opencv_contrib/modules/surface_matching/src/c_utils.hpp

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// Author: Tolga Birdal <tbirdal AT gmail.com>

#ifndef __OPENCV_SURFACE_MATCHING_UTILS_HPP_
#define __OPENCV_SURFACE_MATCHING_UTILS_HPP_

#include <cmath>
#include <cstdio>

namespace cv
{
namespace ppf_match_3d
{

const float EPS = 1.192092896e-07F;        /* smallest such that 1.0+FLT_EPSILON != 1.0 */

#ifndef M_PI
#define M_PI  3.1415926535897932384626433832795
#endif

static inline double TNorm3(const double v[])
{
  return (sqrt(v[0]*v[0]+v[1]*v[1]+v[2]*v[2]));
}

static inline void TNormalize3(double v[])
{
  double normTemp=TNorm3(v);
  if (normTemp>0)
  {
    v[0]/=normTemp;
    v[1]/=normTemp;
    v[2]/=normTemp;
  }
}

static inline double TDot3(const double a[3], const double b[3])
{
  return  ((a[0])*(b[0])+(a[1])*(b[1])+(a[2])*(b[2]));
}

static inline void TCross(const double a[], const double b[], double c[])
{
  c[0] = (a[1])*(b[2])-(a[2])*(b[1]);
  c[1] = (a[2])*(b[0])-(a[0])*(b[2]);
  c[2] = (a[0])*(b[1])-(a[1])*(b[0]);
}

static inline double TAngle3(const double a[3], const double b[3])
{
  double c[3];
  TCross(a,b,c);
  return (atan2(TNorm3(c), TDot3(a, b)));
}

static inline void matrixProduct33(double *A, double *B, double *R)
{
  R[0] = A[0] * B[0] + A[1] * B[3] + A[2] * B[6];
  R[1] = A[0] * B[1] + A[1] * B[4] + A[2] * B[7];
  R[2] = A[0] * B[2] + A[1] * B[5] + A[2] * B[8];

  R[3] = A[3] * B[0] + A[4] * B[3] + A[5] * B[6];
  R[4] = A[3] * B[1] + A[4] * B[4] + A[5] * B[7];
  R[5] = A[3] * B[2] + A[4] * B[5] + A[5] * B[8];

  R[6] = A[6] * B[0] + A[7] * B[3] + A[8] * B[6];
  R[7] = A[6] * B[1] + A[7] * B[4] + A[8] * B[7];
  R[8] = A[6] * B[2] + A[7] * B[5] + A[8] * B[8];
}

// A is a vector
static inline void matrixProduct133(double *A, double *B, double *R)
{
  R[0] = A[0] * B[0] + A[1] * B[3] + A[2] * B[6];
  R[1] = A[0] * B[1] + A[1] * B[4] + A[2] * B[7];
  R[2] = A[0] * B[2] + A[1] * B[5] + A[2] * B[8];
}

static inline void matrixProduct331(const double A[9], const double b[3], double r[3])
{
  r[0] = A[0] * b[0] + A[1] * b[1] + A[2] * b[2];
  r[1] = A[3] * b[0] + A[4] * b[1] + A[5] * b[2];
  r[2] = A[6] * b[0] + A[7] * b[1] + A[8] * b[2];
}

static inline void matrixTranspose33(double *A, double *At)
{
  At[0] = A[0];
  At[4] = A[4];
  At[8] = A[8];
  At[1] = A[3];
  At[2] = A[6];
  At[3] = A[1];
  At[5] = A[7];
  At[6] = A[2];
  At[7] = A[5];
}

static inline void matrixProduct44(const double A[16], const double B[16], double R[16])
{
  R[0] = A[0] * B[0] + A[1] * B[4] + A[2] * B[8] + A[3] * B[12];
  R[1] = A[0] * B[1] + A[1] * B[5] + A[2] * B[9] + A[3] * B[13];
  R[2] = A[0] * B[2] + A[1] * B[6] + A[2] * B[10] + A[3] * B[14];
  R[3] = A[0] * B[3] + A[1] * B[7] + A[2] * B[11] + A[3] * B[15];

