p_1 = (6.72, 2.08)
p_0 = (-1.18, 0.78)
I = (4, 5)
O = (1, 5)
a = Segment(O, I)
t = Point(a)
u = AffineRatio(O, I, t)
p_2 = (10.1, -1.1400000000000001)
p_3 = (2.82, -4.72)
b = AffineRatio(O, I, t)
p_{11} = Dilate(p_2, u, p_1)
p_{21} = Dilate(p_3, u, p_2)
p_{01} = Dilate(p_1, u, p_0)
p_{02} = Dilate(p_{11}, u, p_{01})
p_{12} = Dilate(p_{21}, u, p_{11})
p_{03} = Dilate(p_{12}, u, p_{02})
loc1 = Locus(p_{03}, t)
c = Segment(p_0, p_1)
d = Segment(p_1, p_2)
e = Segment(p_2, p_3)
f = Segment(p_{01}, p_{11})
g = Segment(p_{11}, p_{21})
h = Segment(p_{02}, p_{12})
A = (-2.12, -4.22)
B = (-2.58, -1.52)
C = (0.64, -1.42)
D = (1.72, -4.48)
E = Bezier3(A, B, C, D, u)
loc2 = Locus(E, t)

Tool: Bezier3
Input: p_0, p_1, p_2, p_3, u
Output: p_{03}

p_{11} = Dilate(p_2, u, p_1)
p_{21} = Dilate(p_3, u, p_2)
p_{01} = Dilate(p_1, u, p_0)
p_{02} = Dilate(p_{11}, u, p_{01})
p_{12} = Dilate(p_{21}, u, p_{11})
p_{03} = Dilate(p_{12}, u, p_{02})