math

Vector3D ¶

Python

Vector3D(x: T = 0, y: T = 0, z: T = 0)

A generic 3D vector class supporting basic vector operations.

ATTRIBUTE	DESCRIPTION
`x`	X coordinate TYPE: `T`
`y`	Y coordinate TYPE: `T`
`z`	Z coordinate TYPE: `T`

to_floor ¶

Python

to_floor() -> Vector3D[int]

Convert each component of the vector to its floored integer value.

RETURNS	DESCRIPTION
`Vector3D[int]`	Vector with integer components

to_2d ¶

Python

to_2d() -> Vector2D[T]

Convert a 3D vector to a 2D vector by removing the Y (height) component.

RETURNS	DESCRIPTION
`Vector2D[int]`	A 2D vector with the X and Z components of this vector

magnitude ¶

Python

magnitude() -> float

Calculate the magnitude (length) of the vector.

RETURNS	DESCRIPTION
`float`	Magnitude of the vector

magnitude_squared ¶

Python

magnitude_squared() -> Union[int, float]

Calculate the squared magnitude of the vector (more efficient than magnitude).

RETURNS	DESCRIPTION
`Union[int, float]`	Squared magnitude of the vector

normalize ¶

Python

normalize() -> Vector3D[float]

Return a normalized (unit) vector in the same direction.

RETURNS	DESCRIPTION
`Vector3D[float]`	Normalized vector with magnitude 1, or zero vector if original magnitude is 0

distance_to ¶

Python

distance_to(other: Vector3D[T]) -> float

Calculate the Euclidean distance to another vector.

PARAMETER	DESCRIPTION
`other`	Target vector TYPE: `Vector3D[T]`

RETURNS	DESCRIPTION
`float`	Distance between the two vectors

copy ¶

Python

copy() -> Vector3D[T]

Return a copy of the vector.

RETURNS	DESCRIPTION
`Vector3D[T]`	A new Vector3D instance with the same components.

dot ¶

Python

dot(other: Vector3D[T]) -> float

Calculate the dot product with another vector.

PARAMETER	DESCRIPTION
`other`	The other vector TYPE: `Vector3D[T]`

RETURNS	DESCRIPTION
`float`	The dot product result

cross ¶

Python

cross(other: Vector3D[T]) -> Vector3D[float]

Calculate the cross product with another vector.

PARAMETER	DESCRIPTION
`other`	The other vector TYPE: `Vector3D[T]`

RETURNS	DESCRIPTION
`Vector3D[float]`	The cross product result

is_zero ¶

Python

is_zero(tolerance: float = 1e-06) -> bool

Check if vector is approximately zero within tolerance.

PARAMETER	DESCRIPTION
`tolerance`	Tolerance for zero check (default: 1e-6) TYPE: `float` DEFAULT: `1e-06`

RETURNS	DESCRIPTION
`bool`	True if vector magnitude is below tolerance

lerp ¶

Python

lerp(other: Vector3D[T], t: float) -> Vector3D[float]

Linear interpolation between this vector and another.

PARAMETER	DESCRIPTION
`other`	Target vector TYPE: `Vector3D[T]`
`t`	Interpolation factor (0.0 = this vector, 1.0 = other vector) TYPE: `float`

RETURNS	DESCRIPTION
`Vector3D[float]`	Interpolated vector

clamp_magnitude ¶

Python

clamp_magnitude(max_magnitude: float) -> Vector3D[float]

Clamp vector magnitude to maximum value.

PARAMETER	DESCRIPTION
`max_magnitude`	Maximum allowed magnitude TYPE: `float`

RETURNS	DESCRIPTION
`Vector3D[float]`	Vector with clamped magnitude

angle_to ¶

Python

angle_to(other: Vector3D[T]) -> float

Calculate the angle between this vector and another in radians.

PARAMETER	DESCRIPTION
`other`	Target vector TYPE: `Vector3D[T]`

RETURNS	DESCRIPTION
`float`	Angle in radians (0 to π)

project_onto ¶

Python

project_onto(other: Vector3D[T]) -> Vector3D[float]

Project this vector onto another vector.

PARAMETER	DESCRIPTION
`other`	Vector to project onto TYPE: `Vector3D[T]`

RETURNS	DESCRIPTION
`Vector3D[float]`	Projected vector

reflect ¶

Python

reflect(normal: Vector3D[T]) -> Vector3D[float]

Reflect this vector across a surface with given normal.

PARAMETER	DESCRIPTION
`normal`	Surface normal vector (should be normalized) TYPE: `Vector3D[T]`

RETURNS	DESCRIPTION
`Vector3D[float]`	Reflected vector

average `staticmethod` ¶

Python

average(vectors: List[Vector3D[T]]) -> Vector3D[float]

Calculate the average of multiple vectors.

PARAMETER	DESCRIPTION
`vectors`	List of vectors to average TYPE: `List[Vector3D[T]]`

RETURNS	DESCRIPTION
`Vector3D[float]`	Average vector, or zero vector if list is empty

Vector2D ¶

Python

Vector2D(x: T = 0, y: T = 0)

A generic 2D vector class supporting basic vector operations.

ATTRIBUTE	DESCRIPTION
`x`	X coordinate TYPE: `T`
`y`	Y coordinate TYPE: `T`

to_int ¶

Python

to_int() -> Vector2D[int]

Convert vector components to integers using truncation.

