Method OneBasisFunctionDerivative

src/LNLib/Algorithm/Polynomials.cpp:457–544

}

std::vector<double> LNLib::Polynomials::OneBasisFunctionDerivative(int spanIndex, int degree, int derivative, const std::vector<double>& knotVector, double paramT)
{
	VALIDATE_ARGUMENT(spanIndex >= 0, "spanIndex", "SpanIndex must be greater than or equal zero.");
	VALIDATE_ARGUMENT(degree > 0, "degree", "Degree must be greater than zero.");
	VALIDATE_ARGUMENT(derivative <= 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]);

	std::vector<double> derivatives(derivative + 1, 0.0);

	if (MathUtils::IsLessThan(paramT, knotVector[spanIndex]) ||
		MathUtils::IsGreaterThanOrEqual(paramT, knotVector[spanIndex + degree + 1]))
	{
		return derivatives;
	}

	std::vector<std::vector<double>> N(degree + 1, std::vector<double>(degree + 1,0.0));

	for (int j = 0; j <= degree; j++)
	{
		if (MathUtils::IsGreaterThanOrEqual(paramT, knotVector[spanIndex + j]) &&
			MathUtils::IsLessThan(paramT, knotVector[spanIndex + j + 1]))
		{
			N[j][0] = 1.0;
		}
	}
	for (int k = 1; k <= degree; k++)
	{
		double saved = 0.0;
		if (!MathUtils::IsAlmostEqualTo(N[0][k - 1], 0.0))
		{
			saved = ((paramT - knotVector[spanIndex]) * N[0][k - 1]) / (knotVector[spanIndex + k] - knotVector[spanIndex]);
		}
		for (int j = 0; j < degree - k + 1; j++)
		{
			double knotLeft = knotVector[spanIndex + j + 1];
			double knotRight = knotVector[spanIndex + j + k + 1];

			if (MathUtils::IsAlmostEqualTo(N[j + 1][k - 1], 0.0))
			{
				N[j][k] = saved;
				saved = 0.0;
			}
			else
			{
				double temp = N[j + 1][k - 1] / (knotRight - knotLeft);
				N[j][k] = saved + (knotRight - paramT) * temp;
				saved = (paramT - knotLeft) * temp;
			}
		}
	}

	derivatives[0] = N[0][degree];

	for (int k = 1; k <= derivative; k++)
	{
		std::vector<double> ND(k+1,0.0);