  R[4] = A[4] * B[0] + A[5] * B[4] + A[6] * B[8] + A[7] * B[12];
  R[5] = A[4] * B[1] + A[5] * B[5] + A[6] * B[9] + A[7] * B[13];
  R[6] = A[4] * B[2] + A[5] * B[6] + A[6] * B[10] + A[7] * B[14];
  R[7] = A[4] * B[3] + A[5] * B[7] + A[6] * B[11] + A[7] * B[15];

  R[8] = A[8] * B[0] + A[9] * B[4] + A[10] * B[8] + A[11] * B[12];
  R[9] = A[8] * B[1] + A[9] * B[5] + A[10] * B[9] + A[11] * B[13];
  R[10] = A[8] * B[2] + A[9] * B[6] + A[10] * B[10] + A[11] * B[14];
  R[11] = A[8] * B[3] + A[9] * B[7] + A[10] * B[11] + A[11] * B[15];

  R[12] = A[12] * B[0] + A[13] * B[4] + A[14] * B[8] + A[15] * B[12];
  R[13] = A[12] * B[1] + A[13] * B[5] + A[14] * B[9] + A[15] * B[13];
  R[14] = A[12] * B[2] + A[13] * B[6] + A[14] * B[10] + A[15] * B[14];
  R[15] = A[12] * B[3] + A[13] * B[7] + A[14] * B[11] + A[15] * B[15];
}

static inline void matrixProduct441(const double A[16], const double B[4], double R[4])
{
  R[0] = A[0] * B[0] + A[1] * B[1] + A[2] * B[2] + A[3] * B[3];
  R[1] = A[4] * B[0] + A[5] * B[1] + A[6] * B[2] + A[7] * B[3];
  R[2] = A[8] * B[0] + A[9] * B[1] + A[10] * B[2] + A[11] * B[3];
  R[3] = A[12] * B[0] + A[13] * B[1] + A[14] * B[2] + A[15] * B[3];
}

static inline void matrixPrint(double *A, int m, int n)
{
  int i, j;

  for (i = 0; i < m; i++)
  {
    printf("  ");
    for (j = 0; j < n; j++)
    {
      printf(" %0.6f ", A[i * n + j]);
    }
    printf("\n");
  }
}

static inline void matrixIdentity(int n, double *A)
{
  int i;

  for (i = 0; i < n*n; i++)
  {
    A[i] = 0.0;
  }

  for (i = 0; i < n; i++)
  {
    A[i * n + i] = 1.0;
  }
}

static inline void rtToPose(const double R[9], const double t[3], double Pose[16])
{
  Pose[0]=R[0];
  Pose[1]=R[1];
  Pose[2]=R[2];
  Pose[4]=R[3];
  Pose[5]=R[4];
  Pose[6]=R[5];
  Pose[8]=R[6];
  Pose[9]=R[7];
  Pose[10]=R[8];
  Pose[3]=t[0];
  Pose[7]=t[1];
  Pose[11]=t[2];

  Pose[15] = 1;
}


static inline void poseToRT(const double Pose[16], double R[9], double t[3])
{
  R[0] = Pose[0];
  R[1] = Pose[1];
  R[2] = Pose[2];
  R[3] = Pose[4];
  R[4] = Pose[5];
  R[5] = Pose[6];
  R[6] = Pose[8];
  R[7] = Pose[9];
  R[8] = Pose[10];

  t[0]=Pose[3];
  t[1]=Pose[7];
  t[2]=Pose[11];
}

static inline void poseToR(const double Pose[16], double R[9])
{
  R[0] = Pose[0];
  R[1] = Pose[1];
  R[2] = Pose[2];
  R[3] = Pose[4];
  R[4] = Pose[5];
  R[5] = Pose[6];
  R[6] = Pose[8];
  R[7] = Pose[9];
  R[8] = Pose[10];
}

