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Start

Graph der Krümmung

Klothoide + Kreis
Straßenführung

x(s)=\int_0^s{\cos\left(c\frac{x^2}{2}\right) dx

y(s)=...\sin...

c=\frac{1}{a^2}

mehr

Ende

Haftendorn, Buch:
Kurven erkunden und verstehen
Kap 09:S. 299 

Ha 2016

a = 4.242640687119285
c: 1 / a^(2)
sp = 5 (slider from -20 to 20, step 1)
xs = Integral(cos((c * x^(2) / 2)), 0, sp)
ys = Integral(sin((c * x^(2) / 2)), 0, sp)
P_s: (xs, ys)
f = Circle(P_s, 1 / ((sp * c)))
d: y = (tan((c * sp^(2) / 2)) * (x - xs)) + ys
e = OrthogonalLine(P_s, d)
A, M = Intersect(f, e)
g = Circle(M, P_s)
C = Point(g)
h = Line(M, C)
P'_s = Mirror(P_s, h)
k = Arc(g, P_s, P'_s)
P_k: (sp, (c * sp))
P'_k: (x(P_k) + k, (c * sp))
i = CurveCartesian(xs, ys, s, 0, 20)
K = (6.087004858490452E-11, 2.1660955387922626E-7)
K' = Mirror(K, h)
t_1 = CircleArc(M, P_s, P'_s)
d' = Mirror(d, h)
b_1 = Segment(M, P_s)
B = Intersect(xAxis, yAxis)
End: (x(P'_k) + 5, 0)
Vieleck1, b_2, p_k, p'_k, end = Polygon(B, P_k, P'_k, End)
Start = (0, 0)
o = CurveCartesian(xs, ys, s, 0, 2)
t = 2.3 (slider from 0 to 5, step 0.1)
xt = Integral(cos((c * x^(2) / 2)), 0, t)
x_t = Integral(sin((c * x^(2) / 2)), 0, t)
P_t: (xt, x_t)
Klothoide = Locus(P_t, t)
u = CurveCartesian(Integral[cos((c * x^(2) / 2)), 0, t], Integral[sin((c * x^(2) / 2)), 0, t], t, 0, sp)
A1: 0
A2: A1 + 0.5
A3: A2 + 0.500000000000002
A4: A3 + 0.500000000000002
A5: A4 + 0.500000000000002
A6: A5 + 0.500000000000002
A7: A6 + 0.500000000000002
A8: A7 + 0.500000000000002
A9: A8 + 0.500000000000002
A10: A9 + 0.500000000000002
A11: A10 + 0.500000000000004
B2 = Integral(cos((c * x^(2) / 2)), 0, A2)
B1 = Integral(cos((c * x^(2) / 2)), 0, A1)
B4 = Integral(cos((c * x^(2) / 2)), 0, A4)
B5 = Integral(cos((c * x^(2) / 2)), 0, A5)
B6 = Integral(cos((c * x^(2) / 2)), 0, A6)
B7 = Integral(cos((c * x^(2) / 2)), 0, A7)
B8 = Integral(cos((c * x^(2) / 2)), 0, A8)
B9 = Integral(cos((c * x^(2) / 2)), 0, A9)
B10 = Integral(cos((c * x^(2) / 2)), 0, A10)
B11 = Integral(cos((c * x^(2) / 2)), 0, A11)
B3 = Integral(cos((c * x^(2) / 2)), 0, A3)
C1 = Integral(sin((c * x^(2) / 2)), 0, A1)
C2 = Integral(sin((c * x^(2) / 2)), 0, A2)
C3 = Integral(sin((c * x^(2) / 2)), 0, A3)
C4 = Integral(sin((c * x^(2) / 2)), 0, A4)
C5 = Integral(sin((c * x^(2) / 2)), 0, A5)
C6 = Integral(sin((c * x^(2) / 2)), 0, A6)
C7 = Integral(sin((c * x^(2) / 2)), 0, A7)
C8 = Integral(sin((c * x^(2) / 2)), 0, A8)
C9 = Integral(sin((c * x^(2) / 2)), 0, A9)
C10 = Integral(sin((c * x^(2) / 2)), 0, A10)
C11 = Integral(sin((c * x^(2) / 2)), 0, A11)
D: (B1, C1)
E: (B2, C2)
F: (B3, C3)
G: (B4, C4)
H: (B5, C5)
I: (B6, C6)
J: (B7, C7)
L: (B8, C8)
N: (B9, C9)
O: (B10, C10)
Q: (B11, C11)
Liste1: {D, E, F, G, H, I, J, L, N, O, Q}
S = Mirror(P_t, h)
xAchse' = Mirror(xAxis, h)
Liste1' = Mirror(Liste1, h)
j = PolyLine(Liste1')
A12: A11 + 0.500000000000006
A13: A12 + 0.500000000000006
A14: A13 + 0.500000000000006
A15: A14 + 0.500000000000006
A16: A15 + 0.500000000000006
A17: A16 + 0.500000000000006
A18: A17 + 0.500000000000006
A19: A18 + 0.500000000000006
A20: A19 + 0.500000000000006
B12 = Integral(cos((c * x^(2) / 2)), 0, A12)
C12 = Integral(sin((c * x^(2) / 2)), 0, A12)
B13 = Integral(cos((c * x^(2) / 2)), 0, A13)
C13 = Integral(sin((c * x^(2) / 2)), 0, A13)
B14 = Integral(cos((c * x^(2) / 2)), 0, A14)
C14 = Integral(sin((c * x^(2) / 2)), 0, A14)
B15 = Integral(cos((c * x^(2) / 2)), 0, A15)
C15 = Integral(sin((c * x^(2) / 2)), 0, A15)
B16 = Integral(cos((c * x^(2) / 2)), 0, A16)
C16 = Integral(sin((c * x^(2) / 2)), 0, A16)
B17 = Integral(cos((c * x^(2) / 2)), 0, A17)
C17 = Integral(sin((c * x^(2) / 2)), 0, A17)
B18 = Integral(cos((c * x^(2) / 2)), 0, A18)
C18 = Integral(sin((c * x^(2) / 2)), 0, A18)
B19 = Integral(cos((c * x^(2) / 2)), 0, A19)
C19 = Integral(sin((c * x^(2) / 2)), 0, A19)
B20 = Integral(cos((c * x^(2) / 2)), 0, A20)
C20 = Integral(sin((c * x^(2) / 2)), 0, A20)
P: (B11, C11)
R: (B12, C12)
T: (B13, C13)
U: (B14, C14)
V: (B15, C15)
W: (B16, C16)
Z = Element(Liste1', 1)
A_1: (B18, C18)
B_1: (B19, C19)
C_1: (B20, C20)
Liste2: {P, R, T, U, V, W, A_1, B_1, C_1}
l = PolyLine(Liste2)
m = false
D_1 = Point(xAchse')
E_1 = Point(xAchse')
F_1 = Point(xAxis)
p = Ray(Start, F_1)
n = Ray(Element[Liste1', 1], E_1)
G_1 = Element(Liste1', 1)
H_1 = Element(Liste1', 1)
Zend = Element(Liste1', 1)
b = CurveCartesian(Integral[cos(x^(2) / ((4 * a^(2)))), 0, s], Integral[sin(x^(2) / ((4 * a^(2)))), 0, s], s, 0, 40)
q = false