CoordinateSystemArray

class atompy.CoordinateSystemArray(vectors_1, vectors_2, vectors_3=None)

Class representing a collection of coordinate systems.

Tip

If you want to store a single coordinate systems, consider CoordinateSystem.

Parameters:

vectors_1VectorArrayLike

First set of vectors \(\vec{v}_1\) defining the coordinate system.

vectors_2VectorArrayLike

Second set of vectors \(\vec{v}_2\) defining the coordinate system. Should not be parallel to vectors_1.

vector_3VectorArrayLike or None, default None

Optional third set of vectors. If three sets are provided, use them as the new base vectors (after normalization).

Attributes:

x_axis, y_axis, z_axisVectorArray

x, y, z basis vectors of the coordinate system.

Notes

The three basis vectors \(\hat{x}, \hat{y}, \hat{z}\) will be unit vectors along the directions given by, respectively

\[\begin{split}\vec{z} &= \vec{v_1} \\ \vec{y} &= \vec{v_z} \times \vec{v_2} \\ \vec{x} &= \vec{v_y} \times \vec{z}\end{split}\]

If three vectors are provided, the directions will be given by

\[\begin{split}\vec{x} &= \vec{v_1} \\ \vec{y} &= \vec{v_2} \\ \vec{z} &= \vec{v_3} \\\end{split}\]

Methods

project_vectors(vectors)

Project vectors on the coordinate system.