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import math
import numpy as np
def is_near_equal(a, b, tol=1.0e-12):
return np.allclose(a, b, rtol=0.0, atol=tol)
def signed_simplex_volumes(coords, cells):
assert len(coords.shape) == 2
assert len(cells.shape) == 2
assert (
coords.shape[1] + 1 == cells.shape[1]
), "Signed areas only make sense for n-simplices in in nD."
# bc = coords[:, cells]
# return np.cross((bc[:, :, 1] - bc[:, :, 0]).T, (bc[:, :, 2] - bc[:, :, 0]).T)
# https://en.wikipedia.org/wiki/Simplex#Volume
cp = coords[cells]
n = coords.shape[1]
# append ones; this appends a column instead of a row as suggested by
# wikipedia, but that doesn't change the determinant
cp1 = np.concatenate([cp, np.ones(cp.shape[:-1] + (1,))], axis=-1)
sign = -1 if n % 2 == 1 else 1
return sign * np.linalg.det(cp1) / math.factorial(n)
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