// return point that minimizes quadric error for edge [ea,eb]
Vector3d OptimalPoint(QuadricError q, int ea, int eb)
{
if (MinimizeQuadricPositionError == false)
{
return((mesh.GetVertex(ea) + mesh.GetVertex(eb)) * 0.5);
}
else
{
try {
return(q.OptimalPoint());
} catch {
// degenerate matrix, evaluate quadric at edge end and midpoints
// (could do line search here...)
Vector3d va = mesh.GetVertex(ea);
Vector3d vb = mesh.GetVertex(eb);
Vector3d c = (va + vb) * 0.5;
double fa = q.Evaluate(va);
double fb = q.Evaluate(vb);
double fc = q.Evaluate(c);
double m = MathUtil.Min(fa, fb, fc);
if (m == fa)
{
return(va);
}
else if (m == fb)
{
return(vb);
}
return(c);
}
}
}
// return point that minimizes quadric error for edge [ea,eb]
protected Vector3d OptimalPoint(int eid, ref QuadricError q, int ea, int eb)
{
// if we would like to preserve boundary, we need to know that here
// so that we properly score these edges
if (HaveBoundary && PreserveBoundaryShape)
{
if (mesh.IsBoundaryEdge(eid))
{
return((mesh.GetVertex(ea) + mesh.GetVertex(eb)) * 0.5);
}
else
{
if (IsBoundaryV(ea))
{
return(mesh.GetVertex(ea));
}
else if (IsBoundaryV(eb))
{
return(mesh.GetVertex(eb));
}
}
}
// [TODO] if we have constraints, we should apply them here, for same reason as bdry above...
if (MinimizeQuadricPositionError == false)
{
return(project((mesh.GetVertex(ea) + mesh.GetVertex(eb)) * 0.5));
}
else
{
Vector3d result = Vector3d.Zero;
if (q.OptimalPoint(ref result))
{
return(project(result));
}
// degenerate matrix, evaluate quadric at edge end and midpoints
// (could do line search here...)
Vector3d va = mesh.GetVertex(ea);
Vector3d vb = mesh.GetVertex(eb);
Vector3d c = project((va + vb) * 0.5);
double fa = q.Evaluate(ref va);
double fb = q.Evaluate(ref vb);
double fc = q.Evaluate(ref c);
double m = MathUtil.Min(fa, fb, fc);
if (m == fa)
{
return(va);
}
else if (m == fb)
{
return(vb);
}
return(c);
}
}