RETURNS	DESCRIPTION
`Vector2D[int]`	Vector with integer components

magnitude ¶

Python

magnitude() -> float

Calculate the magnitude (length) of the vector.

RETURNS	DESCRIPTION
`float`	Magnitude of the vector

magnitude_squared ¶

Python

magnitude_squared() -> Union[int, float]

Calculate the squared magnitude of the vector (more efficient than magnitude).

RETURNS	DESCRIPTION
`Union[int, float]`	Squared magnitude of the vector

normalize ¶

Python

normalize() -> Vector2D[float]

Return a normalized (unit) vector in the same direction.

RETURNS	DESCRIPTION
`Vector2D[float]`	Normalized vector with magnitude 1, or zero vector if original magnitude is 0

distance_to ¶

Python

distance_to(other: Vector2D[T]) -> float

Calculate the Euclidean distance to another vector.

PARAMETER	DESCRIPTION
`other`	Target vector TYPE: `Vector2D[T]`

RETURNS	DESCRIPTION
`float`	Distance between the two vectors

copy ¶

Python

copy() -> Vector2D[T]

Return a copy of the vector.

RETURNS	DESCRIPTION
`Vector2D[T]`	A new Vector2D instance with the same components.

dot ¶

Python

dot(other: Vector2D[T]) -> float

Calculate the dot product with another vector.

PARAMETER	DESCRIPTION
`other`	The other vector TYPE: `Vector2D[T]`

RETURNS	DESCRIPTION
`float`	The dot product result

is_zero ¶

Python

is_zero(tolerance: float = 1e-06) -> bool

Check if vector is approximately zero within tolerance.

PARAMETER	DESCRIPTION
`tolerance`	Tolerance for zero check (default: 1e-6) TYPE: `float` DEFAULT: `1e-06`

RETURNS	DESCRIPTION
`bool`	True if vector magnitude is below tolerance

lerp ¶

Python

lerp(other: Vector2D[T], t: float) -> Vector2D[float]

Linear interpolation between this vector and another.

PARAMETER	DESCRIPTION
`other`	Target vector TYPE: `Vector2D[T]`
`t`	Interpolation factor (0.0 = this vector, 1.0 = other vector) TYPE: `float`

RETURNS	DESCRIPTION
`Vector2D[float]`	Interpolated vector

clamp_magnitude ¶

Python

clamp_magnitude(max_magnitude: float) -> Vector2D[float]

Clamp vector magnitude to maximum value.

PARAMETER	DESCRIPTION
`max_magnitude`	Maximum allowed magnitude TYPE: `float`

RETURNS	DESCRIPTION
`Vector2D[float]`	Vector with clamped magnitude

average `staticmethod` ¶

Python

average(vectors: List[Vector2D[T]]) -> Vector2D[float]

Calculate the average of multiple vectors.

PARAMETER	DESCRIPTION
`vectors`	List of vectors to average TYPE: `List[Vector2D[T]]`

RETURNS	DESCRIPTION
`Vector2D[float]`	Average vector, or zero vector if list is empty

Rotation ¶

Python

Rotation(yaw: float, pitch: float)

Represents rotation with pitch and yaw angles in degrees.

Angles are normalized to the range [-180, 180] degrees.

ATTRIBUTE	DESCRIPTION
`yaw`	Yaw angle in degrees, normalized to (-180, 180) TYPE: `float`
`pitch`	Pitch angle in degrees, normalized to (-180, 180) TYPE: `float`

to_radians ¶

Python

to_radians() -> Tuple[float, float]

Convert angles to radians.

RETURNS	DESCRIPTION
`Tuple[float, float]`	Tuple of (pitch_radians, yaw_radians)

to_degrees ¶

Python

to_degrees() -> Tuple[float, float]

Get angles in degrees.

RETURNS	DESCRIPTION
`Tuple[float, float]`	Tuple of (pitch_degrees, yaw_degrees)

from_radians `classmethod` ¶

Python

from_radians(
    pitch_radians: float, yaw_radians: float
) -> Rotation

Create a Rotation from angles in radians.

PARAMETER	DESCRIPTION
`pitch_radians`	Pitch angle in radians TYPE: `float`
`yaw_radians`	Yaw angle in radians TYPE: `float`

RETURNS	DESCRIPTION
`Rotation`	New Rotation instance

copy ¶

Python

copy() -> Rotation

Return a copy of the rotation.

RETURNS	DESCRIPTION
`Rotation`	A new Rotation instance with the same yaw and pitch.

math

Vector3D ¶

to_floor ¶

to_2d ¶

magnitude ¶

magnitude_squared ¶

normalize ¶

distance_to ¶

copy ¶

dot ¶

cross ¶

is_zero ¶

lerp ¶

clamp_magnitude ¶

angle_to ¶

project_onto ¶

reflect ¶

average staticmethod ¶

Vector2D ¶

to_int ¶

magnitude ¶

magnitude_squared ¶

normalize ¶

distance_to ¶

copy ¶

dot ¶

is_zero ¶

lerp ¶

clamp_magnitude ¶

average staticmethod ¶

Rotation ¶

to_radians ¶

to_degrees ¶

from_radians classmethod ¶

copy ¶

average `staticmethod` ¶

average `staticmethod` ¶

from_radians `classmethod` ¶