public override Point ValueAtX(double x, out bool interpolated, out bool extrapolated)
{
interpolated = false;
extrapolated = false;
if (d_bezier == null)
{
extrapolated = true;
return(new Point(0, 0));
}
Range xrange = d_polynomial.XRange;
if (x < xrange.Min)
{
extrapolated = true;
return(new Point(xrange.Min, d_polynomial[0].Begin));
}
else if (x > xrange.Max)
{
extrapolated = true;
return(new Point(xrange.Max, d_polynomial[d_polynomial.Count - 1].End));
}
if (d_periodic != null && (x < d_periodic.Min || x > d_periodic.Max))
{
extrapolated = true;
}
// Do the interpolation
PiecewisePolynomial.Piece piece = d_polynomial.PieceAt(x);
if (x != piece.Begin || x != piece.End)
{
interpolated = true;
}
return(new Point(x, piece.Evaluate(x)));
}
public override PiecewisePolynomial InterpolateSorted(List <Point> points)
{
// Remove points that are very close together
Point[] r = points.ToArray();
for (int i = 1; i < r.Length; ++i)
{
if (System.Math.Abs(r[i - 1].X - r[i].X) < Constants.Epsilon)
{
points.Remove(r[i - 1]);
}
}
int size = points.Count;
if (size < 2)
{
return(new PiecewisePolynomial());
}
double[] slopes = new double[size];
double[] dpdt = new double[size];
double[] dt = new double[size - 1];
for (int i = 0; i < size - 1; ++i)
{
double dp = (points[i + 1].Y - points[i].Y);
dt[i] = (points[i + 1].X - points[i].X);
dpdt[i] = dt[i] == 0 ? 0 : (dp / dt[i]);
}
dpdt[size - 1] = 0;
bool[] samesign = new bool[size - 1];
for (int i = 0; i < size - 2; ++i)
{
samesign[i] = (System.Math.Sign(dpdt[i]) == System.Math.Sign(dpdt[i + 1]) && dpdt[i] != 0);
}
// Three point derivative
for (int i = 0; i < size - 2; ++i)
{
double dpdt1 = dpdt[i];
double dpdt2 = dpdt[i + 1];
if (samesign[i])
{
double hs = dt[i] + dt[i + 1];
double w1 = (dt[i] + hs) / (3 * hs);
double w2 = (hs + dt[i + 1]) / (3 * hs);
double mindpdt;
double maxdpdt;
if (dpdt1 > dpdt2)
{
maxdpdt = dpdt1;
mindpdt = dpdt2;
}
else
{
maxdpdt = dpdt2;
mindpdt = dpdt1;
}
slopes[i + 1] = mindpdt / (w1 * (dpdt[i] / maxdpdt) + w2 * (dpdt[i + 1] / maxdpdt));
}
else
{
slopes[i + 1] = 0;
}
}
if (size > 2)
{
slopes[0] = ((2 * dt[0] + dt[1]) * dpdt[0] - dt[0] * dpdt[1]) / (dt[0] + dt[1]);
}
if (System.Math.Sign(slopes[0]) != System.Math.Sign(dpdt[0]))
{
slopes[0] = 0;
}
else if (System.Math.Sign(dpdt[0]) != System.Math.Sign(dpdt[1]) &&
System.Math.Abs(slopes[0]) > System.Math.Abs(3 * dpdt[0]))
{
slopes[0] = 3 * dpdt[0];
}
if (size > 2)
{
slopes[size - 1] = ((2 * dt[size - 2] + dt[size - 3]) * dpdt[size - 2] -
dt[size - 2] * dpdt[size - 3]) /
(dt[size - 2] + dt[size - 3]);
}
if (System.Math.Sign(slopes[size - 1]) != System.Math.Sign(dpdt[size - 2]))
{
slopes[size - 1] = 0;
}
else if (System.Math.Sign(dpdt[size - 2]) != System.Math.Sign(dpdt[size - 3]) &&
System.Math.Abs(slopes[size - 1]) > System.Math.Abs(3 * dpdt[size - 2]))
{
slopes[size - 1] = 3 * dpdt[size - 2];
}
PiecewisePolynomial.Piece[] pieces = new PiecewisePolynomial.Piece[size - 1];
for (int i = 0; i < size - 1; ++i)
{
double h = points[i + 1].X - points[i].X;
Point p0 = points[i];
Point p1 = points[i + 1];
double m0 = slopes[i] * h;
double m1 = slopes[i + 1] * h;
// O3: 2 * (c1.p - c2.p) + h * (c1.m + c2.m)
// O2: 3 * (c2.p - c1.p) - h * (2 * c1.m + c2.m)
// O1: h * c1.m
// O0: c1.p
double[] coefficients = new double[] {
2 * (p0.Y - p1.Y) + m0 + m1,
3 * (p1.Y - p0.Y) - 2 * m0 - m1,
m0,
p0.Y
};
pieces[i] = new PiecewisePolynomial.Piece(new Range(p0.X, p1.X), coefficients);
}
return(new PiecewisePolynomial(pieces));
}