import numpy as np
from glue.utils import unbroadcast
__all__ = ['points_inside_poly', 'polygon_line_intersections', 'floodfill', 'rotation_matrix_2d']
[docs]def rotation_matrix_2d(alpha):
"""
Return rotation matrix for angle alpha around origin.
Parameters
----------
alpha : float
Rotation angle in radian, increasing for anticlockwise rotation.
"""
if np.asarray(alpha).ndim > 0:
# In principle this works on an array as well; would have to return matrix.T then
raise ValueError("Only scalar input for angle accepted")
return np.array([[np.cos(alpha), -np.sin(alpha)], [np.sin(alpha), np.cos(alpha)]])
[docs]def points_inside_poly(x, y, vx, vy):
"""
Test if coordinates ``x``, ``y`` fall inside polygon of vertices ``vx``, ``vy``.
Parameters
----------
x, y : `~numpy.ndarray`
Coordinates of the points to test
vx, vy : `~numpy.ndarray`
The vertices of the polygon
Returns
-------
contains : `~numpy.ndarray` of bool
Array indicating whether each coordinate pair is inside the polygon.
"""
if x.dtype.kind == 'M' and vx.dtype.kind == 'M':
vx = vx.astype(x.dtype).astype(float)
x = x.astype(float)
if y.dtype.kind == 'M' and vy.dtype.kind == 'M':
vy = vy.astype(y.dtype).astype(float)
y = y.astype(float)
original_shape = x.shape
x = unbroadcast(x)
y = unbroadcast(y)
x = x.astype(float)
y = y.astype(float)
x, y = np.broadcast_arrays(x, y)
reduced_shape = x.shape
x = x.flat
y = y.flat
from matplotlib.path import Path
p = Path(np.column_stack((vx, vy)))
keep = ((x >= np.min(vx)) &
(x <= np.max(vx)) &
(y >= np.min(vy)) &
(y <= np.max(vy)))
inside = np.zeros(len(x), bool)
x = x[keep]
y = y[keep]
coords = np.column_stack((x, y))
inside[keep] = p.contains_points(coords).astype(bool)
good = np.isfinite(x) & np.isfinite(y)
inside[keep][~good] = False
inside = inside.reshape(reduced_shape)
inside = np.broadcast_to(inside, original_shape)
return inside
[docs]def polygon_line_intersections(px, py, xval=None, yval=None):
"""
Find all the segments of intersection between a polygon and an infinite
horizontal/vertical line.
The polygon is assumed to be closed. Due to numerical precision, the
behavior at the edges of polygons is not always predictable, i.e. a point
on the edge of a polygon may be considered inside or outside the polygon.
Parameters
----------
px, py : `~numpy.ndarray`
The vertices of the polygon
xval : float, optional
The x coordinate of the line (for vertical lines). This should only be
specified if yval is not specified.
yval : float, optional
The y coordinate of the line (for horizontal lines). This should only be
specified if xval is not specified.
Returns
-------
segments : list
A list of segments given as tuples of coordinates along the line.
"""
if xval is not None and yval is not None:
raise ValueError("Only one of xval or yval should be specified")
elif xval is None and yval is None:
raise ValueError("xval or yval should be specified")
if yval is not None:
return polygon_line_intersections(py, px, xval=yval)
px = np.asarray(px, dtype=float)
py = np.asarray(py, dtype=float)
# Make sure that the polygon is closed
if px[0] != px[-1] or py[0] != py[-1]:
px = np.hstack([px, px[0]])
py = np.hstack([py, py[0]])
# For convenience
x1, x2 = px[:-1], px[1:]
y1, y2 = py[:-1], py[1:]
# Vertices that intersect
keep1 = (px == xval)
points1 = py[keep1]
# Segments (excluding vertices) that intersect
keep2 = ((x1 < xval) & (x2 > xval)) | ((x2 < xval) & (x1 > xval))
points2 = (y1 + (y2 - y1) * (xval - x1) / (x2 - x1))[keep2]
# Make unique and sort
points = np.array(np.sort(np.unique(np.hstack([points1, points2]))))
# Because of various corner cases, we don't actually know which pairs of
# points are inside the polygon, so we check this using the mid-points
ymid = 0.5 * (points[:-1] + points[1:])
xmid = np.repeat(xval, len(ymid))
keep = points_inside_poly(xmid, ymid, px, py)
segments = list(zip(points[:-1][keep], points[1:][keep]))
return segments
[docs]def floodfill(data, start_coords, threshold):
from scipy.ndimage import label
# Determine value at the starting coordinates
value = data[start_coords]
# Determine all pixels that match
mask = (data > value * (2 - threshold)) & (data < value * threshold)
# Determine all individual chunks
labels, num_features = label(mask)
mask = labels == labels[start_coords]
return mask
