volume_tetrahedron

regridding.geometry.volume_tetrahedron(vertex_1, vertex_2, vertex_3)

Compute the signed volume of the tetrahedron formed by three vertices and the origin

If the vertices are oriented counterclockwise as viewed from the outside, the volume will be positive, otherwise it will be negative.

Parameters:

• vertex_1 (tuple[float, float, float]) – The first vertex of the tetrahedron.

• vertex_2 (tuple[float, float, float]) – The second vertex of the tetrahedron.

• vertex_3 (tuple[float, float, float]) – The third vertex of the tetrahedron.

Return type:

float

Notes

The volume of a tetrahedron with one vertex located at the origin is

\[V = \frac{1}{6} \vec{a} \cdot (\vec{b} \times \vec{c})\]

where \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) are the three other vertices of the tetrahedron.