Katakaustik mit Nephroide
Author: Prof. Dr. Dörte Haftendorn

P

Ort von P

Nephroide als Kaustik

Ziehe T, wenn P auf seiner Ortskurve laufen soll.

Ha Jan 09

Nephroide, 
errechnet

F = (6, 4.5)
C = (-0.5877777777777784, 4.461111111111112)
n = Segment(C, F)
T = Point(n)
p = Segment(C, T)
A = Intersect(xAxis, yAxis)
B = Point(xAxis)
c = Circle(A, B)
Q = Point(c)
a = OrthogonalLine(Q, yAxis)
D = Point(a)
b = Ray(Q, D)
d = Segment(Q, A)
C' = Mirror(Q, d)
D' = Mirror(D, d)
e = Ray(C', D')
E = Intersect(e, xAxis)
f = Segment(Q, E)
Q' = Mirror(Q, xAxis)
E' = Mirror(E, xAxis)
g = Segment(Q', E')
C'_2 = Mirror(Q, xAxis)
D'_1 = Mirror(D, xAxis)
h = Ray(C'_2, D'_1)
E'' = Mirror(E', d)
i = Segment(Q, E)
j = Segment(E, Q')
k = Segment(D'_1, Q')
l = Segment(D, Q)
r = 4
P: (r * (cos(p) - cos(p) * cos(2.0 * p) / 2.0), r * (sin(p) - cos(p) * sin(2.0 * p) / 2.0))
o = true
loc1 = Locus(P, T)
m = true