Bézierspline als Parameterkurve
Author: Prof. Dr. Dörte Haftendorn
Date: 15. Februar 2013

Ha 2011

Notenbogen

zu A

zu B

zu C

zu D

Zum Anhalten links klicken oder auf te klicken.

A = (0.2983047102577273, 0.41663327784246784)
B = (0.47109823161991016, 1.4100457505069208)
C = (1.7626558683169289, 1.7839176979718465)
D = (2.5446863862328724, 0.6884849832802575)
b0(x) = (1 - x)^(3)
b1(x) = ((3 * (1 - x)^(2)) * x)
b2(x) = ((3 * (1 - x)) * x^(2))
b3(x) = x^(3)
c = Segment(B, A)
d = Segment(C, D)
b = false
Axb0(x) = (x(A) * b0(x))
Ayb0(x) = (y(A) * b0(x))
Byb1(x) = (y(B) * b1(x))
G: (-0.10402, -0.8)
H = (2.9417068242863533, -0.7975112897727293)
Cyb2(x) = (y(C) * b2(x))
Cxb2(x) = (x(C) * b2(x))
Bxb1(x) = (x(B) * b1(x))
Dyb3(x) = (y(D) * b3(x))
Dxb3(x) = (x(D) * b3(x))
e = false
f = true
g = false
h = false
te = 0.55 (slider from 0 to 1, step 0.05)
kurve = CurveCartesian((x(A) * b0(t)) + (x(B) * b1(t)) + (x(C) * b2(t)) + (x(D) * b3(t)), (y(A) * b0(t)) + (y(B) * b1(t)) + (y(C) * b2(t)) + (y(D) * b3(t)), t, 0, te)
P_a: ((x(A) * b0(te)) + (x(B) * b1(te)) + (x(C) * b2(te)) + (x(D) * b3(te)), (y(A) * b0(te)) + (y(B) * b1(te)) + (y(C) * b2(te)) + (y(D) * b3(te)))
i = Segment(B, C)
k = Circle(A, (te * c))
p = Circle(B, (te * i))
q = Circle(C, (te * d))
I = Intersect(k, c)
J = Intersect(p, i)
K = Intersect(q, d)
j = Segment(I, J)
l = Segment(J, K)
r = Circle(I, (te * j))
s = Circle(J, (te * l))
O = Intersect(r, j)
Q = Intersect(s, l)
m = Segment(O, Q)