def path_bezier(control_points, weight=1, interpolation_count=50):
"""
Rational Bezier curve.
"""
## cycle weights...
if isinstance(weight, (list, tuple)):
w_len = len(weight)
p_len = len(control_points)
weight = weight * (p_len // w_len) + weight[: p_len % w_len]
plot_points = bezier_interpolation(control_points, interpolation_count, weight)
return Path(plot_points)
def path_bezier(control_points, weight=1, interpolation_count=50):
"""
Rational Bezier curve.
"""
## cycle weights...
if isinstance(weight, (list, tuple)):
w_len = len(weight)
p_len = len(control_points)
weight = weight * (p_len // w_len) + weight[: p_len % w_len]
plot_points = bezier_interpolation(control_points,
interpolation_count,
weight)
return Path(plot_points)
def path_interpolated(points, curvature, interpolation_count=50):
"""Returns a Path with bezier interpolation between the given `points`.
The interpolation is computed so that the resulting path touches the
given points.
- `points` the key points from which to interpolate.
- `curvature` the smoothness of the curve [0, 1].
- `interpolation_count` is the number of points to add by interpolation,
per segment.
"""
if not (0 <= curvature <= 1):
raise ValueError("`curvature` must be between 0 and 1 inclusive.")
if curvature == 0:
return Path(points)
## else we have a curve...
points = CoordinateArray(points)
curvature = 4 + (1.0 - curvature) * 40
bi = [0, -0.25]
a = [Coordinate(0, 0), (points[2] - points[0] - Coordinate(0, 0)) / 4.0]
## compute bi and a...
for i in range(2, len(points) - 1):
bi.append(-1 / (curvature + bi[i - 1]))
a.append(-(points[i + 1] - points[i - 1] - a[i - 1]) * bi[i])
## compute dxy...
dxy = [Coordinate(0, 0)]
for i in reversed(list(range(len(points) - 1))):
dxy.insert(0, a[i] + dxy[0] * bi[i])
## compute interpolated points...
plot_points = []
for i in range(len(points) - 1):
control_points = [
points[i],
points[i] + dxy[i],
points[i + 1] - dxy[i + 1],
points[i + 1],
]
plot_points += bezier_interpolation(control_points,
interpolation_count, 1)[:-1]
return Path(plot_points)
def path_interpolated(points, curvature, interpolation_count = 50):
'''Returns a Path with bezier interpolation between the given `points`.
The interpolation is computed so that the resulting path touches the
given points.
- `points` the key points from which to interpolate.
- `curvature` the smoothness of the curve [0, 1].
- `interpolation_count` is the number of points to add by interpolation,
per segment.
'''
if not (0 <= curvature <= 1):
raise ValueError('`curvature` must be between 0 and 1 inclusive.')
if curvature == 0:
return Path(points)
## else we have a curve...
points = CoordinateArray(points)
curvature = 4 + (1.0 - curvature) * 40
bi = [0, -0.25]
a = [Coordinate(0, 0), (points[2] - points[0] - Coordinate(0, 0)) / 4.0]
## compute bi and a...
for i in range(2, len(points)-1):
bi.append(-1 / (curvature + bi[i - 1]))
a.append(-(points[i+1] - points[i-1] - a[i-1]) * bi[i])
## compute dxy...
dxy = [Coordinate(0, 0)]
for i in reversed(range(len(points) - 1)):
dxy.insert(0, a[i] + dxy[0] * bi[i])
## compute interpolated points...
plot_points = [ ]
for i in range(len(points) - 1):
control_points = [
points[i],
points[i] + dxy[i],
points[i+1] - dxy[i+1],
points[i+1]]
plot_points += bezier_interpolation(control_points,
interpolation_count, 1)[:-1]
return Path(plot_points)