pygame 2.1.1.

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. (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).

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. (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).

rotates the vector around the z-axis by the angle in radians in place.

Deprecated since pygame 2.1.1.

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. (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()
Creates a Vector3(x, y, z) or sets x, y and z from a spherical coordinates 3-tuple.
Vector3.from_spherical((r, theta, phi)) -> Vector3
Vector3().from_spherical((r, theta, phi)) -> None

If used from the class creates a Vector3(x, y, z), else sets x, y, and z. The values of x, y, and z are 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

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 2.1.3.

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

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

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 2.1.3.

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

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