def _xy(s):
if th == 0:
return Coord2(0.0, 0.0)
elif s <= Ltot / 2:
(fsin, fcos) = fresnel(s / (sq2pi * a))
X = sq2pi * a * fcos
Y = sq2pi * a * fsin
else:
(fsin, fcos) = fresnel((Ltot - s) / (sq2pi * a))
X = (
sq2pi
* a
* (
facos
+ np.cos(2 * th) * (facos - fcos)
+ np.sin(2 * th) * (fasin - fsin)
)
)
Y = (
sq2pi
* a
* (
fasin
- np.cos(2 * th) * (fasin - fsin)
+ np.sin(2 * th) * (facos - fcos)
)
)
return Coord2(X, Y)
def euler_end_pt(
start_point=(0.0, 0.0), radius=10.0, input_angle=0.0,
angle_amount=90.0):
"""Gives the end point of a simple Euler bend as a Coord2"""
th = abs(angle_amount) * DEG2RAD / 2.0
R = radius
clockwise = bool(angle_amount < 0)
(fsin, fcos) = fresnel(sqrt(2 * th / pi))
a = 2 * sqrt(2 * pi * th) * (np.cos(th) * fcos + np.sin(th) * fsin)
r = a * R
X = r * np.cos(th)
Y = r * np.sin(th)
if clockwise:
Y *= -1
pt = Coord2(X, Y) + start_point
pt.rotate(rotation_center=start_point, rotation=input_angle)
return pt
def euler_bend_points(
angle_amount: float = 90.0,
radius: float = 10.0,
resolution: float = 150.0,
use_cache: bool = True,
) -> List[Coord2]:
""" Base euler bend, no transformation, emerging from the origin."""
# Check if we've calculated this already
key = (angle_amount, radius, resolution)
if key in __euler_bend_cache__ and use_cache:
return __euler_bend_cache__[key]
if angle_amount < 0:
raise ValueError(
"angle_amount should be positive. Got {}".format(angle_amount))
# End angle
eth = angle_amount * DEG2RAD
# If bend is trivial, return a trivial shape
if eth == 0.0:
return [Coord2(0, 0)]
# Curve min radius
R = radius
# Total displaced angle
th = eth / 2.0
# Total length of curve
Ltot = 4 * R * th
# Compute curve ##
a = sqrt(R**2.0 * np.abs(th))
sq2pi = sqrt(2.0 * pi)
# Function for computing curve coords
(fasin, facos) = fresnel(sqrt(2.0 / pi) * R * th / a)
def _xy(s):
if th == 0:
return Coord2(0.0, 0.0)
elif s <= Ltot / 2:
(fsin, fcos) = fresnel(s / (sq2pi * a))
X = sq2pi * a * fcos
Y = sq2pi * a * fsin
else:
(fsin, fcos) = fresnel((Ltot - s) / (sq2pi * a))
X = (sq2pi * a *
(facos + np.cos(2 * th) * (facos - fcos) + np.sin(2 * th) *
(fasin - fsin)))
Y = (sq2pi * a *
(fasin - np.cos(2 * th) * (fasin - fsin) + np.sin(2 * th) *
(facos - fcos)))
return Coord2(X, Y)
# Parametric step size
step = Ltot / int(th * resolution)
# Generate points
points = []
for i in range(0, int(round(Ltot / step)) + 1):
points += [_xy(i * step)]
# Cache calculated points
if use_cache:
__euler_bend_cache__[(angle_amount, radius, resolution)] = points
return points