Talk:De Casteljau's algorithm

I would like to see this illustrated: any takers? --Phil | Talk 12:49, Sep 22, 2004 (UTC)

Illustration would be really nice. Perhaps Κσυπ Cyp would do one if asked nicely.MathMartin 13:40, 22 Sep 2004 (UTC)

Just added the illustration and few words disscussing the geomtric interpretation of what is going on. The image was prepared in Asymptote ([1]), I include herewith the sources in case someone wishes to modifie the image one day (don't worry about licensing, I release it under public domain). Pkoprowski 17:36, 7 October 2006 (UTC)[reply]

Is there a reason the images from the Bezier_curves page aren't shown here? RaydenUni 20:33, 18 December 2006 (UTC)[reply]

Image sources

size(10cm,4cm);

real t = 0.33;

pair[][] P = {{(0,0), (0.25,1.5), (1,2), (1,0)},

{(0,0), (0.5,1), (1,2), (1,0)}, {(0,0), (0.5,1), (1,2), (1,0)}, {(0,0), (0.5,1), (1,2), (1,0)}};

path C[] = {nullpath, nullpath, nullpath, nullpath};
path g,ctr,d;
g = P[0][0]..controls P[0][1] and P[0][2]..P[0][3];
d = scale(0.025)*unitcircle;

int i,j,k;
C[0] = P[0][0]--P[0][1]--P[0][2]--P[0][3];
for(i = 1; i <= 3; ++i) {

for(j = 0; j <= 3-i; ++j) { P[i][j] = (1-t)*P[i-1][j] + t*P[i-1][j+1]; C[i] = C[i]--P[i][j]; }

for(k =  0; k < 3; ++k) {
   draw(shift((2*k,0)) * C[k]);
   for(i = 0; i < 4-k; ++i) {
       string L = format("$P_%d$",i);
       label(L, shift((2*k,0)) * P[k][i], i < (4-k)/2 ? W : E);

filldraw(shift((2*k,0)) * shift(P[k][i])*d); }

   draw(shift((2*k,0)) * C[k+1], dashed);
   for(i = 0; i < 3-k; ++i)

draw(shift((2*k,0)) * shift(P[k+1][i])*d);

   draw(shift((2*k,0)) * g);
}

I'm confused. What is little b? --jivy 16:48, 29 October 2005 (UTC)[reply]

Never mind. For anyone else who was wondering this, little b is the Bernstein basis polynomial. --jivy 03:58, 30 October 2005 (UTC)[reply]

de or De

The article header says "The correct title of this article is de Casteljau's algorithm. The initial letter is capitalized due to technical restrictions." However, according to the style guides I have handy (NY Times and USGPO), it should be capitalized here (regardless of any technical restrictions). The NYT Manual of Style and Usage says that, while the "de" particle remains in lowercase when it appears in the interior of a sentence, it should be capitalized when it begins a sentence or a headline or a subhead. The USGPO Style Manual goes even farther, saying that "de" (also d', da, della, du, van, and von) should be capitalized unless preceded by a forename or title. So according to the latter, that first sentence should read "The correct title of this article is De Casteljau's algorithm." But then, it's not needed, is it? :-) The Wikipedia style guide http://en.wikipedia.org/wiki/Capitalization#Compound_names mentions this case only for the Dutch: Franky van der Elst, but Van der Elst, Franky in a list.--BillFlis 12:14, 2 May 2006 (UTC)[reply]

German article in english Wikipedia?

The article http://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm is written in german. Is this a mistake, a stopgap until an english translation becomes available or something else? -- Roland Kaufmann Insert non-formatted text here