/// <summary>
/// Computes the coefficients of the B-spline recursive formula.
/// Based on the Cox - De Boor algorithm. 'The NURBS Book' page 50.
/// </summary>
/// <param name="a">u_j / (u_j - u_(j+p))</param>
/// <param name="b">u_(j+p+1) / (u_(j+p+1) - u_(j+1))</param>
/// <param name="c">1 / (u_(j+p) - u_j)</param>
/// <param name="d">1 / (u_(j+1) - u_(j+p+1))</param>
/// <param name="nurbsValues">NurbsValues class with the knots vector and degree</param>
/// <param name="degree">degree of the iteration of the recursive formula</param>
/// <param name="j">knot index</param>
public void EvaluateMuliplyingValues(ref double a,
ref double b,
ref double c,
ref double d,
NurbsValues nurbsValues,
int degree,
int j)
{
a = nurbsValues.KnotVector[j] / (nurbsValues.KnotVector[j] - nurbsValues.KnotVector[j + degree]);
a = ModifyIfNotValid(a);
b = nurbsValues.KnotVector[j + degree + 1] / (nurbsValues.KnotVector[j + degree + 1] - nurbsValues.KnotVector[j + 1]);
b = ModifyIfNotValid(b);
c = 1.0 / (nurbsValues.KnotVector[j + degree] - nurbsValues.KnotVector[j]);
c = ModifyIfNotValid(c);
d = 1.0 / (nurbsValues.KnotVector[j + 1] - nurbsValues.KnotVector[j + degree + 1]);
d = ModifyIfNotValid(d);
}
/// <summary>
/// Constructor used to evaluate the coefficients of the non vanishing
/// B-splines over the knot span, and to evaluate the limits of the knot span,
/// mapped to the non parametric space.
/// </summary>
/// <param name="nurbsValues">NurbsValues class with the NURBS charachteristic values</param>
/// <param name="knotIndex">Index of the lower limit knot</param>
public BSplinesCoefficients(NurbsValues nurbsValues, int knotIndex)
{
LowerLimit = nurbsValues.KnotVector[knotIndex] * nurbsValues.MaxValue;
UpperLimit = nurbsValues.KnotVector[knotIndex + 1] * nurbsValues.MaxValue;
Coefficients = new double[nurbsValues.Degree + 1, nurbsValues.Degree + 2];
if (nurbsValues.KnotVector[knotIndex] != nurbsValues.KnotVector[knotIndex + 1])
{
Coefficients[0, nurbsValues.Degree] = 1.0;
double[,] tempCoefficients = Coefficients;
double a = 0.0;
double b = 0.0;
double c = 0.0;
double d = 0.0;
for (int degree = 1; degree <= nurbsValues.Degree; degree++)
{
tempCoefficients = new double[nurbsValues.Degree + 1, nurbsValues.Degree + 2];
for (int column = nurbsValues.Degree - degree; column <= nurbsValues.Degree; column++)
{
int j = knotIndex + (column - nurbsValues.Degree);
EvaluateMuliplyingValues(ref a, ref b, ref c, ref d, nurbsValues, degree, j);
for (int row = 0; row < degree; row++)
{
tempCoefficients[row, column] +=
Coefficients[row, column] * a + Coefficients[row, column + 1] * b;
tempCoefficients[row + 1, column] +=
Coefficients[row, column] * c + Coefficients[row, column + 1] * d;
}
}
Coefficients = tempCoefficients;
}
Coefficients = Normalize(Coefficients, nurbsValues.MaxValue);
}
}