File indexing completed on 2025-01-05 03:58:40

 // SPDX-License-Identifier: LGPL-2.1-or-later
 //
 // SPDX-FileCopyrightText: 2014 Gerhard Holtkamp
 //
 
 /***********************************************************************
    3-Dim Vector and Matrix Definitions and Operations
 
    License:GNU LGPL Version 2+
 
   Author: Gerhard HOLTKAMP                   14-JAN-2012
  ***********************************************************************/
 
 //#include <iostream>
 #include "attlib.h"
 #include <cmath>
 using namespace std;
 
 /*********************************************************************/
 double atan20 (double y, double x)
 {
  /* redefine atan2 so that it doesn't crash when both x and y are 0 */
  double result;
 
  if ((x == 0) && (y == 0)) result = 0;
  else result = atan2 (y, x);
 
   return result;
 }
 
 
  Vec3::Vec3(double x, double y, double z)
          {assign(x, y, z);}
 
  Vec3::Vec3 (const Vec3& c)
   {
    for (int j = 0; j<3; j++) v[j] = c.v[j];
   }
 
 
  void Vec3::assign (double x, double y, double z)
   {
    v[0]=x; v[1]=y; v[2]=z;
   }
 
  double& Vec3::operator [] (unsigned index)
   {
    return (index < 3) ? * (v + index) : *v;
   }
 
  Vec3& Vec3::operator = (const Vec3& c)
   {
    for (int j = 0; j<3; j++) v[j] = c.v[j];
    return *this;
   }
 
  Vec3& Vec3::operator += (const Vec3& c)
   {
    for (int j = 0; j<3; j++) v[j] = v[j] + c.v[j];
    return *this;
   }
 
  Vec3& Vec3::operator -= (const Vec3& c)
   {
    for (int j = 0; j<3; j++) v[j] = v[j] - c.v[j];
    return *this;
   }
 
  Vec3& Vec3::operator *= (const Vec3& c)   // cross product
   {
    Vec3 result;
    result.v[0] = v[1] * c.v[2] - v[2] * c.v[1];
    result.v[1] = v[2] * c.v[0] - v[0] * c.v[2];
    result.v[2] = v[0] * c.v[1] - v[1] * c.v[0];
    for (int j = 0; j<3; j++) v[j] = result.v[j];
    return *this;
   }
 
  Vec3& Vec3::operator *= (double r)
   {
    for (int j = 0; j<3; j++) v[j] = r * v[j];
    return *this;
   }
 
  Vec3& Vec3::operator /= (double r)
   {
    double q;
 
    if (r < 1E-100) q = 0.0;
    else q = 1.0 / r;
    for (int j = 0; j<3; j++) v[j] = q * v[j];
    return *this;
   }
 
  double abs(const Vec3& c)    // absolute value
   {
    double result=0;
 
    for (int j=0; j<3; j++) result += c.v[j]*c.v[j];
    return sqrt(result);
   }
 
  double dot (const Vec3& c1, const Vec3& c2)  // dot product
   {
    double result=0;
 
    for (int j = 0; j<3; j++) result += c1.v[j]*c2.v[j];
    return result;
   }
 
  Vec3 operator + (const Vec3& c1, const Vec3& c2)
   {
    Vec3 result;
 
    for (int j = 0; j<3; j++) result.v[j] = c1.v[j] + c2.v[j];
    return result;
   }
 
  Vec3 operator - (const Vec3& c1, const Vec3& c2)
   {
    Vec3 result;
 
    for (int j = 0; j<3; j++) result.v[j] = c1.v[j] - c2.v[j];
 
    return result;
   }
 
  Vec3 operator * (double r, const Vec3& c1)
   {
    Vec3 result;
 
    for (int j = 0; j<3; j++) result.v[j] = r * c1.v[j];
    return result;
   }
 
  Vec3 operator * (const Vec3& c1, double r)
   {
    Vec3 result;
 
    for (int j = 0; j<3; j++) result.v[j] = c1.v[j] * r;
    return result;
   }
 
  Vec3 operator * (const Vec3& c1, const Vec3& c2)  // cross product
   {
    Vec3 result;
 
    result.v[0] = c1.v[1] * c2.v[2] - c1.v[2] * c2.v[1];
    result.v[1] = c1.v[2] * c2.v[0] - c1.v[0] * c2.v[2];
    result.v[2] = c1.v[0] * c2.v[1] - c1.v[1] * c2.v[0];
    return result;
   }
 
  Vec3 operator / (const Vec3& c1, double r)
   {
    double q;
    Vec3 result;
 
    if (r < 1E-100) q = 0.0;
    else q = 1.0 / r;
    for (int j = 0; j<3; j++) result.v[j] = q * c1.v[j];
    return result;
   }
 
  Vec3 vnorm (const Vec3& c)   // norm vector
   {
    int j;
    double q=0;
    Vec3 result;
 
    for (j=0; j<3; j++) q += c.v[j]*c.v[j];
    q =  sqrt(q);
    if (q < 1E-100) q = 0.0;
    else q = 1.0 / q;
    for (j=0; j<3; j++) result.v[j] = c.v[j]*q;
    return result;
   }
 
