SimPEG.utils.volume_tetrahedron#
- SimPEG.utils.volume_tetrahedron(xyz, A, B, C, D)[source]#
Returns the tetrahedron volumes for a specified set of verticies.
Let xyz be an (n, 3) array denoting a set of vertex locations. Any 4 vertex locations a, b, c and d can be used to define a tetrahedron. For the set of tetrahedra whose verticies are indexed in vectors A, B, C and D, this function returns the corresponding volumes. See algorithm: https://en.wikipedia.org/wiki/Tetrahedron#Volume
\[vol = {1 \over 6} \big | ( \mathbf{a - d} ) \cdot ( ( \mathbf{b - d} ) \times ( \mathbf{c - d} ) ) \big |\]- Parameters
- xyz(
n_pts, 3)numpy.ndarray x,y, and z locations for all verticies
- A(
n_tetra)numpy.ndarrayofint Vector containing the indicies for the a vertex locations
- B(
n_tetra)numpy.ndarrayofint Vector containing the indicies for the b vertex locations
- C(
n_tetra)numpy.ndarrayofint Vector containing the indicies for the c vertex locations
- D(
n_tetra)numpy.ndarrayofint Vector containing the indicies for the d vertex locations
- xyz(
- Returns
- (
n_tetra)numpy.ndarray Volumes of the tetrahedra whose vertices are indexed by A, B, C and D.
- (
Examples