private static void DecomposeCurve(int n, int p, double[] U,
Point[] P, out int nb, out Point[][] Q)
{
int m = n + p + 1;
int a = p;
int b = p + 1;
nb = 0;
// If there are m+1 knots and a clamped knot vector
// The number of knot intervals would ideally be (m-2p)
// which is also the max number of Bezier curves that can be created
point[,] qq = new point[m - 2 * p, p + 1];
for (int i = 0; i <= p; i++)
{
qq[nb, i].X = P[i].X;
qq[nb, i].Y = P[i].Y;
qq[nb, i].Z = P[i].Z;
}
while (b < m)
{
int i = b;
while (b < m && U[b + 1] == U[b])
{
b++;
}
int mult = b - i + 1;
if (mult < p)
{
double[] alphas = new double[p];
var numer = U[b] - U[a];
for (int j = p; j > mult; j--)
{
alphas[j - mult - 1] = numer / (U[a + j] - U[a]);
}
int r = p - mult;
for (int j = 1; j <= r; j++)
{
var save = r - j;
int s = mult + j;
for (int k = p; k >= s; k--)
{
var alpha = alphas[k - s];
qq[nb, k].X = alpha * qq[nb, k].X + (1 - alpha) * qq[nb, k - 1].X;
qq[nb, k].Y = alpha * qq[nb, k].Y + (1 - alpha) * qq[nb, k - 1].Y;
qq[nb, k].Z = alpha * qq[nb, k].Z + (1 - alpha) * qq[nb, k - 1].Z;
}
if (b < m)
{
qq[nb + 1, save] = qq[nb, p];
}
}
}
nb = nb + 1;
if (b < m)
{
for (int j = p - mult; j <= p; j++)
{
qq[nb, j].X = P[b - p + j].X;
qq[nb, j].Y = P[b - p + j].Y;
qq[nb, j].Z = P[b - p + j].Z;
}
a = b;
b = b + 1;
}
}
int nrows = qq.GetLength(0);
Q = new Point[nrows][];
for (int i = 0; i < nrows; i++)
{
Q[i] = new Point[p + 1];
for (int j = 0; j <= p; j++)
{
Q[i][j] = Point.ByCoordinates(
qq[i, j].X, qq[i, j].Y, qq[i, j].Z);
}
}
}
