splajn

SplineInterpolator::SplineInterpolator(std::vector<GMath::Point2D> data) : cache(0)
{
	DataSizeCheck(data);
	sort(data.begin(), data.end());
	for (auto& elem : data)
	{
		x.push_back(elem.first);
		y.push_back(elem.second);
	}

	SameXCheck(data);

	r.resize(data.size(), 0);
	s.resize(data.size(), 0);
	q.resize(data.size(), 0);

	int n = GetSize();

	for (int i = 1; i <= n - 2; i++)
	{
		s[i] = 2 * (x[i + 1] - x[i - 1]);
		r[i] = 3 * ((y[i + 1] - y[i]) / (x[i + 1] - x[i]) - (y[i] - y[i - 1] / (x[i] - x[i - 1])));
	}

	for (int i = 1; i < n - 2; i++)
	{
		double mi = (x[i] - x[i - 1]) / s[i];
		s[i + 1] -= mi * (x[i] - x[i - 1]);
		r[i + 1] -= mi * r[i];
	}

	r[n - 2] /= s[n - 2];

	for (int i = n - 3; i > 0; i--)
		r[i] = (r[i] - (x[i] - x[i - 1]) * r[i + 1]) / s[i];

	for (int i = 0; i < n - 1; i++)
	{
		double dx = x[i + 1] - x[i];
		s[i] = (r[i + 1] - r[i]) / (3 * dx);
		q[i] = (y[i + 1] - y[i]) / dx - dx * (r[i + 1] + 2 * r[i]) / 3;
	}

}