Incorrect tangent ending of spline

[josyb]

I am trying to create a train switch - using the following code for a single rail (simplified to a round bar).

def splinetrack(x, y):
    pts = [(0, 0), (x / 2, y / 2), (x, y)]
    tgts = [(x, 0), None, (2 * x, y)] # 1
    # tgts = [(x, 0), (x / 2, y / 2 + x * 10), (2 * x, y)] # 2
    # tgts = [(x, 0), None, (2 * x, 0)] # 3
    path = cq.Workplane("XY").spline(pts, tgts)
    return cq.Workplane("YZ").circle(3.0).sweep(path)

generates this:

If I (try to) force a 90 degrees tangent in the middle you see the effect even better:

Experimenting I stumbled on the third 'tgts' definition which produces the correct 90 degrees angle.
Can someone explain?

Oops! I found it myself: the tangent vectors in the spline function are specified as starting from (0,0) - It would be good if the CadQuery 2 Documentation mentioned that :)

[josyb]

I have another question though: how can I find the actual angle of the tangent in the middle of the generated spline; I am sure it will be calculated somewhere in the code?

[lorenzncode]

I have another question though: how can I find the actual angle of the tangent in the middle of the generated spline; I am sure it will be calculated somewhere in the code?

import cadquery as cq
from math import degrees

x = 170
y = 50

pts = [(0, 0), (x / 2, y / 2), (x, y)]

tgts = [(1, 0), (1, 1)]  # ~15 deg at midpoint
# tgts = [(1, 0), None, (1, 1)]  # ~15 deg same as above
# tgts = [(1, 0), (1, 0)]  # ~27 deg
# tgts = [(1, 0), (1, 1), (1, 0)]  # 45 deg
# tgts = [(1, 0), (0, 1), (1, 0)]  # 90 deg

path = cq.Workplane("XY").spline(pts, tgts)

# tangetAt(0.5) is default
tangent_mid = path.val().tangentAt()
anglex = degrees(tangent_mid.getAngle(cq.Vector(1, 0, 0)))
print(tangent_mid)
print(anglex)

res = cq.Workplane("YZ").circle(3.0).sweep(path)

Here is a free function example, for a simpler spline specifying tangents at endpoints only:

from cadquery.func import *
from math import degrees

# free function spline 
# tgts should be of length 2 for endpoints only

x = 170
y = 50

pts = [(0, 0), (x / 2, y / 2), (x, y)]

tgts = [(1, 0), (1, 1)] # ~15 deg 
# tgts = [(1, 0), (1, 0)] # ~27

path = spline(pts, tgts)

tangent_mid = path.tangentAt()
anglex = degrees(tangent_mid.getAngle(Vector(1, 0, 0)))
print(tangent_mid)
print(anglex)

res = sweep(circle(3.0).move(ry=90), path, cap=True)

[josyb]

Thanks for that quick answer!

The calculated angle of 27.35 degrees corroborates with the ruler/pencil/set square result of 26.5 degrees.

A (rhetorical?) side question: could I have found the answer in the documentation? Please don't take offence, I know that documentation is difficult (I maintain the MyHDL repo ...)

While experimenting I found a little inconvenience:
print(f'{tangent_mid=:9.3f}, {anglex=:9.3f}')
throws a TypeError: unsupported format string passed to Vector.format

Thanks again for the answer.
Best regards,
Josy