Image:DeCasteljau1.png

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DeCasteljau1.png‎ (15KB, MIME type: image/png)

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[edit] Summary

author: Przemysław Koprowski source: created by in Asymptote description: This image depictes the de Casteljau algorithm geometrically data: created on 7th of October 2006

[edit] Licensing

I, the creator of this work, hereby release it into the public domain. This applies worldwide.
In case this is not legally possible,
I grant any entity the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

[edit] Asymptote sources

Here are the Asymptote sources of the image in case someone wonts to modifie it.

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);
}

File history

Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version.
Click on date to download the file or see the image uploaded on that date.

(del) (cur) 17:19, 7 October 2006 . . Pkoprowski (Talk | contribs) . . 600×300 (15,317 bytes) (author: Przemysław Koprowski (myself) source: created by me in Asymptote description: This image depictes the de Casteljau algorithm geometrically data: created on 7th of October 2006)