netgen/libsrc/meshing/findip.hpp

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// find inner point
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inline void Minimize (const NgArray<Vec3d> & a,
const NgArray<double> & c,
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int * act,
Vec<3> & x, double & f,
int * sol)
{
int act1[4];
Mat<3> m, inv;
Vec<3> rs, xmax, center;
f = 1e99;
for (int j = 0; j < 5; j++)
{
for (int hk = 0, k = 0; hk < 4; hk++)
{
if (hk == j) k++;
act1[hk] = act[k];
k++;
}
for (int k = 0; k < 3; k++)
{
m(k, 0) = a[act1[0]].X() - a[act1[k+1]].X();
m(k, 1) = a[act1[0]].Y() - a[act1[k+1]].Y();
m(k, 2) = a[act1[0]].Z() - a[act1[k+1]].Z();
rs(k) = c[act1[k+1]] - c[act1[0]];
}
/*
(*testout) << "act1 = "
<< act1[0] << " "
<< act1[1] << " "
<< act1[2] << " "
<< act1[3] << endl;
(*testout) << "Det = " << Det(m) << endl;
*/
if (fabs (Det (m)) > 1e-10)
{
CalcInverse (m, inv);
xmax = inv * rs;
double fmax = -1e10;
for (int k = 0; k < 5; k++)
{
double hd =
xmax(0) * a[act[k]].X() + xmax(1) * a[act[k]].Y() + xmax(2) * a[act[k]].Z() + c[act[k]];
if (hd > fmax) fmax = hd;
}
if (fmax < f)
{
f = fmax;
x = xmax;
for (int k = 0; k < 4; k++)
sol[k] = act1[k];
}
}
}
}
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template <typename POINTArray, typename FACEArray>
inline int FindInnerPoint (POINTArray & points,
FACEArray & faces,
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Point3d & p)
{
static int timer = NgProfiler::CreateTimer ("FindInnerPoint");
NgProfiler::RegionTimer reg (timer);
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NgArray<Vec3d> a;
NgArray<double> c;
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Mat<3> m, inv;
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Vec<3> rs, x = 0.0, center;
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double f;
int nf = faces.Size();
// minimize_x max_i a_i x + c_i
a.SetSize (nf+4);
c.SetSize (nf+4);
for (int i = 0; i < nf; i++)
{
Point3d p1 = points.Get(faces[i][0]);
a[i] = Cross (points.Get(faces[i][1]) - p1,
points.Get(faces[i][2]) - p1);
a[i] /= a[i].Length();
c[i] = - (a[i].X() * p1.X() + a[i].Y() * p1.Y() + a[i].Z() * p1.Z());
}
/*
center = 0;
for (int i = 0; i < points.Size(); i++)
center += Vec<3> (points[i]);
center /= points.Size();
*/
center = 0;
for (int i = 0; i < faces.Size(); i++)
for (int j = 0; j < 3; j++)
center += Vec<3> (points.Get(faces[i][j]));
center /= (3*faces.Size());
// (*testout) << "center = " << center << endl;
double hmax = 0;
for (int i = 0; i < nf; i++)
{
// const Element2d & el = faces[i];
// (*testout) << "el[" << i << "] = " << el << endl;
for (int j = 1; j <= 3; j++)
{
double hi = Dist (points.Get(faces[i].PNumMod(j)),
points.Get(faces[i].PNumMod(j+1)));
if (hi > hmax) hmax = hi;
}
}
// (*testout) << "hmax = " << hmax << endl;
a[nf] = Vec<3> (1, 0, 0);
c[nf] = -center(0) - hmax;
a[nf+1] = Vec<3> (0, 1, 0);
c[nf+1] = -center(1) - hmax;
a[nf+2] = Vec<3> (0, 0, 1);
c[nf+2] = -center(2) - hmax;
a[nf+3] = Vec<3> (-1, -1, -1);
c[nf+3] = center(0)+center(1)+center(2)-3*hmax;
/*
(*testout) << "findip, a now = " << endl << a << endl;
(*testout) << "findip, c now = " << endl << c << endl;
*/
int act[5] = { 0, nf, nf+1, nf+2, nf+3 };
int sol[4];
while (1)
{
/*
(*testout) << "try ";
for (int j = 0; j < 5; j++)
(*testout) << act[j] << " ";
*/
Minimize (a, c, act, x, f, sol);
/*
(*testout) << endl << "sol = ";
for (int j = 0; j < 4; j++)
(*testout) << sol[j] << " ";
(*testout) << " fmin = " << f << endl;
*/
for (int j = 0; j < 4; j++) act[j] = sol[j];
bool found = 0;
double maxval = f;
for (int j = 0; j < nf; j++)
{
double val = x(0) * a[j].X() + x(1) * a[j].Y() + x(2) * a[j].Z() + c[j];
if (val > maxval + hmax * 1e-6)
{
found = 1;
maxval = val;
act[4] = j;
}
}
// (*testout) << "maxval = " << maxval << endl;
if (!found) break;
}
// cout << "converged, f = " << f << endl;
p = Point3d (x(0), x(1), x(2));
// (*testout) << "findip, f = " << f << ", hmax = " << hmax << endl;
return (f < -1e-5 * hmax);
}