Method BasisFunctionsFirstOrderDerivative

src/LNLib/Algorithm/Polynomials.cpp:300–397

}

void LNLib::Polynomials::BasisFunctionsFirstOrderDerivative(int spanIndex, int degree, const std::vector<double>& knotVector, double paramT, double derivatives[2][Constants::NURBSMaxDegree + 1])
{
	VALIDATE_ARGUMENT(spanIndex >= 0, "spanIndex", "SpanIndex must be greater than or equal zero.");
	VALIDATE_ARGUMENT(degree >= 0 && degree <= Constants::NURBSMaxDegree, "degree", "Degree must be greater than or equal zero and not exceed the maximun degree.");
	VALIDATE_ARGUMENT(1 <= degree, "derivative", "Derivative must not be greater than degree.");
	VALIDATE_ARGUMENT(knotVector.size() > 0, "knotVector", "KnotVector size must be greater than zero.");
	VALIDATE_ARGUMENT(ValidationUtils::IsValidKnotVector(knotVector), "knotVector", "KnotVector must be a nondecreasing sequence of real numbers.");
	VALIDATE_ARGUMENT_RANGE(paramT, knotVector[0], knotVector[knotVector.size() - 1]);

	double ndu[Constants::NURBSMaxDegree + 1][Constants::NURBSMaxDegree + 1];

	ndu[0][0] = 1.0;

	double left[Constants::NURBSMaxDegree + 1];
	double right[Constants::NURBSMaxDegree + 1];

	double saved = 0.0;
	double temp = 0.0;

	for (int j = 1; j <= degree; j++)
	{
		left[j] = paramT - knotVector[spanIndex + 1 - j];
		right[j] = knotVector[spanIndex + j] - paramT;

		saved = 0.0;
		for (int r = 0; r < j; r++)
		{
			ndu[j][r] = right[r + 1] + left[j - r];
			temp = ndu[r][j - 1] / ndu[j][r];

			ndu[r][j] = saved + right[r + 1] * temp;
			saved = left[j - r] * temp;
		}
		ndu[j][j] = saved;
	}

	for (int j = 0; j <= degree; j++)
	{
		derivatives[0][j] = ndu[j][degree];
	}

	double a[2][Constants::NURBSMaxDegree + 1];
	for (int r = 0; r <= degree; r++)
	{
		int s1 = 0; 
		int s2 = 1;
		a[0][0] = 1.0;

		const int k = 1;
		{
			double d = 0.0;
			int rk = r - k;
			int pk = degree - k;

			if (r >= k)
			{
				a[s2][0] = a[s1][0] / ndu[pk + 1][rk];
				d = a[s2][0] * ndu[rk][pk];