public override Vector2d GetThirdDerivative(double t)
{
CurveDerivatives cd = new CurveDerivatives();
cd.init(false, false, false, true);
Get(t, ref cd);
return(cd.d3);
}
public override Vector2D GetSecondDerivative(double t)
{
CurveDerivatives cd = new CurveDerivatives();
cd.init(false, false, true, false);
Get(t, ref cd);
return(cd.d2);
}
public void Get(double t, ref CurveDerivatives result)
{
int i, imin = 0, imax = 0;
if (result.bDer3)
{
mBasis.Compute(t, 0, ref imin, ref imax);
mBasis.Compute(t, 1, ref imin, ref imax);
mBasis.Compute(t, 2, ref imin, ref imax);
mBasis.Compute(t, 3, ref imin, ref imax);
}
else if (result.bDer2)
{
mBasis.Compute(t, 0, ref imin, ref imax);
mBasis.Compute(t, 1, ref imin, ref imax);
mBasis.Compute(t, 2, ref imin, ref imax);
}
else if (result.bDer1)
{
mBasis.Compute(t, 0, ref imin, ref imax);
mBasis.Compute(t, 1, ref imin, ref imax);
}
else // pos
{
mBasis.Compute(t, 0, ref imin, ref imax);
}
double tmp;
// Compute position.
Vector2d X = Vector2d.Zero;
double w = (double)0;
for (i = imin; i <= imax; ++i)
{
tmp = mBasis.GetD0(i) * mCtrlWeight[i];
X += tmp * mCtrlPoint[i];
w += tmp;
}
double invW = 1.0 / w;
Vector2d P = invW * X;
result.p = P;
result.bPosition = true;
if (result.bDer1 == false && result.bDer2 == false && result.bDer3 == false)
{
return;
}
// Compute first derivative.
Vector2d XDer1 = Vector2d.Zero;
double wDer1 = (double)0;
for (i = imin; i <= imax; ++i)
{
tmp = mBasis.GetD1(i) * mCtrlWeight[i];
XDer1 += tmp * mCtrlPoint[i];
wDer1 += tmp;
}
Vector2d PDer1 = invW * (XDer1 - wDer1 * P);
result.d1 = PDer1;
result.bDer1 = true;
if (result.bDer2 == false && result.bDer3 == false)
{
return;
}
// Compute second derivative.
Vector2d XDer2 = Vector2d.Zero;
double wDer2 = (double)0;
for (i = imin; i <= imax; ++i)
{
tmp = mBasis.GetD2(i) * mCtrlWeight[i];
XDer2 += tmp * mCtrlPoint[i];
wDer2 += tmp;
}
Vector2d PDer2 = invW * (XDer2 - ((double)2) * wDer1 * PDer1 - wDer2 * P);
result.d2 = PDer2;
result.bDer2 = true;
if (result.bDer3 == false)
{
return;
}
// Compute third derivative.
Vector2d XDer3 = Vector2d.Zero;
double wDer3 = (double)0;
for (i = imin; i <= imax; i++)
{
tmp = mBasis.GetD3(i) * mCtrlWeight[i];
XDer3 += tmp * mCtrlPoint[i];
wDer3 += tmp;
}
result.d3 = invW * (XDer3 - ((double)3) * wDer1 * PDer2 -
((double)3) * wDer2 * PDer1 - wDer3 * P);
}
