pymo/Pivots.py

import numpy as np

from pymo.Quaternions import Quaternions


class Pivots:
    """
    Pivots is an ndarray of angular rotations

    This wrapper provides some functions for
    working with pivots.

    These are particularly useful as a number
    of atomic operations (such as adding or
    subtracting) cannot be achieved using
    the standard arithmatic and need to be
    defined differently to work correctly
    """

    def __init__(self, ps):
        self.ps = np.array(ps)

    def __str__(self):
        return "Pivots(" + str(self.ps) + ")"

    def __repr__(self):
        return "Pivots(" + repr(self.ps) + ")"

    def __add__(self, other):
        return Pivots(np.arctan2(np.sin(self.ps + other.ps), np.cos(self.ps + other.ps)))

    def __sub__(self, other):
        return Pivots(np.arctan2(np.sin(self.ps - other.ps), np.cos(self.ps - other.ps)))

    def __mul__(self, other):
        return Pivots(self.ps * other.ps)

    def __div__(self, other):
        return Pivots(self.ps / other.ps)

    def __mod__(self, other):
        return Pivots(self.ps % other.ps)

    def __pow__(self, other):
        return Pivots(self.ps**other.ps)

    def __lt__(self, other):
        return self.ps < other.ps

    def __le__(self, other):
        return self.ps <= other.ps

    def __eq__(self, other):
        return self.ps == other.ps

    def __ne__(self, other):
        return self.ps != other.ps

    def __ge__(self, other):
        return self.ps >= other.ps

    def __gt__(self, other):
        return self.ps > other.ps

    def __abs__(self):
        return Pivots(abs(self.ps))

    def __neg__(self):
        return Pivots(-self.ps)

    def __iter__(self):
        return iter(self.ps)

    def __len__(self):
        return len(self.ps)

    def __getitem__(self, k):
        return Pivots(self.ps[k])

    def __setitem__(self, k, v):
        self.ps[k] = v.ps

    def _ellipsis(self):
        return tuple(map(lambda x: slice(None), self.shape))

    def quaternions(self, plane="xz"):
        fa = self._ellipsis()
        axises = np.ones(self.ps.shape + (3,))
        axises[fa + ("xyz".index(plane[0]),)] = 0.0
        axises[fa + ("xyz".index(plane[1]),)] = 0.0
        return Quaternions.from_angle_axis(self.ps, axises)

    def directions(self, plane="xz"):
        dirs = np.zeros((len(self.ps), 3))
        dirs["xyz".index(plane[0])] = np.sin(self.ps)
        dirs["xyz".index(plane[1])] = np.cos(self.ps)
        return dirs

    def normalized(self):
        xs = np.copy(self.ps)
        while np.any(xs > np.pi):
            xs[xs > np.pi] = xs[xs > np.pi] - 2 * np.pi
        while np.any(xs < -np.pi):
            xs[xs < -np.pi] = xs[xs < -np.pi] + 2 * np.pi
        return Pivots(xs)

    def interpolate(self, ws):
        dir = np.average(self.directions, weights=ws, axis=0)
        return np.arctan2(dir[2], dir[0])

    def copy(self):
        return Pivots(np.copy(self.ps))

    @property
    def shape(self):
        return self.ps.shape

    @classmethod
    def from_quaternions(cls, qs, forward="z", plane="xz"):
        ds = np.zeros(qs.shape + (3,))
        ds[..., "xyz".index(forward)] = 1.0
        return Pivots.from_directions(qs * ds, plane=plane)

    @classmethod
    def from_directions(cls, ds, plane="xz"):
        ys = ds[..., "xyz".index(plane[0])]
        xs = ds[..., "xyz".index(plane[1])]
        return Pivots(np.arctan2(ys, xs))