/**
 *  \brief Axis angle to rotation but only compute y and z components
 */
static inline void aaToRyz(double angle, const double r[3], double row2[3], double row3[3])
{
  const double sinA=sin(angle);
  const double cosA=cos(angle);
  const double cos1A=(1-cosA);

  row2[0] =  0.f;
  row2[1] = cosA;
  row2[2] =  0.f;
  row3[0] =  0.f;
  row3[1] =  0.f;
  row3[2] = cosA;

  row2[0] +=  r[2] * sinA;
  row2[2] += -r[0] * sinA;
  row3[0] += -r[1] * sinA;
  row3[1] +=  r[0] * sinA;

  row2[0] += r[1] * r[0] * cos1A;
  row2[1] += r[1] * r[1] * cos1A;
  row2[2] += r[1] * r[2] * cos1A;
  row3[0] += r[2] * r[0] * cos1A;
  row3[1] += r[2] * r[1] * cos1A;
  row3[2] += r[2] * r[2] * cos1A;
}

/**
 *  \brief Axis angle to rotation
 */
static inline void aaToR(double angle, const double r[3], double R[9])
{
  const double sinA=sin(angle);
  const double cosA=cos(angle);
  const double cos1A=(1-cosA);
  double *row1 = &R[0];
  double *row2 = &R[3];
  double *row3 = &R[6];

  row1[0] =  cosA;
  row1[1] = 0.0f;
  row1[2] =  0.f;
  row2[0] =  0.f;
  row2[1] = cosA;
  row2[2] =  0.f;
  row3[0] =  0.f;
  row3[1] =  0.f;
  row3[2] = cosA;

  row1[1] += -r[2] * sinA;
  row1[2] +=  r[1] * sinA;
  row2[0] +=  r[2] * sinA;
  row2[2] += -r[0] * sinA;
  row3[0] += -r[1] * sinA;
  row3[1] +=  r[0] * sinA;

  row1[0] += r[0] * r[0] * cos1A;
  row1[1] += r[0] * r[1] * cos1A;
  row1[2] += r[0] * r[2] * cos1A;
  row2[0] += r[1] * r[0] * cos1A;
  row2[1] += r[1] * r[1] * cos1A;
  row2[2] += r[1] * r[2] * cos1A;
  row3[0] += r[2] * r[0] * cos1A;
  row3[1] += r[2] * r[1] * cos1A;
  row3[2] += r[2] * r[2] * cos1A;
}

/**
 *  \brief Compute a rotation in order to rotate around X direction
 */
static inline void getUnitXRotation(double angle, double R[9])
{
  const double sinA=sin(angle);
  const double cosA=cos(angle);
  double *row1 = &R[0];
  double *row2 = &R[3];
  double *row3 = &R[6];

  row1[0] =  1;
  row1[1] = 0.0f;
  row1[2] =  0.f;
  row2[0] =  0.f;
  row2[1] = cosA;
  row2[2] =  -sinA;
  row3[0] =  0.f;
  row3[1] =  sinA;
  row3[2] = cosA;
}
/**
 *  \brief Compute a transformation in order to rotate around X direction
 */
static inline void getUnitXRotation_44(double angle, double T[16])
{
  const double sinA=sin(angle);
  const double cosA=cos(angle);
  double *row1 = &T[0];
  double *row2 = &T[4];
  double *row3 = &T[8];

  row1[0] =  1;
  row1[1] = 0.0f;
  row1[2] =  0.f;
  row2[0] =  0.f;
  row2[1] = cosA;
  row2[2] =  -sinA;
  row3[0] =  0.f;
  row3[1] =  sinA;
  row3[2] = cosA;

  row1[3]=0;
  row2[3]=0;
  row3[3]=0;
  T[3]=0;
  T[7]=0;
  T[11]=0;
  T[15] = 1;
}

