int CalcTriangleCenter (const Point3d ** pts, Point3d & c)
{
static DenseMatrix a(2), inva(2);
static Vector rs(2), sol(2);
double h = Dist(*pts[0], *pts[1]);
Vec3d v1(*pts[0], *pts[1]);
Vec3d v2(*pts[0], *pts[2]);
rs.Elem(1) = v1 * v1;
rs.Elem(2) = v2 * v2;
a.Elem(1,1) = 2 * rs.Get(1);
a.Elem(1,2) = a.Elem(2,1) = 2 * (v1 * v2);
a.Elem(2,2) = 2 * rs.Get(2);
if (fabs (a.Det()) <= 1e-12 * h * h)
{
(*testout) << "CalcTriangleCenter: degenerated" << endl;
return 1;
}
CalcInverse (a, inva);
inva.Mult (rs, sol);
c = *pts[0];
v1 *= sol.Get(1);
v2 *= sol.Get(2);
c += v1;
c += v2;
return 0;
}
void Cholesky (const DenseMatrix & a,
DenseMatrix & l, Vector & d)
{
// Factors A = L D L^T
double x;
int i, j, k;
int n = a.Height();
// (*testout) << "a = " << a << endl;
l = a;
for (i = 1; i <= n; i++)
{
for (j = i; j <= n; j++)
{
x = l.Get(i, j);
for (k = 1; k < i; k++)
x -= l.Get(i, k) * l.Get(j, k) * d.Get(k);
if (i == j)
{
d.Elem(i) = x;
}
else
{
l.Elem(j, i) = x / d.Get(k);
}
}
}
for (i = 1; i <= n; i++)
{
l.Elem(i, i) = 1;
for (j = i+1; j <= n; j++)
l.Elem(i, j) = 0;
}
/*
// Multiply:
(*testout) << "multiplied factors: " << endl;
for (i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
{
x = 0;
for (k = 1; k <= n; k++)
x += l.Get(i, k) * l.Get(j, k) * d.Get(k);
(*testout) << x << " ";
}
(*testout) << endl;
*/
}
void MinFunction :: ApproximateHesse (const Vector & x,
DenseMatrix & hesse) const
{
int n = x.Size();
int i, j;
static Vector hx;
hx.SetSize(n);
double eps = 1e-6;
double f, f11, f12, f21, f22;
for (i = 1; i <= n; i++)
{
for (j = 1; j < i; j++)
{
hx = x;
hx.Elem(i) = x.Get(i) + eps;
hx.Elem(j) = x.Get(j) + eps;
f11 = Func(hx);
hx.Elem(i) = x.Get(i) + eps;
hx.Elem(j) = x.Get(j) - eps;
f12 = Func(hx);
hx.Elem(i) = x.Get(i) - eps;
hx.Elem(j) = x.Get(j) + eps;
f21 = Func(hx);
hx.Elem(i) = x.Get(i) - eps;
hx.Elem(j) = x.Get(j) - eps;
f22 = Func(hx);
hesse.Elem(i, j) = hesse.Elem(j, i) =
(f11 + f22 - f12 - f21) / (2 * eps * eps);
}
hx = x;
f = Func(x);
hx.Elem(i) = x.Get(i) + eps;
f11 = Func(hx);
hx.Elem(i) = x.Get(i) - eps;
f22 = Func(hx);
hesse.Elem(i, i) = (f11 + f22 - 2 * f) / (eps * eps);
}
// (*testout) << "hesse = " << hesse << endl;
}
int LDLtUpdate (DenseMatrix & l, Vector & d, double a, const Vector & u)
{
// Bemerkung: Es wird a aus R erlaubt
// Rueckgabewert: 0 .. D bleibt positiv definit
// 1 .. sonst
int i, j, n;
n = l.Height();
Vector v(n);
double t, told, xi;
told = 1;
v = u;
for (j = 1; j <= n; j++)
{
t = told + a * sqr (v.Elem(j)) / d.Get(j);
if (t <= 0)
{
(*testout) << "update err, t = " << t << endl;
return 1;
}
xi = a * v.Elem(j) / (d.Get(j) * t);
d.Elem(j) *= t / told;
for (i = j + 1; i <= n; i++)
