File:DeCasteljau1.svg

import settings;
outformat="pdf";

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);
}