# Here we define a small 3D tensor mesh. 4 nodes are chosen to
# be the verticies of a tetrahedron. We compute the volume of this
# tetrahedron. Note that xyz locations for the verticies can be
# scattered and do not require regular spacing.
#
from discretize.utils import volume_tetrahedron
from discretize import TensorMesh
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
#
# Define corners of a uniform cube
#
h = [1, 1]
mesh = TensorMesh([h, h, h])
xyz = mesh.nodes
#
# Specify the indicies of the corner points
#
A = np.array([0])
B = np.array([6])
C = np.array([8])
D = np.array([24])
#
# Compute volume for all tetrahedra and the extract first one
#
vol = volume_tetrahedron(xyz, A, B, C, D)
vol = vol[0]
vol
# Expected:
## array([1.33333333])
#
# Plotting small mesh and tetrahedron
#
fig = plt.figure(figsize=(7, 7))
ax = plt.subplot(projection='3d')
mesh.plot_grid(ax=ax)
k = [0, 6, 8, 0, 24, 6, 24, 8]
xyz_tetra = xyz[k, :]
ax.plot(xyz_tetra[:, 0], xyz_tetra[:, 1], xyz_tetra[:, 2], 'r')
ax.text(-0.25, 0., 3., 'Volume of the tetrahedron: {:g} $m^3$'.format(vol))
plt.show()