Illustration of bezier curves - modeling and rendering, Computer Graphics

To prove ‾P (1) = pn

Solution: since in the above case we determine each term excluding Bn,n (u) will have numerous of (1 - u)i (i = 0 to n) consequently by using u = 1 will lead to outcome = 0 of all terms except of Bn, n (u).

Bn,n(u) = n!(n!(n-n)!). un .(1 -u)n - n = un

P(u - 1) = p0.0 + p1.0 + .............+ pn.1n

= pn

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