Method BezierToPowerMatrix

src/LNLib/Algorithm/Polynomials.cpp:578–620

}

std::vector<std::vector<double>> LNLib::Polynomials::BezierToPowerMatrix(int degree)
{
	std::vector<std::vector<double>> matrix(degree+1, std::vector<double>(degree + 1));
	for (int i = 0; i < degree; i++)
	{
		for (int j = i + 1; j <= degree; j++)
		{
			matrix[i][j] = 0.0;
		}
	}

	matrix[0][0] = matrix[degree][degree] = 1.0;
	if (degree % 2)
	{
		matrix[degree][0] = -1.0;
	}
	else
	{
		matrix[degree][0] = 1.0;
	}

	double sign = -1.0;
	for (int i = 1; i < degree; i++)
	{
		matrix[i][i] = MathUtils::Binomial(degree,i);
		matrix[i][0] = matrix[degree][degree - i] = sign * matrix[i][i];
		sign = -sign;
	}

	int k1 = (degree + 1) / 2;
	int pk = degree - 1;
	for (int k = 1; k < k1; k++)
	{
		sign = -1.0;
		for (int j = k + 1; j <= pk; j++)
		{
			matrix[j][k] = matrix[pk][degree - j] = sign * MathUtils::Binomial(degree, k) * MathUtils::Binomial(degree - k, j - k);
			sign = -sign;
		}
		pk = pk - 1;
	}
	return matrix;
}

std::vector<std::vector<double>> LNLib::Polynomials::PowerToBezierMatrix(int degree, const std::vector<std::vector<double>>& matrix)
{