/**
 *  \brief Compute the yz components of the transformation needed to rotate n1 onto x axis and p1 to origin
 */
static inline void computeTransformRTyz(const double p1[4], const double n1[4], double row2[3], double row3[3], double t[3])
{
  // dot product with x axis
  double angle=acos( n1[0] );

  // cross product with x axis
  double axis[3]={0, n1[2], -n1[1]};
  double axisNorm;

  // we try to project on the ground plane but it's already parallel
  if (n1[1]==0 && n1[2]==0)
  {
    axis[1]=1;
    axis[2]=0;
  }
  else
  {
    axisNorm=sqrt(axis[2]*axis[2]+axis[1]*axis[1]);

    if (axisNorm>EPS)
    {
      axis[1]/=axisNorm;
      axis[2]/=axisNorm;
    }
  }

  aaToRyz(angle, axis, row2, row3);

  t[1] = row2[0] * (-p1[0]) + row2[1] * (-p1[1]) + row2[2] * (-p1[2]);
  t[2] = row3[0] * (-p1[0]) + row3[1] * (-p1[1]) + row3[2] * (-p1[2]);
}

/**
 *  \brief Compute the transformation needed to rotate n1 onto x axis and p1 to origin
 */
static inline void computeTransformRT(const double p1[4], const double n1[4], double R[9], double t[3])
{
  // dot product with x axis
  double angle=acos( n1[0] );

  // cross product with x axis
  double axis[3]={0, n1[2], -n1[1]};
  double axisNorm;
  double *row1, *row2, *row3;

  // we try to project on the ground plane but it's already parallel
  if (n1[1]==0 && n1[2]==0)
  {
    axis[1]=1;
    axis[2]=0;
  }
  else
  {
    axisNorm=sqrt(axis[2]*axis[2]+axis[1]*axis[1]);

    if (axisNorm>EPS)
    {
      axis[1]/=axisNorm;
      axis[2]/=axisNorm;
    }
  }

  aaToR(angle, axis, R);
  row1 = &R[0];
  row2 = &R[3];
  row3 = &R[6];

  t[0] = row1[0] * (-p1[0]) + row1[1] * (-p1[1]) + row1[2] * (-p1[2]);
  t[1] = row2[0] * (-p1[0]) + row2[1] * (-p1[1]) + row2[2] * (-p1[2]);
  t[2] = row3[0] * (-p1[0]) + row3[1] * (-p1[1]) + row3[2] * (-p1[2]);
}

/**
 *  \brief Flip a normal to the viewing direction
 *
 *  \param [in] point Scene point
 *  \param [in] vp_x X component of view direction
 *  \param [in] vp_y Y component of view direction
 *  \param [in] vp_z Z component of view direction
 *  \param [in] nx X component of normal
 *  \param [in] ny Y component of normal
 *  \param [in] nz Z component of normal
 */
static inline void flipNormalViewpoint(const float* point, double vp_x, double vp_y, double vp_z, double *nx, double *ny, double *nz)
{
  double cos_theta;

  // See if we need to flip any plane normals
  vp_x -= (double)point[0];
  vp_y -= (double)point[1];
  vp_z -= (double)point[2];

  // Dot product between the (viewpoint - point) and the plane normal
  cos_theta = (vp_x * (*nx) + vp_y * (*ny) + vp_z * (*nz));

  // Flip the plane normal
  if (cos_theta < 0)
  {
    (*nx) *= -1;
    (*ny) *= -1;
    (*nz) *= -1;
  }
}
/**
 *  \brief Flip a normal to the viewing direction
 *
 *  \param [in] point Scene point
 *  \param [in] vp_x X component of view direction
 *  \param [in] vp_y Y component of view direction
 *  \param [in] vp_z Z component of view direction
 *  \param [in] nx X component of normal
 *  \param [in] ny Y component of normal
 *  \param [in] nz Z component of normal
 */
static inline void flipNormalViewpoint_32f(const float* point, float vp_x, float vp_y, float vp_z, float *nx, float *ny, float *nz)
{
  float cos_theta;

