cross_vectors

compas.geometry.cross_vectors(u, v)

Compute the cross product of two vectors.

Parameters:

u[float, float, float] | compas.geometry.Vector

XYZ components of the first vector.

v[float, float, float] | compas.geometry.Vector

XYZ components of the second vector.

Returns:

[float, float, float]

The cross product of the two vectors.

Notes

The xyz components of the cross product of two vectors $\mathbf{u}$ and $\mathbf{v}$ can be computed as the minors of the following matrix:

$$\left[\begin{array}{ccc}x& y& z\\ u_x& u_y& u_z\\ v_x& v_y& v_z\end{array}\right]$$

Therefore, the cross product can be written as:

$$\begin{array}{rc}\mathbf{u}\times \mathbf{v}& =\left[\begin{array}{c}{u}_y\ast v_z-u_z\ast v_y\\ u_z\ast v_x-u_x\ast v_z\\ u_x\ast v_y-u_y\ast v_x\end{array}\right]\end{array}$$

Examples

>>> cross_vectors([1.0, 0.0, 0.0], [0.0, 1.0, 0.0])
[0.0, 0.0, 1.0]