pythagoras.r3.vector module

class pythagoras.r3.vector.Vector3D(x: float, y: float, z: float)

Bases: object

Three-dimensional vector with common operations.

Variables:

• x (float) – \(x\) component of the vector.

• y (float) – \(y\) component of the vector.

• z (float) – \(z\) component of the vector.

classmethod cylindrical(r: float, theta: float, z: float) → Self

Constructs a vector expressed in cylindrical coordinates.

Parameters:

• r – Magnitude of the projection of the vector onto the \(xy\) plane.

• theta – Angle of the projection onto the \(xy\) plane with respect to the positive \(x\)-axis.

• z – \(z\) component of the vector.

Returns:

The corresponding vector.

classmethod from_two_points(p1: tuple[float, float, float], p2: tuple[float, float, float]) → Self

Constructor for the vector that joins two points.

Parameters:

• p1 – Initial point.

• p2 – End point.

Returns:

The vector that goes from p1 to p2.

classmethod spherical(rho: float, phi: float, theta: float) → Self

Constructs a vector expressed in spherical coordinates.

Parameters:

• rho – Magnitude of the vector.

• phi – Angle formed with the positive \(z\) axis.

• theta – Angle of the projection onto the \(xy\) plane with respect to the positive \(x\)-axis.

Returns:

The corresponding vector.

property unitary: Self

Vector normalized to have unit norm.

x: float

y: float

z: float

pythagoras.r3.vector.dist3(p1: tuple[float, float, float], p2: tuple[float, float, float]) → float

Computes the Euclidean distance between two points in \(\mathbf R^3\).

Parameters:

• p1 – First point.

• p2 – Second point.