bool IntpQdrNonuniform2<Real>::Evaluate (const Vector2<Real>& P, Real& F,
Real& FX, Real& FY)
{
int i = mDT->GetContainingTriangle(P);
if (i == -1)
{
return false;
}
// Get triangle information.
Vector2<Real> V[3];
mDT->GetVertexSet(i, V);
int invDet[3];
mDT->GetIndexSet(i, invDet);
TriangleData& tData = mTData[i];
// Determine which of the six subtriangles contains the target point.
Vector2<Real> sub0 = tData.Center;
Vector2<Real> sub1;
Vector2<Real> sub2 = tData.Intersect[2];
Real bary[3];
int index;
for (index = 1; index <= 6; ++index)
{
sub1 = sub2;
if (index % 2)
{
sub2 = V[index/2];
}
else
{
sub2 = tData.Intersect[index/2 - 1];
}
P.GetBarycentrics(sub0, sub1, sub2, bary);
if (bary[0] >= (Real)0 && bary[1] >= (Real)0 && bary[2] >= (Real)0)
{
// P is in triangle <Sub0,Sub1,Sub2>
break;
}
}
// This should not happen theoretically, but it can happen due to
// numerical round-off errors. Just in case, select an index and go
// with it. Probably better is to keep track of the dot products in
// InTriangle and find the one closest to zero and use a triangle that
// contains the edge as the one that contains the input point.
assertion(index <= 6, "Unexpected condition\n");
if (index > 6)
{
// Use this index because bary[] was computed last for it.
index = 5;
}
// Fetch Bezier control points.
Real bez[6] =
{
tData.Coeff[0],
tData.Coeff[12 + index],
tData.Coeff[13 + (index % 6)],
tData.Coeff[index],
tData.Coeff[6 + index],
tData.Coeff[1 + (index % 6)]
};
// Evaluate Bezier quadratic.
F = bary[0]*(bez[0]*bary[0] + bez[1]*bary[1] + bez[2]*bary[2]) +
bary[1]*(bez[1]*bary[0] + bez[3]*bary[1] + bez[4]*bary[2]) +
bary[2]*(bez[2]*bary[0] + bez[4]*bary[1] + bez[5]*bary[2]);
// Evaluate barycentric derivatives of F.
Real FU = ((Real)2.0)*(bez[0]*bary[0] + bez[1]*bary[1] +
bez[2]*bary[2]);
Real FV = ((Real)2.0)*(bez[1]*bary[0] + bez[3]*bary[1] +
bez[4]*bary[2]);
Real FW = ((Real)2.0)*(bez[2]*bary[0] + bez[4]*bary[1] +
bez[5]*bary[2]);
Real duw = FU - FW;
Real dvw = FV - FW;
// Convert back to (x,y) coordinates.
Real m00 = sub0.X() - sub2.X();
Real m10 = sub0.Y() - sub2.Y();
Real m01 = sub1.X() - sub2.X();
Real m11 = sub1.Y() - sub2.Y();
Real inv = ((Real)1)/(m00*m11 - m10*m01);
FX = inv*(m11*duw - m10*dvw);
FY = inv*(m00*dvw - m01*duw);
return true;
}
