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[utils.curves.euler_bend] add num_point arg and improve naming

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Jan Petykiewicz 2025-03-03 00:53:34 -08:00
parent b27b1d93d8
commit 858ef4a114
1 changed files with 22 additions and 17 deletions
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39
masque/utils/curves.py
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@ -44,7 +44,10 @@ def bezier(
def euler_bend(switchover_angle: float) -> NDArray[numpy.float64]:
def euler_bend(
switchover_angle: float,
num_points: int = 200,
) -> NDArray[numpy.float64]:
"""
Generate a 90 degree Euler bend (AKA Clothoid bend or Cornu spiral).
@ -52,42 +55,44 @@ def euler_bend(switchover_angle: float) -> NDArray[numpy.float64]:
switchover_angle: After this angle, the bend will transition into a circular arc
(and transition back to an Euler spiral on the far side). If this is set to
`>= pi / 4`, no circular arc will be added.
num_points: Number of points in the curve
Returns:
`[[x0, y0], ...]` for the curve
"""
# Switchover angle
# AKA: Clothoid bend, Cornu spiral
theta_max = numpy.sqrt(2 * switchover_angle)
ll_max = numpy.sqrt(2 * switchover_angle) # total length of (one) spiral portion
ll_tot = 2 * ll_max + (pi / 2 - 2 * switchover_angle)
num_points_spiral = numpy.floor(ll_max / ll_tot * num_points).astype(int)
num_points_arc = num_points - 2 * num_points_spiral
def gen_curve(theta_max: float):
def gen_spiral(ll_max: float):
xx = []
yy = []
for theta in numpy.linspace(0, theta_max, 100):
qq = numpy.linspace(0, theta, 1000)
for ll in numpy.linspace(0, ll_max, num_points_spiral):
qq = numpy.linspace(0, ll, 1000) # integrate to current arclength
xx.append(numpy.trapz( numpy.cos(qq * qq / 2), qq))
yy.append(numpy.trapz(-numpy.sin(qq * qq / 2), qq))
xy_part = numpy.stack((xx, yy), axis=1)
return xy_part
xy_part = gen_curve(theta_max)
xy_parts = [xy_part]
xy_spiral = gen_spiral(ll_max)
xy_parts = [xy_spiral]
if switchover_angle < pi / 4:
# Build a circular segment to join the two euler portions
rmin = 1.0 / theta_max
rmin = 1.0 / ll_max
half_angle = pi / 4 - switchover_angle
qq = numpy.linspace(half_angle * 2, 0, 10) + switchover_angle
qq = numpy.linspace(half_angle * 2, 0, num_points_arc + 1) + switchover_angle
xc = rmin * numpy.cos(qq)
yc = rmin * numpy.sin(qq) + xy_part[-1, 1]
xc += xy_part[-1, 0] - xc[0]
yc += xy_part[-1, 1] - yc[0]
xy_parts.append(numpy.stack((xc, yc), axis=1))
yc = rmin * numpy.sin(qq) + xy_spiral[-1, 1]
xc += xy_spiral[-1, 0] - xc[0]
yc += xy_spiral[-1, 1] - yc[0]
xy_parts.append(numpy.stack((xc[1:], yc[1:]), axis=1))
endpoint_xy = xy_parts[-1][-1, :]
second_curve = xy_part[::-1, ::-1] + endpoint_xy - xy_part[-1, ::-1]
second_spiral = xy_spiral[::-1, ::-1] + endpoint_xy - xy_spiral[-1, ::-1]
xy_parts.append(second_curve)
xy_parts.append(second_spiral)
xy = numpy.concatenate(xy_parts)
# Remove any 2x-duplicate points