/// <summary>
/// Creates a interpolated curve through a set of points.<br/>
/// <em>Refer to Algorithm A9.1 on The NURBS Book, pp.369-370 for details.</em>
/// </summary>
/// <param name="pts">The set of points to interpolate.</param>
/// <param name="degree">The Curve degree.</param>
/// <param name="startTangent">The tangent vector for the first point.</param>
/// <param name="endTangent">The tangent vector for the last point.</param>
/// <param name="centripetal">True use the chord as per knot spacing, false use the squared chord.</param>
/// <returns>A the interpolated curve.</returns>
public static NurbsBase Interpolated(List <Point3> pts, int degree, Vector3?startTangent = null,
Vector3?endTangent = null, bool centripetal = false)
{
if (pts.Count < degree + 1)
{
throw new Exception($"You must supply at least degree + 1 points. You supplied {pts.Count} pts.");
}
// Gets uk parameters.
List <double> uk = CurveHelpers.Parametrization(pts, centripetal);
// Compute knot vectors.
bool hasTangents = startTangent != null && endTangent != null;
KnotVector knots = ComputeKnotsForInterpolation(uk, degree, hasTangents);
// Global interpolation.
// Build matrix of basis function coefficients.
Matrix coeffMatrix = BuildCoefficientsMatrix(pts, degree, hasTangents, uk, knots);
// Solve for each points.
List <Point4> ctrlPts = (hasTangents)
? SolveCtrlPtsWithTangents(knots, pts, coeffMatrix, degree, new Vector3(startTangent.Value), new Vector3(endTangent.Value))
: SolveCtrlPts(pts, coeffMatrix);
return(new NurbsCurve(degree, knots, ctrlPts));
}
public static NurbsBase Approximate(List <Point3> pts, int degree, bool centripetal = false)
{
int numberCpts = pts.Count - 1;
// Gets the parameters curve uk.
List <double> uk = CurveHelpers.Parametrization(pts, centripetal);
// Computes knot vectors.
KnotVector knots = ComputeKnotsForCurveApproximation(uk, degree, numberCpts, pts.Count);
// Compute matrix N
Matrix matrixN = new Matrix();
for (int i = 1; i < pts.Count - 1; i++)
{
List <double> tempRow = new List <double>();
for (int j = 1; j < numberCpts - 1; j++)
{
tempRow.Add(Evaluate.Curve.OneBasisFunction(degree, knots, j, uk[i]));
}
matrixN.Add(tempRow);
}
// Compute NT matrix.
Matrix matrixNt = matrixN.Transpose();
// Compute NTN matrix.
Matrix matrixNtN = matrixNt * matrixN;
// Computes Rk - Eqn 9.63.
List <Point3> Rk = ComputesValuesRk(knots, uk, degree, pts, numberCpts);
// Compute R - Eqn 9.67.
var vectorR = ComputeValuesR(knots, uk, Rk, degree, numberCpts);
// Computes control points, fixing the first and last point from the input points.
List <Point4> ctrlPts = new List <Point4> {
pts[0]
};
ctrlPts.AddRange(SolveCtrlPts(vectorR, matrixNtN));
ctrlPts.Add(pts[pts.Count - 1]);
return(new NurbsCurve(degree, knots, ctrlPts));
}