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import numpy as np
from scipy.interpolate import splprep, splev
from .geometry import Point, coordinate_list_to_point_list
from ..stitches.running_stitch import running_stitch
def _remove_duplicate_coordinates(coords_array):
"""Remove consecutive duplicate points from an array.
Arguments:
coords_array -- numpy.array
Returns:
a numpy.array of coordinates, minus consecutive duplicates
"""
differences = np.diff(coords_array, axis=0)
zero_differences = np.isclose(differences, 0)
keepers = np.r_[True, np.any(zero_differences == False, axis=1)] # noqa: E712
return coords_array[keepers]
def smooth_path(path, smoothness=1.0):
"""Smooth a path of coordinates.
Arguments:
path -- an iterable of coordinate tuples or Points
smoothness -- float, how much smoothing to apply. Bigger numbers
smooth more.
Returns:
A list of Points.
"""
from ..debug import debug
if smoothness == 0:
# s of exactly zero seems to indicate a default level of smoothing
# in splprep, so we'll just exit instead.
return path
# Smoothing seems to look nicer if the line segments in the path are mostly
# similar in length. If we have some especially long segments, then the
# smoothed path sometimes diverges more from the original path as the
# spline curve struggles to fit the path. This can be especially bad at
# the start and end.
#
# Fortunately, we can convert the path to segments that are mostly the same
# length by using the running stitch algorithm.
path = running_stitch(coordinate_list_to_point_list(path), 5 * smoothness, smoothness / 2)
# splprep blows up on duplicated consecutive points with "Invalid inputs"
coords = _remove_duplicate_coordinates(np.array(path))
num_points = len(coords)
if num_points <= 3:
# splprep throws an error unless num_points > k
return path
# s is explained in this issue: https://github.com/scipy/scipy/issues/11916
# the smoothness parameter limits how much the smoothed path can deviate
# from the original path. The standard deviation of the distance between
# the smoothed path and the original path is equal to the smoothness.
# In practical terms, if smoothness is 1mm, then the smoothed path can be
# up to 1mm away from the original path.
s = num_points * (smoothness ** 2)
# .T transposes the array (for some reason splprep expects
# [[x1, x2, ...], [y1, y2, ...]]
tck, fp, ier, msg = splprep(coords.T, s=s, k=3, nest=-1, full_output=1)
if ier > 0:
debug.log(f"error {ier} smoothing path: {msg}")
return path
# Evaluate the spline curve at many points along its length to produce the
# smoothed point list. 2 * num_points seems to be a good number, but it
# does produce a lot of points.
smoothed_x_values, smoothed_y_values = splev(np.linspace(0, 1, int(num_points * 2)), tck[0])
coords = np.array([smoothed_x_values, smoothed_y_values]).T
return [Point(x, y) for x, y in coords]
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