Talk:Bernstein polynomial

message: how is the pointwise convergence works for this polynomial? — Preceding unsigned comment added by 130.113.226.6 (talk) 19:33, 22 April 2004 (UTC)
thread_title: [Untitled]

message: Where does this notion that deCastlejau's is the stable way to evaluate Bernstein polynomials come from?  I don't see it in the references for this article, and as discussed in http://mae.engr.ucdavis.edu/~farouki/bernstein.pdf (one of the references on the Bezier Curves Wikipedia page): 
"it was shown that, in fact, the Bernstein basis is “optimally stable”".  As far as I know, no sane person actually writes code that evaluates Bezier curves using de Castlejau's algorithm, unless they are doing it to teach about the properties of Bezier curves, or if the only thing they know about Bezier curves is what they read on Wikipedia (which currently seems to suggest that if you want numerical stability you have to use the inefficient de Castlejau's algo).  Most code in the real world evaluates Beziers using Bernstein polynomials. — Preceding unsigned comment added by 2620:0:1009:0:baac:6fff:fe98:e716 (talk) 00:40, 26 April 2013 (UTC)
thread_title: Bernstein polynomial stability

message: I want to merge Bézier curve and Bernstein polynomial. I do not care what the resulting article is called. The two article are talking about the same subject and so there is a lot of duplicated material and inconsistent notation. Any comments ?MathMartin 12:53, 19 Sep 2004 (UTC)
thread_title: Merging Bezier curve & Bernstein polynomial

message: bν,n(x) = n · (bν − 1,n − 1(x) − bν,n − 1(x))??? 
is it just me or is this equation wrong?!
 Looks wrong to me:
 
 b2,4(3) = 216
 b1,3(3) = 36
 b2,3(3) = -54
 4 * (36 - -54) = 360
 
 Last time I checked, 360 and 216 were different numbers.
 
 I'm going to pull that statement from the article.
:shouldn't that equation be for the derivative?
: \tfrac{d}{dx} b_{\nu,n}(x) = n \cdot (b_{\nu-1,n-1}(x) - b_{\nu,n-1}(x))  —MoA)gnome (talk) 17:29, 7 February 2008 (UTC)
replies: text: Yes, second that. Also just proved this on paper.Methossant (talk) 16:14, 29 May 2009 (UTC)
thread_title:  Wrong statement 

message: : Specifically, the word uniformly signifies that the approximation will meet the original function, but not go above it…
I don't know what "go above it" means here, but if it means that the approximation is bounded above by the true function, then it is not only wrong but contradicted by the graphic at the top of the page.  — Preceding unsigned comment added by 207.10.142.163 (talk) 01:47, 6 October 2011 (UTC)
replies: text:  Yes, you are right. The wrong phrase is now deleted. Thank you. Boris Tsirelson (talk) 13:20, 6 October 2011 (UTC)
thread_title:  Go above it? 

message: Correct me if I'm wrong, but I can't think of a Bernstein polynomial that would look like the one depicted in the plot.
Specifically, at the value x=1, the Bernstein polynomial always has value zero, since it has a factor of (1-x) in it.  The only case in which it doesn't have this zero value is when v=x, in which case, the Bernstein polynomial just becomes x^n, which certainly doesn't look like the plot shown.
Am I missing something?
Monsterman222 (talk) 00:40, 2 December 2013 (UTC)
replies: text: Probably you miss the distinction between "Bernstein polynomial" and "Bernstein basis polynomial". Boris Tsirelson (talk) 06:14, 2 December 2013 (UTC)
thread_title:  Plot is Incorrect 

message: It seems something is wrong in the attribution page for planet math,  but I am not insightful enough to correct it.  — Preceding unsigned comment added by Dansynek (talk • contribs) 05:47, 3 January 2014 (UTC)
thread_title:  Reference to planet math does not work