wulfric.geometry.get_volume

wulfric.geometry.get_volume(*args)

Computes volume.

Three types of arguments are expected:

• One argument.

  Matrix cell. Volume is computed as:

  \[V = \boldsymbol{v_1} \cdot (\boldsymbol{v_2} \times \boldsymbol{v_3})\]

• Three arguments.

  Vectors v1, v2, v3. Volume is computed as:

  \[V = \boldsymbol{v_1} \cdot (\boldsymbol{v_2} \times \boldsymbol{v_3})\]

• Six arguments.

  Parameters a, b, c, alpha, beta, gamma. Volume is computed as:

  \[V = abc\sqrt{1+2\cos(\alpha)\cos(\beta)\cos(\gamma)-\cos^2(\alpha)-\cos^2(\beta)-\cos^2(\gamma)}\]

Parameters:

v1(3,) array-like

First vector.

v2(3,) array-like

Second vector.

v3(3,) array-like

Third vector.

cell(3, 3) array-like

Matrix of a cell, rows are interpreted as vectors.

afloat, default 1

Length of the \(v_1\) vector.

bfloat, default 1

Length of the \(v_2\) vector.

cfloat, default 1

Length of the \(v_3\) vector.

alphafloat, default 90

Angle between vectors \(v_2\) and \(v_3\). In degrees.

betafloat, default 90

Angle between vectors \(v_1\) and \(v_3\). In degrees.

gammafloat, default 90

Angle between vectors \(v_1\) and \(v_2\). In degrees.

Returns:

volumefloat

Volume of corresponding region in space.

Examples

>>> import wulfric
>>> wulfric.geometry.get_volume([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
1.0
>>> wulfric.geometry.get_volume([1, 0, 0], [0, 1, 0], [0, 0, 1])
1.0
>>> wulfric.geometry.get_volume(1, 1, 1, 90, 90, 90)
1.0