Convex Hull (2)
A Point which is defined by P = S ai
Mi is inside the convex hull of {Mi}
Sai = 1
ai >= 0
lemme : the convex Hull of of a subset of a set is inside the convex hull
of the set
recurrence demonstration
n = 1 => P = M
n = 2 => M1 M2
for 0<=t<=1 P = (1-t) M1 + t M2
= M1 + t M1M2
H : true for n, what about n+1
Pn+1 = S ai
Mi = (1-an+1)S
ai/(1-an+1)
Mi + an+1Mn+1
= (1-an+1)M'
+ an+1
Mn+1