// (1-t) * m1 + t * m2
SMetric3 interpolation (const SMetric3 &m1,
const SMetric3 &m2,
const double t)
{
SMetric3 im1 = m1.invert();
SMetric3 im2 = m2.invert();
im1 *= (1.-t);
im2 *= t;
im1 += im2;
return im1.invert();
}
SMetric3 intersection (const SMetric3 &m1, const SMetric3 &m2)
{
SMetric3 im1 = m1.invert();
fullMatrix<double> V(3,3);
fullVector<double> S(3);
im1 *= m2;
im1.eig(V,S,true);
SVector3 v0(V(0,0),V(1,0),V(2,0));
SVector3 v1(V(0,1),V(1,1),V(2,1));
SVector3 v2(V(0,2),V(1,2),V(2,2));
double l0 = std::max(dot(v0,m1,v0),dot(v0,m2,v0));
double l1 = std::max(dot(v1,m1,v1),dot(v1,m2,v1));
double l2 = std::max(dot(v2,m1,v2),dot(v2,m2,v2));
// Correction from the PhD thesis of Frederic Alauzet p.16
// If m2 = alpha*m1, then take the largest metric
static const double eps = 1.e-2; // Tolerance to detect triple eigenvalue (i.e. proportional metrics)
const double max_eig = std::max(S(0), std::max(S(1), S(2)));
const double min_eig = std::min(S(0), std::min(S(1), S(2)));
const double range_eig = fabs((max_eig-min_eig)/max_eig);
if (range_eig < eps) return (max_eig >= 1.) ? m2 : m1;
SMetric3 iv(l0,l1,l2,v0,v1,v2);
return iv;
}
SMetric3 interpolation (const SMetric3 &m1,
const SMetric3 &m2,
const SMetric3 &m3,
const double u,
const double v)
{
SMetric3 im1 = m1.invert();
SMetric3 im2 = m2.invert();
SMetric3 im3 = m3.invert();
im1 *= (1.-u-v);
im2 *= u;
im3 *= v;
im1 += im2;
im1 += im3;
return im1.invert();
}
SMetric3 interpolation (const SMetric3 &m1,
const SMetric3 &m2,
const SMetric3 &m3,
const SMetric3 &m4,
const double u,
const double v,
const double w)
{
SMetric3 im1 = m1.invert();
SMetric3 im2 = m2.invert();
SMetric3 im3 = m3.invert();
SMetric3 im4 = m4.invert();
im1 *= (1.-u-v-w);
im2 *= u;
im3 *= v;
im4 *= w;
im1 += im2;
im1 += im3;
im1 += im4;
return im1.invert();
}
