Jump to content
  • Advertisement

Archived

This topic is now archived and is closed to further replies.

Bino

Bernstein Function Derivatives

This topic is 6272 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Recommended Posts

I've been reading about bezier curves and the basis, or Bernstein, function which is defined as: Jn,i(t) = (n, i)t^i(1 - t)^n-i. Since I'm not very good at differentiating could some tell me how they got this first derivative: J'n, i(n, i) = i - nt/t(1-t) ? If you can't tell me how they got the first derivative could someone at least tell me what "differentiation technique" was used? Thanks, Bino Edited by - Bino on March 20, 2001 10:14:59 PM

Share this post


Link to post
Share on other sites
Advertisement
Guest Anonymous Poster
well i remember right from discrete math, n choose k is actually

n!/k!(n-k)! therefore,

if (n!/k!(n-k)!)*x^k(1-x)^n-k is the nth degree polynomial you wish to find the derivative of, then simply use the power rule and the rule for multiplication(err...forgot the name, duh) and find the derivative directly, remember (n,k) is actually a constant!

eventually the derivative ends up being
n(C(k-1,n-1)(t) - C(k,n-1)(t))

or d/dx =

n((n-1)!/((k-1)!*((n-1)-(k-1))!) - (n-1)!/k!((n-1)-k)!

i think thats right anyhow, ok later

Share this post


Link to post
Share on other sites
Guest Anonymous Poster
Wow...math looks even more ugly in pure text.

Share this post


Link to post
Share on other sites
Guest Anonymous Poster
Wow...math looks even more ugly in pure text.

Share this post


Link to post
Share on other sites

  • Advertisement
×

Important Information

By using GameDev.net, you agree to our community Guidelines, Terms of Use, and Privacy Policy.

Participate in the game development conversation and more when you create an account on GameDev.net!

Sign me up!