private double GetRationalBasisDenominator(double u, double v)
{
// u
int n = GetUCount() - 1;
// v
int m = GetVCount() - 1;
double denominator = 0;
for (int i = 0; i <= n; i++)
{
for (int j = 0; j <= m; j++)
{
BasisInfo info1 = new BSplineBasisInfo(i, uDegree, uKnotVector);
BasisInfo info2 = new BSplineBasisInfo(j, vDegree, vKnotVector);
Func <double, double> basis1 = GetBasisFunction(info1);
Func <double, double> basis2 = GetBasisFunction(info2);
Point3d pt = this.pointsGrid[i][j];
double weight = this.weights[i][j];
denominator += basis1(u) * basis2(v) * weight;
}
}
return(denominator);
}
public double[] ParameterAt(double t)
{
int n = points.Length - 1;
Point3d result = new Point3d(0, 0, 0);
if (t == this.knotVector.GetMaxKnot())
{
result = points.Last();
}
else
{
for (int i = 0; i <= n; i++)
{
Point3d pt = points[i];
double weight = this.weights[i];
BasisInfo info = new BSplineBasisInfo(i, degree, knotVector);
var basis = GetBasisFunction(info);
double val = basis(t);
result += val * pt * weight;
}
double denominator = GetRationalBasisDenominator(t);
if (denominator == 0)
{
throw new DivideByZeroException();
}
result /= denominator;
}
return(new double[] { result.X, result.Y, result.Z });
}
public virtual double[] ParameterAt(double t)
{
int n = points.Length - 1;
Point3d result = new Point3d(0, 0, 0);
// Boundary condition
if (t == this.knotVector.GetMaxKnot())
{
result = points.Last();
}
else
{
for (int i = 0; i <= n; i++)
{
Point3d pt = points[i];
BasisInfo info = new BSplineBasisInfo(i, degree, knotVector);
Func <double, double> basis = this.GetBasisFunction(info);
double val = basis(t);
result += val * pt;
}
}
return(new double[] { result.X, result.Y, result.Z });
}
protected override Func <double, double> GetBasisFunction(BasisInfo _info)
{
BSplineBasisInfo info = (BSplineBasisInfo)_info;
int i = info.I;
int j = info.J;
KnotSet knots = info.Knots;
Func <double, double> basis = GetBasis(i, j, knots);
return(basis);
}
public double[] ParameterAt(double u, double v)
{
// u
int n = GetUCount() - 1;
// v
int m = GetVCount() - 1;
Point3d accumulation = new Point3d(0, 0, 0);
for (int i = 0; i <= n; i++)
{
BasisInfo info1 = new BSplineBasisInfo(i, uDegree, uKnotVector);
Func <double, double> basis1 = GetBasisFunction(info1);
// Boundary condition
if (u == 1 && i == n)
{
basis1 = (t) => 1;
}
for (int j = 0; j <= m; j++)
{
BasisInfo info2 = new BSplineBasisInfo(j, vDegree, vKnotVector);
Func <double, double> basis2 = GetBasisFunction(info2);
// Boundary condition
if (v == 1 && j == m)
{
basis2 = (t) => 1;
}
Point3d pt = this.pointsGrid[i][j];
double weight = this.weights[i][j];
accumulation += pt * basis1(u) * basis2(v) * weight;
}
}
double denominator = GetRationalBasisDenominator(u, v);
if (denominator == 0)
{
denominator = 1;
//throw new DivideByZeroException();
}
accumulation /= denominator;
return(new double[] { accumulation.X, accumulation.Y, accumulation.Z });
}
private double GetRationalBasisDenominator(double t)
{
int n = weights.Length - 1;
double denominator = 0;
for (int i = 0; i <= n; i++)
{
BasisInfo info = new BSplineBasisInfo(i, degree, knotVector);
Func <double, double> basis = GetBasisFunction(info);
double weight = this.weights[i];
denominator += basis(t) * weight;
}
return(denominator);
}
public double[] ParameterAt(double u, double v)
{
// u
int n = GetUCount() - 1;
// v
int m = GetVCount() - 1;
Point3d accumulation = new Point3d(0, 0, 0);
for (int i = 0; i <= n; i++)
{
BasisInfo info1 = new BSplineBasisInfo(i, uDegree, uKnotVector);
Func <double, double> basis1 = GetBasisFunction(info1);
// Boundary condition
if (u == 1 && i == n)
{
basis1 = (t) => 1;
}
for (int j = 0; j <= m; j++)
{
BasisInfo info2 = new BSplineBasisInfo(j, vDegree, vKnotVector);
Func <double, double> basis2 = GetBasisFunction(info2);
// Boundary condition
if (v == 1 && j == m)
{
basis2 = (t) => 1;
}
Point3d pt = this.pointsGrid[i][j];
accumulation += pt * basis1(u) * basis2(v);
}
}
return(new double[] { accumulation.X, accumulation.Y, accumulation.Z });
}
