def T(self):
""":math:`\\frac{1}{6}` the volume of the tetrahedron defined by \
:class:`~sknano.core.math.Vector`\ s `V1`, `V2`, and `V3`.
.. math::
T =
\\frac{|\\mathbf{V}_1\\cdot(\\mathbf{V}_2\\times\\mathbf{V}_3)|}{6}
"""
return np.abs(vec.scalar_triple_product(self.V1, self.V2, self.V3) / 6)
def T(self):
""":math:`\\frac{1}{6}` the volume of the tetrahedron defined by \
:class:`~sknano.core.math.Vector`\ s `V1`, `V2`, and `V3`.
.. math::
T =
\\frac{|\\mathbf{V}_1\\cdot(\\mathbf{V}_2\\times\\mathbf{V}_3)|}{6}
"""
return np.abs(vec.scalar_triple_product(self.V1, self.V2, self.V3) / 6)
def volume(self):
"""Parallelepiped volume, :math:`V`.
Computed as:
.. math::
V = |\\mathbf{u}\\cdot\\mathbf{v}\\times\\mathbf{w}|
"""
return np.abs(vec.scalar_triple_product(self.u, self.v, self.w))
def volume(self):
"""Parallelepiped volume, :math:`V`.
Computed as:
.. math::
V = |\\mathbf{u}\\cdot\\mathbf{v}\\times\\mathbf{w}|
"""
return np.abs(vec.scalar_triple_product(self.u, self.v, self.w))
def Vv1v2v3(self):
"""Volume of the parallelepiped defined by \
:class:`~sknano.core.math.Vector`\ s `v1`, `v2`, and `v3`.
Computes the scalar triple product of vectors :math:`\\mathbf{v}_1`,
:math:`\\mathbf{v}_2`, and :math:`\\mathbf{v}_3`:
.. math::
V_{v_1v_2v_3} =
|\\mathbf{v}_1\\cdot(\\mathbf{v}_2\\times\\mathbf{v}_3)|
"""
return np.abs(vec.scalar_triple_product(self.v1, self.v2, self.v3))
def Vv1v2v3(self):
"""Volume of the parallelepiped defined by \
:class:`~sknano.core.math.Vector`\ s `v1`, `v2`, and `v3`.
Computes the scalar triple product of vectors :math:`\\mathbf{v}_1`,
:math:`\\mathbf{v}_2`, and :math:`\\mathbf{v}_3`:
.. math::
V_{v_1v_2v_3} =
|\\mathbf{v}_1\\cdot(\\mathbf{v}_2\\times\\mathbf{v}_3)|
"""
return np.abs(vec.scalar_triple_product(self.v1, self.v2, self.v3))
def test16():
u = Vector([1, 0, 0])
v = Vector([1, 1, 0])
w = Vector([0, 1, 1])
assert_equals(vec.scalar_triple_product(u, v, w), 1)
def test16():
u = Vector([1, 0, 0])
v = Vector([1, 1, 0])
w = Vector([0, 1, 1])
assert_equals(vec.scalar_triple_product(u, v, w), 1)
