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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). 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 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 (and transition back to an Euler spiral on the far side). If this is set to
`>= pi / 4`, no circular arc will be added. `>= pi / 4`, no circular arc will be added.
num_points: Number of points in the curve
Returns: Returns:
`[[x0, y0], ...]` for the curve `[[x0, y0], ...]` for the curve
""" """
# Switchover angle ll_max = numpy.sqrt(2 * switchover_angle) # total length of (one) spiral portion
# AKA: Clothoid bend, Cornu spiral ll_tot = 2 * ll_max + (pi / 2 - 2 * switchover_angle)
theta_max = numpy.sqrt(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 = [] xx = []
yy = [] yy = []
for theta in numpy.linspace(0, theta_max, 100): for ll in numpy.linspace(0, ll_max, num_points_spiral):
qq = numpy.linspace(0, theta, 1000) qq = numpy.linspace(0, ll, 1000) # integrate to current arclength
xx.append(numpy.trapz( numpy.cos(qq * qq / 2), qq)) xx.append(numpy.trapz( numpy.cos(qq * qq / 2), qq))
yy.append(numpy.trapz(-numpy.sin(qq * qq / 2), qq)) yy.append(numpy.trapz(-numpy.sin(qq * qq / 2), qq))
xy_part = numpy.stack((xx, yy), axis=1) xy_part = numpy.stack((xx, yy), axis=1)
return xy_part return xy_part
xy_part = gen_curve(theta_max) xy_spiral = gen_spiral(ll_max)
xy_parts = [xy_part] xy_parts = [xy_spiral]
if switchover_angle < pi / 4: if switchover_angle < pi / 4:
# Build a circular segment to join the two euler portions # 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 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) xc = rmin * numpy.cos(qq)
yc = rmin * numpy.sin(qq) + xy_part[-1, 1] yc = rmin * numpy.sin(qq) + xy_spiral[-1, 1]
xc += xy_part[-1, 0] - xc[0] xc += xy_spiral[-1, 0] - xc[0]
yc += xy_part[-1, 1] - yc[0] yc += xy_spiral[-1, 1] - yc[0]
xy_parts.append(numpy.stack((xc, yc), axis=1)) xy_parts.append(numpy.stack((xc[1:], yc[1:]), axis=1))
endpoint_xy = xy_parts[-1][-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) xy = numpy.concatenate(xy_parts)
# Remove any 2x-duplicate points # Remove any 2x-duplicate points