Method OneBasisFunction

src/LNLib/Algorithm/Polynomials.cpp:399–455

}

double LNLib::Polynomials::OneBasisFunction(int spanIndex, int degree, 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(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]);

	int m = knotVector.size() - 1;
	if ((spanIndex == 0 && MathUtils::IsAlmostEqualTo(paramT, knotVector[0])) ||
		(spanIndex == m - degree - 1 && MathUtils::IsAlmostEqualTo(paramT, knotVector[m])))
	{
		return 1.0;
	}
	if (MathUtils::IsLessThan(paramT, knotVector[spanIndex]) || 
		MathUtils::IsGreaterThanOrEqual(paramT, knotVector[spanIndex + degree + 1]))
	{
		return 0.0;
	}

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