pole_density_function#

orix.measure.pole_density_function(*args: ndarray | Vector3d, resolution: float = 1, sigma: float = 5, weights: ndarray | None = None, hemisphere: str = 'upper', symmetry: Symmetry | None = None, log: bool = False, mrd: bool = True) → Tuple[MaskedArray, Tuple[ndarray, ndarray]][source]#

Compute the Pole Density Function (PDF) of vectors in the stereographic projection. See [Rohrer et al., 2004].

If symmetry is defined then the PDF is folded back into the point group fundamental sector and accumulated.

Parameters:

args: Vector(s), or azimuth and polar angles of the vectors, the latter passed as two separate arguments.
resolution: The angular resolution of the sampling grid in degrees. Default value is 1.
sigma: The angular resolution of the applied broadening in degrees. Default value is 5.
weights: The weights for the individual vectors. Default is None, in which case the weight of each vector is 1.
hemisphere: Which hemisphere(s) to plot the vectors on, options are "upper" and "lower". Default is "upper".
symmetry: If provided the PDF is calculated within the fundamental sector of the point group symmetry, otherwise the PDF is calculated on hemisphere. Default is None.
log: If True the log(PDF) is calculated. Default is True.
mrd: If True the returned PDF is in units of Multiples of Random Distribution (MRD), otherwise the units are bin counts. Default is True.

Returns:

hist: The computed histogram, shape is (N, M).
x, y: Tuple of coordinate grids for the bin edges of hist. The units of x and y are cartesian coordinates on the stereographic projection plane and the shape of both x and y is (N + 1, M + 1).