def smooth(points=[
(20, 0),
(40, 0),
(80, 40),
(80, 10),
(100, 10),
],
radius=4,
corner_fun=euler,
**kwargs):
""" Create a smooth path from a series of waypoints. Corners will be rounded
using `corner_fun` and any additional key word arguments (for example,
`use_eff = True` when `corner_fun = pp.euler`)
Parameters
----------
points : array-like[N][2]
List of waypoints for the path to follow
radius : int or float
Radius of curvature, this argument will be passed to `corner_fun`
corner_fun : function
The function that controls how the corners are rounded. Typically either
`arc()` or `euler()`
**kwargs : dict
Extra keyword arguments that will be passed to `corner_fun`
Returns
-------
Path
A Path object with the specified smoothed path.
"""
points = np.asfarray(points)
normals = np.diff(points, axis=0)
normals = (normals.T / np.linalg.norm(normals, axis=1)).T
# normals_rev = normals*np.array([1,-1])
dx = np.diff(points[:, 0])
dy = np.diff(points[:, 1])
ds = np.sqrt(dx**2 + dy**2)
theta = np.degrees(np.arctan2(dy, dx))
dtheta = np.diff(theta)
# FIXME add caching
# Create arcs
paths = []
radii = []
for dt in dtheta:
P = corner_fun(radius=radius, angle=dt, **kwargs)
chord = np.linalg.norm(P.points[-1, :] - P.points[0, :])
r = (chord / 2) / np.sin(np.radians(dt / 2))
r = np.abs(r)
radii.append(r)
paths.append(P)
d = np.abs(np.array(radii) / np.tan(np.radians(180 - dtheta) / 2))
encroachment = np.concatenate([[0], d]) + np.concatenate([d, [0]])
if np.any(encroachment > ds):
raise ValueError(
'[PHIDL] smooth(): Not enough distance between points to to fit curves. Try reducing the radius or spacing the points out farther'
)
p1 = points[1:-1, :] - normals[:-1, :] * d[:, np.newaxis]
# Move arcs into position
new_points = []
new_points.append([points[0, :]])
for n, dt in enumerate(dtheta):
P = paths[n]
P.rotate(theta[n] - 0)
P.move(p1[n])
new_points.append(P.points)
new_points.append([points[-1, :]])
new_points = np.concatenate(new_points)
P = Path(new_points)
P.move(points[0, :])
return P
def smooth(points=[
(20, 0),
(40, 0),
(80, 40),
(80, 10),
(100, 10),
],
radius=4,
corner_fun=euler,
**kwargs):
""" Create a smooth path from a series of waypoints. Corners will be rounded
using `corner_fun` and any additional key word arguments (for example,
`use_eff = True` when `corner_fun = pp.euler`)
Parameters
----------
points : array-like[N][2]
List of waypoints for the path to follow
radius : int or float
Radius of curvature, this argument will be passed to `corner_fun`
corner_fun : function
The function that controls how the corners are rounded. Typically either
`arc()` or `euler()`
**kwargs : dict
Extra keyword arguments that will be passed to `corner_fun`
Returns
-------
Path
A Path object with the specified smoothed path.
"""
points, normals, ds, theta, dtheta = _compute_segments(points)
colinear_elements = np.concatenate([[False],
np.abs(dtheta) < 1e-6, [False]])
if np.any(colinear_elements):
new_points = points[~colinear_elements, :]
points, normals, ds, theta, dtheta = _compute_segments(new_points)
if np.any(np.abs(np.abs(dtheta) - 180) < 1e-6):
raise ValueError(
'[PHIDL] smooth() received points which double-back on themselves'
+
'--turns cannot be computed when going forwards then exactly backwards.'
)
# FIXME add caching
# Create arcs
paths = []
radii = []
for dt in dtheta:
P = corner_fun(radius=radius, angle=dt, **kwargs)
chord = np.linalg.norm(P.points[-1, :] - P.points[0, :])
r = (chord / 2) / np.sin(np.radians(dt / 2))
r = np.abs(r)
radii.append(r)
paths.append(P)
d = np.abs(np.array(radii) / np.tan(np.radians(180 - dtheta) / 2))
encroachment = np.concatenate([[0], d]) + np.concatenate([d, [0]])
if np.any(encroachment > ds):
raise ValueError(
'[PHIDL] smooth(): Not enough distance between points to to fit curves. Try reducing the radius or spacing the points out farther'
)
p1 = points[1:-1, :] - normals[:-1, :] * d[:, np.newaxis]
# Move arcs into position
new_points = []
new_points.append([points[0, :]])
for n, dt in enumerate(dtheta):
P = paths[n]
P.rotate(theta[n] - 0)
P.move(p1[n])
new_points.append(P.points)
new_points.append([points[-1, :]])
new_points = np.concatenate(new_points)
P = Path()
P.rotate(theta[0])
P.append(new_points)
P.move(points[0, :])
return P