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draw_nd.py
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draw_nd.py
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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 neighbors 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 = np.linspace(start, stop, num=npoints, endpoint=endpoint).T
if integer:
for dim in range(len(start)):
coords[dim, :] = _round_safe(coords[dim, :])
coords = coords.astype(int)
return tuple(coords)