{
v.Elem(i) -= v.Elem(j) * l.Elem(i, j);
l.Elem(i, j) += xi * v.Elem(i);
}
told = t;
}
return 0;
}
int
IntersectTriangleLine (const Point<3> ** tri, const Point<3> ** line)
{
Vec3d vl(*line[0], *line[1]);
Vec3d vt1(*tri[0], *tri[1]);
Vec3d vt2(*tri[0], *tri[2]);
Vec3d vrs(*tri[0], *line[0]);
static DenseMatrix a(3), ainv(3);
static Vector rs(3), lami(3);
int i;
/*
(*testout) << "Tri-Line inters: " << endl
<< "tri = " << *tri[0] << ", " << *tri[1] << ", " << *tri[2] << endl
<< "line = " << *line[0] << ", " << *line[1] << endl;
*/
for (i = 1; i <= 3; i++)
{
a.Elem(i, 1) = -vl.X(i);
a.Elem(i, 2) = vt1.X(i);
a.Elem(i, 3) = vt2.X(i);
rs.Elem(i) = vrs.X(i);
}
double det = a.Det();
double arel = vl.Length() * vt1.Length() * vt2.Length();
/*
double amax = 0;
for (i = 1; i <= 9; i++)
if (fabs (a.Get(i)) > amax)
amax = fabs(a.Get(i));
*/
// new !!!!
if (fabs (det) <= 1e-10 * arel)
{
#ifdef DEVELOP
// line parallel to triangle !
// cout << "ERROR: IntersectTriangleLine degenerated" << endl;
// (*testout) << "WARNING: IntersectTriangleLine degenerated\n";
/*
(*testout) << "lin-tri intersection: " << endl
<< "line = " << *line[0] << " - " << *line[1] << endl
<< "tri = " << *tri[0] << " - " << *tri[1] << " - " << *tri[2] << endl
<< "lami = " << lami << endl
<< "pc = " << ( *line[0] + lami.Get(1) * vl ) << endl
<< " = " << ( *tri[0] + lami.Get(2) * vt1 + lami.Get(3) * vt2) << endl
<< " a = " << a << endl
<< " ainv = " << ainv << endl
<< " det(a) = " << det << endl
<< " rs = " << rs << endl;
*/
#endif
return 0;
}
CalcInverse (a, ainv);
ainv.Mult (rs, lami);
// (*testout) << "lami = " << lami << endl;
double eps = 1e-6;
if (
(lami.Get(1) >= -eps && lami.Get(1) <= 1+eps &&
lami.Get(2) >= -eps && lami.Get(3) >= -eps &&
lami.Get(2) + lami.Get(3) <= 1+eps) && !
(lami.Get(1) >= eps && lami.Get(1) <= 1-eps &&
lami.Get(2) >= eps && lami.Get(3) >= eps &&
lami.Get(2) + lami.Get(3) <= 1-eps) )
{
#ifdef DEVELOP
// cout << "WARNING: IntersectTriangleLine degenerated" << endl;
(*testout) << "WARNING: IntersectTriangleLine numerical inexact" << endl;
(*testout) << "lin-tri intersection: " << endl
<< "line = " << *line[0] << " - " << *line[1] << endl
<< "tri = " << *tri[0] << " - " << *tri[1] << " - " << *tri[2] << endl
<< "lami = " << lami << endl
<< "pc = " << ( *line[0] + lami.Get(1) * vl ) << endl
<< " = " << ( *tri[0] + lami.Get(2) * vt1 + lami.Get(3) * vt2) << endl
<< " a = " << a << endl
<< " ainv = " << ainv << endl
<< " det(a) = " << det << endl
<< " rs = " << rs << endl;
#endif
}
if (lami.Get(1) >= 0 && lami.Get(1) <= 1 &&
lami.Get(2) >= 0 && lami.Get(3) >= 0 && lami.Get(2) + lami.Get(3) <= 1)
{
return 1;
}
return 0;
}