  // See if we need to flip any plane normals
  vp_x -= (float)point[0];
  vp_y -= (float)point[1];
  vp_z -= (float)point[2];

  // Dot product between the (viewpoint - point) and the plane normal
  cos_theta = (vp_x * (*nx) + vp_y * (*ny) + vp_z * (*nz));

  // Flip the plane normal
  if (cos_theta < 0)
  {
    (*nx) *= -1;
    (*ny) *= -1;
    (*nz) *= -1;
  }
}

/**
 *  \brief Convert a rotation matrix to axis angle representation
 *
 *  \param [in] R Rotation matrix
 *  \param [in] axis Axis vector
 *  \param [in] angle Angle in radians
 */
static inline void dcmToAA(double *R, double *axis, double *angle)
{
  double d1 = R[7] - R[5];
  double d2 = R[2] - R[6];
  double d3 = R[3] - R[1];

  double norm = sqrt(d1 * d1 + d2 * d2 + d3 * d3);
  double x = (R[7] - R[5]) / norm;
  double y = (R[2] - R[6]) / norm;
  double z = (R[3] - R[1]) / norm;

  *angle = acos((R[0] + R[4] + R[8] - 1.0) * 0.5);

  axis[0] = x;
  axis[1] = y;
  axis[2] = z;
}

/**
 *  \brief Convert axis angle representation to rotation matrix
 *
 *  \param [in] axis Axis Vector
 *  \param [in] angle Angle (In radians)
 *  \param [in] R 3x3 Rotation matrix
 */
static inline void aaToDCM(double *axis, double angle, double *R)
{
  double ident[9]={1,0,0,0,1,0,0,0,1};
  double n[9] = { 0.0, -axis[2], axis[1],
                  axis[2], 0.0, -axis[0],
                  -axis[1], axis[0], 0.0
                };

  double nsq[9];
  double c, s;
  int i;

  //c = 1-cos(angle);
  c = cos(angle);
  s = sin(angle);

  matrixProduct33(n, n, nsq);

  for (i = 0; i < 9; i++)
  {
    const double sni = n[i]*s;
    const double cnsqi = nsq[i]*(c);
    R[i]=ident[i]+sni+cnsqi;
  }

  // The below code is the matrix based implemntation of the above
  // double nsq[9], sn[9], cnsq[9], tmp[9];
  //matrix_scale(3, 3, n, s, sn);
  //matrix_scale(3, 3, nsq, (1 - c), cnsq);
  //matrix_sum(3, 3, 3, 3, ident, sn, tmp);
  //matrix_sum(3, 3, 3, 3, tmp, cnsq, R);
}

/**
 *  \brief Convert a discrete cosine matrix to quaternion
 *
 *  \param [in] R Rotation Matrix
 *  \param [in] q Quaternion
 */
static inline void dcmToQuat(double *R, double *q)
{
  double n4; // the norm of quaternion multiplied by 4
  double tr = R[0] + R[4] + R[8]; // trace of martix
  double factor;

  if (tr > 0.0)
  {
    q[1] = R[5] - R[7];
    q[2] = R[6] - R[2];
    q[3] = R[1] - R[3];
    q[0] = tr + 1.0;
    n4 = q[0];
  }
  else
    if ((R[0] > R[4]) && (R[0] > R[8]))
    {
      q[1] = 1.0 + R[0] - R[4] - R[8];
      q[2] = R[3] + R[1];
      q[3] = R[6] + R[2];
      q[0] = R[5] - R[7];
      n4 = q[1];
    }
    else
      if (R[4] > R[8])
      {
        q[1] = R[3] + R[1];
        q[2] = 1.0 + R[4] - R[0] - R[8];
        q[3] = R[7] + R[5];
        q[0] = R[6] - R[2];
        n4 = q[2];
      }
      else
      {
        q[1] = R[6] + R[2];
        q[2] = R[7] + R[5];
        q[3] = 1.0 + R[8] - R[0] - R[4];
        q[0] = R[1] - R[3];
        n4 = q[3];
      }

  factor = 0.5 / sqrt(n4);
  q[0] *= factor;
  q[1] *= factor;
  q[2] *= factor;
  q[3] *= factor;
}

