// Gmsh - Copyright (C) 1997-2019 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// issues on https://gitlab.onelab.info/gmsh/gmsh/issues.

#include <algorithm>
#include "STensor3.h"

// compute the largest inscribed ellipsoid

void SMetric3::print(const char *s) const
{
  printf(" metric %s : %12.5E %12.5E %12.5E %12.5E %12.5E %12.5E \n", s,
         (*this)(0, 0), (*this)(1, 1), (*this)(2, 2), (*this)(0, 1),
         (*this)(0, 2), (*this)(1, 2));
}

void STensor3::print(const char *s) const
{
  printf(
    " tensor %s : \n"
    " %12.5E %12.5E %12.5E \n %12.5E %12.5E %12.5E \n %12.5E %12.5E %12.5E \n",
    s, (*this)(0, 0), (*this)(0, 1), (*this)(0, 2), (*this)(1, 0),
    (*this)(1, 1), (*this)(1, 2), (*this)(2, 0), (*this)(2, 1), (*this)(2, 2));
}

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 intersection_alauzet(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));
  // is this required??
  v0.normalize();
  v1.normalize();
  v2.normalize();
  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));
  SMetric3 iv(l0, l1, l2, v0, v1, v2);
  return iv;
}

// preserve orientation of m1 !!!
SMetric3 intersection_conserveM1(const SMetric3 &m1, const SMetric3 &m2)
{
  // we should do
  // return intersection (m1,m2);
  fullMatrix<double> V(3, 3);
  fullVector<double> S(3);
  m1.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));
  SMetric3 iv(l0, l1, l2, v0, v1, v2);
  return iv;
}

namespace {

  double anisoRatio2D(double v0x, double v0y, double v0z, double v1x,
                      double v1y, double v1z, double v2x, double v2y,
                      double v2z, double s0, double s1, double s2)
  {
    static const double eps = 1.e-8;

    double ratio;
    if(v0x * v0x + v0y * v0y + (v0z - 1.) * (v0z - 1.) <
       eps) // If 1st eigenvect corresponds to z dir. ...
      ratio =
        std::min(fabs(s1 / s2),
                 fabs(s2 / s1)); // ... consider ratio of 2nd and 3rd eigenval.
    else if(v1x * v1x + v1y * v1y + (v1z - 1.) * (v1z - 1.) <
            eps) // If 2nd eigenvect corresponds to z dir. ...
      ratio =
        std::min(fabs(s0 / s2),
                 fabs(s2 / s0)); // ... consider ratio of 1st and 3rd eigenval.
    else if(v2x * v2x + v2y * v2y + (v2z - 1.) * (v2z - 1.) <
            eps) // If 3rd eigenvect corresponds to z dir. ...
      ratio =
        std::min(fabs(s0 / s1),
                 fabs(s1 / s0)); // ... consider ratio of 1st and 2nd eigenval.
    else {
      printf("Error in anisoRatio2D: z direction not found!\n");
      ratio = 0.;
    }

    return ratio;
  }

} // namespace

// preserve orientation of the most anisotropic metric !!!
SMetric3 intersection_conserve_mostaniso(const SMetric3 &m1, const SMetric3 &m2)
{
  fullMatrix<double> V1(3, 3);
  fullVector<double> S1(3);
  m1.eig(V1, S1, true);
  double ratio1 =
    fabs(S1(0) / S1(2)); // Minimum ratio because we take sorted eigenvalues
  fullMatrix<double> V2(3, 3);
  fullVector<double> S2(3);
  m2.eig(V2, S2, true);
  double ratio2 =
    fabs(S2(0) / S2(2)); // Minimum ratio because we take sorted eigenvalues

  if(ratio1 < ratio2)
    return intersection_conserveM1(m1, m2);
  else
    return intersection_conserveM1(m2, m1);
}

// preserve orientation of the most anisotropic metric in 2D!!!
SMetric3 intersection_conserve_mostaniso_2d(const SMetric3 &m1,
                                            const SMetric3 &m2)
{
  fullMatrix<double> V1(3, 3);
  fullVector<double> S1(3);
  m1.eig(V1, S1, false);
  double ratio1 =
    anisoRatio2D(V1(0, 0), V1(1, 0), V1(2, 0), V1(0, 1), V1(1, 1), V1(2, 1),
                 V1(0, 2), V1(1, 2), V1(2, 2), S1(0), S1(1), S1(2));

  fullMatrix<double> V2(3, 3);
  fullVector<double> S2(3);
  m2.eig(V2, S2, false);
  double ratio2 =
    anisoRatio2D(V2(0, 0), V2(1, 0), V2(2, 0), V2(0, 1), V2(1, 1), V2(2, 1),
                 V2(0, 2), V2(1, 2), V2(2, 2), S2(0), S2(1), S2(2));

  if(ratio1 < ratio2)
    return intersection_conserveM1(m1, m2);
  else
    return intersection_conserveM1(m2, m1);
}

// (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 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();
}
