tools.h

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#ifndef COAL_INTERNAL_TOOLS_H
#define COAL_INTERNAL_TOOLS_H
 
#include "coal/fwd.hh"
 
#include <cmath>
#include <iostream>
#include <limits>
 
#include "coal/data_types.h"
 
namespace coal {
 
template <typename Derived>
static inline typename Derived::Scalar triple(
    const Eigen::MatrixBase<Derived>& x, const Eigen::MatrixBase<Derived>& y,
    const Eigen::MatrixBase<Derived>& z) {
  return x.derived().dot(y.derived().cross(z.derived()));
}
 
template <typename Derived1, typename Derived2, typename Derived3>
void generateCoordinateSystem(const Eigen::MatrixBase<Derived1>& _w,
                              const Eigen::MatrixBase<Derived2>& _u,
                              const Eigen::MatrixBase<Derived3>& _v) {
  typedef typename Derived1::Scalar T;
 
  Eigen::MatrixBase<Derived1>& w = const_cast<Eigen::MatrixBase<Derived1>&>(_w);
  Eigen::MatrixBase<Derived2>& u = const_cast<Eigen::MatrixBase<Derived2>&>(_u);
  Eigen::MatrixBase<Derived3>& v = const_cast<Eigen::MatrixBase<Derived3>&>(_v);
 
  T inv_length;
  if (std::abs(w[0]) >= std::abs(w[1])) {
    inv_length = (T)1.0 / sqrt(w[0] * w[0] + w[2] * w[2]);
    u[0] = -w[2] * inv_length;
    u[1] = (T)0;
    u[2] = w[0] * inv_length;
    v[0] = w[1] * u[2];
    v[1] = w[2] * u[0] - w[0] * u[2];
    v[2] = -w[1] * u[0];
  } else {
    inv_length = (T)1.0 / sqrt(w[1] * w[1] + w[2] * w[2]);
    u[0] = (T)0;
    u[1] = w[2] * inv_length;
    u[2] = -w[1] * inv_length;
    v[0] = w[1] * u[2] - w[2] * u[1];
    v[1] = -w[0] * u[2];
    v[2] = w[0] * u[1];
  }
}
 
/* ----- Start Matrices ------ */
template <typename Derived, typename OtherDerived>
void relativeTransform(const Eigen::MatrixBase<Derived>& R1,
                       const Eigen::MatrixBase<OtherDerived>& t1,
                       const Eigen::MatrixBase<Derived>& R2,
                       const Eigen::MatrixBase<OtherDerived>& t2,
                       const Eigen::MatrixBase<Derived>& R,
                       const Eigen::MatrixBase<OtherDerived>& t) {
  const_cast<Eigen::MatrixBase<Derived>&>(R) = R1.transpose() * R2;
  const_cast<Eigen::MatrixBase<OtherDerived>&>(t) = R1.transpose() * (t2 - t1);
}
 
template <typename Derived, typename Vector>
void eigen(const Eigen::MatrixBase<Derived>& m,
           typename Derived::Scalar dout[3], Vector* vout) {
  typedef typename Derived::Scalar S;
  Derived R(m.derived());
  int n = 3;
  int j, iq, ip, i;
  S tresh, theta, tau, t, sm, s, h, g, c;
 
  S b[3];
  S z[3];
  S v[3][3] = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
  S d[3];
 
  for (ip = 0; ip < n; ++ip) {
    b[ip] = d[ip] = R(ip, ip);
    z[ip] = 0;
  }
 
  for (i = 0; i < 50; ++i) {
    sm = 0;
    for (ip = 0; ip < n; ++ip)
      for (iq = ip + 1; iq < n; ++iq) sm += std::abs(R(ip, iq));
    if (sm == 0.0) {
      vout[0] << v[0][0], v[0][1], v[0][2];
      vout[1] << v[1][0], v[1][1], v[1][2];
      vout[2] << v[2][0], v[2][1], v[2][2];
      dout[0] = d[0];
      dout[1] = d[1];
      dout[2] = d[2];
      return;
    }
 
    if (i < 3)
      tresh = Scalar(0.2 * sm / (n * n));
    else
      tresh = 0.0;
 
    for (ip = 0; ip < n; ++ip) {
      for (iq = ip + 1; iq < n; ++iq) {
        g = Scalar(100) * std::abs(R(ip, iq));
        if (i > 3 && std::abs(d[ip]) + g == std::abs(d[ip]) &&
            std::abs(d[iq]) + g == std::abs(d[iq]))
          R(ip, iq) = 0.0;
        else if (std::abs(R(ip, iq)) > tresh) {
          h = d[iq] - d[ip];
          if (std::abs(h) + g == std::abs(h))
            t = (R(ip, iq)) / h;
          else {
            theta = Scalar(0.5) * h / (R(ip, iq));
            t = 1 / (std::abs(theta) + std::sqrt(1 + theta * theta));
            if (theta < 0.0) t = -t;
          }
          c = 1 / std::sqrt(1 + t * t);
          s = t * c;
          tau = s / (1 + c);
          h = t * R(ip, iq);
          z[ip] -= h;
          z[iq] += h;
          d[ip] -= h;
          d[iq] += h;
          R(ip, iq) = 0.0;
          for (j = 0; j < ip; ++j) {
            g = R(j, ip);
            h = R(j, iq);
            R(j, ip) = g - s * (h + g * tau);
            R(j, iq) = h + s * (g - h * tau);
          }
          for (j = ip + 1; j < iq; ++j) {
            g = R(ip, j);
            h = R(j, iq);
            R(ip, j) = g - s * (h + g * tau);
            R(j, iq) = h + s * (g - h * tau);
          }
          for (j = iq + 1; j < n; ++j) {
            g = R(ip, j);
            h = R(iq, j);
            R(ip, j) = g - s * (h + g * tau);
            R(iq, j) = h + s * (g - h * tau);
          }
          for (j = 0; j < n; ++j) {
            g = v[j][ip];
            h = v[j][iq];
            v[j][ip] = g - s * (h + g * tau);
            v[j][iq] = h + s * (g - h * tau);
          }
        }
      }
    }
    for (ip = 0; ip < n; ++ip) {
      b[ip] += z[ip];
      d[ip] = b[ip];
      z[ip] = 0.0;
    }
  }
 
  std::cerr << "eigen: too many iterations in Jacobi transform." << std::endl;
 
  return;
}
 
template <typename Derived, typename OtherDerived>
bool isEqual(const Eigen::MatrixBase<Derived>& lhs,
             const Eigen::MatrixBase<OtherDerived>& rhs,
             const Scalar tol = std::numeric_limits<Scalar>::epsilon() * 100) {
  return ((lhs - rhs).array().abs() < tol).all();
}
 
}  // namespace coal
 
#endif