/**
 *  \brief Convert quaternion to a discrete cosine matrix
 *
 *  \param [in] q Quaternion (w is at first element)
 *  \param [in] R Rotation Matrix
 *
 */
static inline void quatToDCM(double *q, double *R)
{
  double sqw = q[0] * q[0];
  double sqx = q[1] * q[1];
  double sqy = q[2] * q[2];
  double sqz = q[3] * q[3];

  double tmp1, tmp2;

  R[0] =  sqx - sqy - sqz + sqw; // since sqw + sqx + sqy + sqz = 1
  R[4] = -sqx + sqy - sqz + sqw;
  R[8] = -sqx - sqy + sqz + sqw;

  tmp1 = q[1] * q[2];
  tmp2 = q[3] * q[0];

  R[1] = 2.0 * (tmp1 + tmp2);
  R[3] = 2.0 * (tmp1 - tmp2);

  tmp1 = q[1] * q[3];
  tmp2 = q[2] * q[0];

  R[2] = 2.0 * (tmp1 - tmp2);
  R[6] = 2.0 * (tmp1 + tmp2);

  tmp1 = q[2] * q[3];
  tmp2 = q[1] * q[0];

  R[5] = 2.0 * (tmp1 + tmp2);
  R[7] = 2.0 * (tmp1 - tmp2);
}

/**
 *  @brief Analytical solution to find the eigenvector corresponding to the smallest
 *  eigenvalue of a 3x3 matrix. As this implements the analytical solution, it's not
 *  really the most robust way. Whenever possible, this implementation can be replaced
 *  via a robust numerical scheme.
 *  @param [in] C The matrix
 *  @param [in] A The eigenvector corresponding to the lowest eigenvalue
 *  @author Tolga Birdal
 */
static inline void eigenLowest33(const double C[3][3], double A[3])
{
  const double a = C[0][0];
  const double b = C[0][1];
  const double c = C[0][2];
  const double d = C[1][1];
  const double e = C[1][2];
  const double f = C[2][2];
  const double t2 = c*c;
  const double t3 = e*e;
  const double t4 = b*t2;
  const double t5 = c*d*e;
  const double t34 = b*t3;
  const double t35 = a*c*e;
  const double t6 = t4+t5-t34-t35;
  const double t7 = 1.0/t6;
  const double t8 = a+d+f;
  const double t9 = b*b;
  const double t23 = a*d;
  const double t24 = a*f;
  const double t25 = d*f;
  const double t10 = t2+t3+t9-t23-t24-t25;
  const double t11 = t8*t10*(1.0/6.0);
  const double t12 = t8*t8;
  const double t20 = t8*t12*(1.0/2.7E1);
  const double t21 = b*c*e;
  const double t22 = a*d*f*(1.0/2.0);
  const double t26 = a*t3*(1.0/2.0);
  const double t27 = d*t2*(1.0/2.0);
  const double t28 = f*t9*(1.0/2.0);
  const double t14 = t9*(1.0/3.0);
  const double t15 = t2*(1.0/3.0);
  const double t16 = t3*(1.0/3.0);
  const double t17 = t12*(1.0/9.0);
  const double t30 = a*d*(1.0/3.0);
  const double t31 = a*f*(1.0/3.0);
  const double t32 = d*f*(1.0/3.0);
  const double t18 = t14+t15+t16+t17-t30-t31-t32;
  const double t19 = t18*t18;
  const double t36 = a*(1.0/3.0);
  const double t37 = d*(1.0/3.0);
  const double t38 = f*(1.0/3.0);
  const double t39 = t8*(t2+t3+t9-t23-t24-t25)*(1.0/6.0);
  const double t41 = t18*t19;
  const double t43 = e*t2;
  const double t60 = b*c*f;
  const double t61 = d*e*f;
  const double t44 = t43-t60-t61+e*t3;
  const double t45 = t7*t44;
