import numpy as np


def _round_safe(coords):
    """Round coords while ensuring successive values are less than 1 apart.

    When rounding coordinates for `line_nd`, we want coordinates that are less
    than 1 apart (always the case, by design) to remain less than one apart.
    However, NumPy rounds values to the nearest *even* integer, so:

    >>> np.round([0.5, 1.5, 2.5, 3.5, 4.5])
    array([ 0.,  2.,  2.,  4.,  4.])

    So, for our application, we detect whether the above case occurs, and use
    ``np.floor`` if so. It is sufficient to detect that the first coordinate
    falls on 0.5 and that the second coordinate is 1.0 apart, since we assume
    by construction that the inter-point distance is less than or equal to 1
    and that all successive points are equidistant.

    Parameters
    ----------
    coords : 1D array of float
        The coordinates array. We assume that all successive values are
        equidistant (``np.all(np.diff(coords) = coords[1] - coords[0])``)
        and that this distance is no more than 1
        (``np.abs(coords[1] - coords[0]) <= 1``).

    Returns
    -------
    rounded : 1D array of int
        The array correctly rounded for an indexing operation, such that no
        successive indices will be more than 1 apart.

    Examples
    --------
    >>> coords0 = np.array([0.5, 1.25, 2., 2.75, 3.5])
    >>> _round_safe(coords0)
    array([0, 1, 2, 3, 4])
    >>> coords1 = np.arange(0.5, 8, 1)
    >>> coords1
    array([ 0.5,  1.5,  2.5,  3.5,  4.5,  5.5,  6.5,  7.5])
    >>> _round_safe(coords1)
    array([0, 1, 2, 3, 4, 5, 6, 7])
    """
    if (len(coords) > 1
            and coords[0] % 1 == 0.5
            and coords[1] - coords[0] == 1):
        _round_function = np.floor
    else:
        _round_function = np.round
    return _round_function(coords).astype(int)


def line_nd(start, stop, *, endpoint=False, integer=True):
    """Draw a single-pixel thick line in n dimensions.

    The line produced will be ndim-connected. That is, two subsequent
    pixels in the line will be either direct or diagonal neighbours in
    n dimensions.

    Parameters
    ----------
    start : array-like, shape (N,)
        The start coordinates of the line.
    stop : array-like, shape (N,)
        The end coordinates of the line.
    endpoint : bool, optional
        Whether to include the endpoint in the returned line. Defaults
        to False, which allows for easy drawing of multi-point paths.
    integer : bool, optional
        Whether to round the coordinates to integer. If True (default),
        the returned coordinates can be used to directly index into an
        array. `False` could be used for e.g. vector drawing.

    Returns
    -------
    coords : tuple of arrays
        The coordinates of points on the line.

    Examples
    --------
    >>> lin = line_nd((1, 1), (5, 2.5), endpoint=False)
    >>> lin
    (array([1, 2, 3, 4]), array([1, 1, 2, 2]))
    >>> im = np.zeros((6, 5), dtype=int)
    >>> im[lin] = 1
    >>> im
    array([[0, 0, 0, 0, 0],
           [0, 1, 0, 0, 0],
           [0, 1, 0, 0, 0],
           [0, 0, 1, 0, 0],
           [0, 0, 1, 0, 0],
           [0, 0, 0, 0, 0]])
    >>> line_nd([2, 1, 1], [5, 5, 2.5], endpoint=True)
    (array([2, 3, 4, 4, 5]), array([1, 2, 3, 4, 5]), array([1, 1, 2, 2, 2]))
    """
    start = np.asarray(start)
    stop = np.asarray(stop)
    npoints = int(np.ceil(np.max(np.abs(stop - start))))
    if endpoint:
        npoints += 1
    coords = []
    for dim in range(len(start)):
        dimcoords = np.linspace(start[dim], stop[dim], npoints, endpoint)
        if integer:
            dimcoords = _round_safe(dimcoords).astype(int)
        coords.append(dimcoords)
    return tuple(coords)
