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

t

Ha 2011

Notenbogen

zu A

zu B

zu C

zu D

x(t)=x(A)\cdot b0(t)+x(B)\cdot b1(t)+x(C)\cdot b2(t)+x(D)\cdot b3(t)

y(t)=y(A)\cdot b0(t)+y(B)\cdot b1(t)+y(C)\cdot b2(t)+y(D)\cdot b3(t)

x(B)b_1(t)

y(B) b_1{(t)}

b_1(t)=3 (1-t)^2t

t

x
\ y

A = (0.2983047102577273, 0.41663327784246784)
B = (0.47109823161991016, 1.4100457505069208)
C = (1.7626558683169289, 1.7839176979718465)
D = (2.4152323584375277, 0.8458389934234872)
b0(x) = (1 - x)^(3)
b1(x) = ((3 * (1 - x)^(2)) * x)
b2(x) = ((3 * (1 - x)) * x^(2))
b3(x) = x^(3)
E = (0, 2)
F = (3, 2)
a = Segment(E, F)
T = Point(a)
ts = Segment(E, T)
t: ts / a
xbez: (x(A) * b0(t)) + (x(B) * b1(t)) + (x(C) * b2(t)) + (x(D) * b3(t))
ybez: (y(A) * b0(t)) + (y(B) * b1(t)) + (y(C) * b2(t)) + (y(D) * b3(t))
P: (xbez, ybez)
Bézierkurve = Locus(P, T)
c = Segment(B, A)
d = Segment(C, D)
Text2: "t= " + t
b = true
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
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, 1)
i: y = 0.98
j: y = 0.84
k: y = 0.8
I = Point(i)
J = Point(i)
K = Point(i)
L = Point(i)
M = Point(i)
N = Point(i)
O = Point(i)
Q = Point(i)
R = Point(j)
S = Point(j)
U = Point(j)
V = Point(j)
W = Point(j)
Z = Point(j)
A_1 = Point(j)
B_1 = Point(j)
C_1 = Point(k)
D_1 = Point(k)
E_1 = Point(k)
F_1 = Point(k)
G_1 = Point(k)
H_1 = Point(k)
I_1 = Point(k)
J_1 = Point(k)
l = Segment(I, J)
m = Segment(K, L)
n = Segment(M, N)
p = Segment(O, Q)
q = Segment(R, S)
r = Segment(D_1, C_1)
s = Segment(U, V)
f_1 = Segment(W, Z)
g_1 = Segment(A_1, B_1)
h_1 = Segment(E_1, F_1)
i_1 = Segment(G_1, H_1)
j_1 = Segment(I_1, J_1)
K_1: (0.52, 0.6)
L_1: (1.25, 0.6)
k_1 = Segment(K_1, L_1)