  const double t57 = sqrt(3.0);
  const double t51 = b*c;
  const double t52 = d*e;
  const double t53 = e*f;
  const double t54 = t51+t52+t53;
  const double t62 = t11+t20+t21+t22-t26-t27-t28;
  const double t63 = t11+t20+t21+t22-t26-t27-t28;
  const double t64 = t11+t20+t21+t22-t26-t27-t28;
  const double t65 = t11+t20+t21+t22-t26-t27-t28;
  const double t66 = t36+t37+t38-t18*1.0/pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t62*t62),1.0/3.0)*(1.0/2.0)+t57*(t18*1.0/pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t64*t64),1.0/3.0)-pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t65*t65),1.0/3.0))*5.0E-1*sqrt(-1.0)-pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t63*t63),1.0/3.0)*(1.0/2.0);
  const double t67 = t11+t20+t21+t22-t26-t27-t28;
  const double t68 = t11+t20+t21+t22-t26-t27-t28;
  const double t69 = t11+t20+t21+t22-t26-t27-t28;
  const double t70 = t11+t20+t21+t22-t26-t27-t28;
  const double t76 = c*t3;
  const double t91 = a*c*f;
  const double t92 = b*e*f;
  const double t77 = t76-t91-t92+c*t2;
  const double t83 = a*c;
  const double t84 = b*e;
  const double t85 = c*f;
  const double t86 = t83+t84+t85;
  const double t93 = t11+t20+t21+t22-t26-t27-t28;
  const double t94 = t11+t20+t21+t22-t26-t27-t28;
  const double t95 = t11+t20+t21+t22-t26-t27-t28;
  const double t96 = t11+t20+t21+t22-t26-t27-t28;
  const double t97 = t36+t37+t38-t18*1.0/pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t93*t93),1.0/3.0)*(1.0/2.0)+t57*(t18*1.0/pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t95*t95),1.0/3.0)-pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t96*t96),1.0/3.0))*5.0E-1*sqrt(-1.0)-pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t94*t94),1.0/3.0)*(1.0/2.0);
  const double t98 = t11+t20+t21+t22-t26-t27-t28;
  const double t99 = t11+t20+t21+t22-t26-t27-t28;
  const double t100 = t11+t20+t21+t22-t26-t27-t28;
  const double t101 = t11+t20+t21+t22-t26-t27-t28;
  A[0] = t45-e*t7*(t66*t66)+t7*t54*(t36+t37+t38-t18*1.0/pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t67*t67),1.0/3.0)*(1.0/2.0)+t57*(t18*1.0/pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t69*t69),1.0/3.0)-pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t70*t70),1.0/3.0))*5.0E-1*sqrt(-1.0)-pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t68*t68),1.0/3.0)*(1.0/2.0));
  A[1] = -t7*t77+c*t7*(t97*t97)-t7*t86*(t36+t37+t38-t18*1.0/pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t98*t98),1.0/3.0)*(1.0/2.0)+t57*(t18*1.0/pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t100*t100),1.0/3.0)-pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t101*t101),1.0/3.0))*5.0E-1*sqrt(-1.0)-pow(t20+t21+t22-t26-t27-t28+t39+sqrt(-t41+t99*t99),1.0/3.0)*(1.0/2.0));
  A[2] = 1.0;
}

} // namespace ppf_match_3d

} // namespace cv

#endif