from_path_ends

classmethod Miller.from_path_ends(vectors: list | tuple | Vector3d, close: bool = False, steps: int = 100) → Vector3d

Return vectors along the shortest path on the sphere between two or more consectutive vectors.

Parameters:

vectors

Two or more vectors to get paths between.

close

Whether to append the first to the end of vectors in order to close the paths when more than two vectors are passed. Default is False.

steps

Number of vectors in the great circle about the normal vector between each two vectors before restricting the circle to the path between the two. Default is 100. More steps give a smoother path on the sphere.

Returns:

paths

Vectors along the shortest path(s) between given vectors.

Notes

The vectors along the shortest path on the sphere between two vectors \(v_1\) and \(v_2\) are found by first getting the vectors \(v_i\) along the great circle about the vector normal to these two vectors, and then only keeping the part of the circle between the two vectors. Vectors within this part satisfy these two conditions

\[(v_1 \times v_i) \cdot (v_1 \times v_2) \geq 0, (v_2 \times v_i) \cdot (v_2 \times v_1) \geq 0.\]