  Vec3 carpol (const Vec3& c)    // Cartesian -> Polar
   /* Convert vector from cartesian coordinates c = [x, y, z]
      into polar coordinates v = [rho, phi, theta]
      where rho is the radius, phi the "azimuth" and theta the
      "declination" (equatorial plane = 0, pole = 90ø)
   */
   {
    double  x, y, z, r;
    Vec3 result;
 
    x = c.v[0];
    y = c.v[1];
    z = c.v[2];
    r = x*x + y*y;
    result.v[0] = sqrt (r + z*z);
    result.v[1] = atan20 (y, x);
    if (result.v[1] < 0) result.v[1] += 2.0*M_PI;
    r = sqrt (r);
    result.v[2] = atan20 (z, r);
 
    return result;
   }
 
  Vec3 polcar (const Vec3& c)    // Polar -> Cartesian
   /* Convert vector from polar coordinates c = [rho, phi, theta]
      where rho is the radius, phi the "azimuth" and theta the
      "declination" (equatorial plane = 0, pole = 90ø)
      into vector v = [x, y, z] of cartesian coordinates.
   */
   {
    double  r;
    Vec3 result;
 
    r = c.v[0] * cos(c.v[2]);
    result.v[0] = r * cos(c.v[1]);
    result.v[1] = r * sin(c.v[1]);
    result.v[2] = c.v[0] * sin(c.v[2]);
 
    return result;
   }
 
  ostream& operator << (ostream& os, const Vec3& c)
   {
    os << "[" << c.v[0] << "," << c.v[1] << "," << c.v[2] << "]";
    return os;
   }
 
 /*******************************************************************/
 
 Mat3::Mat3 (double x)
  {
   int i, j;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) m[i][j] = x;
  }
 
 Mat3::Mat3 (const Mat3& c)
  {
   int i, j;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) m[i][j] = c.m[i][j];
  }
 
 void Mat3::assign (double x11, double x12, double x13,
                    double x21, double x22, double x23,
                    double x31, double x32, double x33)
  {
   m[0][0] = x11;
   m[0][1] = x12;
   m[0][2] = x13;
   m[1][0] = x21;
   m[1][1] = x22;
   m[1][2] = x23;
   m[2][0] = x31;
   m[2][1] = x32;
   m[2][2] = x33;
  }
 
 void Mat3::assign (double x[3][3])
  {
   int i, j;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) m[i][j] = x[i][j];
  }
 
 void Mat3::PutMij (double x, int i, int j)
  {
   if ((i>0) && (i<4) && (j>0) && (j<4)) m[i-1][j-1] = x;
  }
 
 double Mat3::GetMij (int i, int j)
  {
   double result;
 
   if ((i>0) && (i<4) && (j>0) && (j<4)) result = m[i-1][j-1];
   else result = 0;
   return result;
  }
 
 
 Mat3& Mat3::operator = (const Mat3& c)
  {
   int i, j;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) m[i][j] = c.m[i][j];
 
   return (*this);
  }
 
 Mat3& Mat3::operator += (const Mat3& c)
  {
   int i, j;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) m[i][j] = m[i][j] + c.m[i][j];
   return *this;
  }
 
 Mat3& Mat3::operator -= (const Mat3& c)
  {
   int i, j;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) m[i][j] = m[i][j] - c.m[i][j];
   return *this;
  }
 
 Mat3& Mat3::operator *= (const Mat3& c)
  {
   int i, j, k;
   double r;
   Mat3 b;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++)
     {
      r = 0;
      for (k=0; k<3; k++) r = r + c.m[i][k] * m[k][j];
      b.m[i][j] = r;
     }
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) m[i][j] = b.m[i][j];
 
   return *this;
  }
 
 Mat3& Mat3::operator *= (double r)
  {
   int i, j;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) m[i][j] = r*m[i][j];
   return *this;
  }
 
 Mat3& Mat3::operator /= (double r)
  {
   int i, j;
   double q;
 
   if (r < 1E-100) q = 0.0;
   else q = 1.0 / r;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) m[i][j] = m[i][j] * q;
   return *this;
  }
 
 Mat3 mxcon (double r)  // constant matrix with all elements of value r
  {
   Mat3 result;
   int i, j;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) result.m[i][j] = r;
 
   return result;
  }
 
 Mat3 mxidn ()          // identity matrix
  {
   Mat3 result;
   int i;
 
   result = mxcon (0);
   for (i=0; i<3; i++) result.m[i][i] = 1.0;
 
   return result;
  }
 
 Mat3 mxtrn (const Mat3& m1)  // returns transposed of matrix m1
  {
   Mat3 result;
   int i, j;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) result.m[i][j] = m1.m[j][i];
 
   return result;
  }
 
 double mxdet (const Mat3& c) // returns determinant of matrix m1
  {
   double result;
 
   result = c.m[0][0]*c.m[1][1]*c.m[2][2] + c.m[0][1]*c.m[1][2]*c.m[2][0]
          + c.m[0][2]*c.m[1][0]*c.m[2][1] - c.m[0][2]*c.m[1][1]*c.m[2][0]
          - c.m[0][0]*c.m[1][2]*c.m[2][1] - c.m[0][1]*c.m[1][0]*c.m[2][2];
 
   return result;
  }
 
 Mat3 operator + (const Mat3& c1, const Mat3& c2)
  {
   Mat3 result;
   int i, j;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) result.m[i][j] = c1.m[i][j] + c2.m[i][j];
   return result;
  }
 
 Mat3 operator - (const Mat3& c1, const Mat3& c2)
  {
   Mat3 result;
   int i, j;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) result.m[i][j] = c1.m[i][j] - c2.m[i][j];
   return result;
  }
 
 Mat3 operator * (double r, const Mat3& c1)
  {
   Mat3 result;
   int i, j;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) result.m[i][j] = c1.m[i][j] * r;
   return result;
  }
 
 
 Mat3 operator * (const Mat3& c1, double r)
  {
   int i, j;
   Mat3 result;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) result.m[i][j] = c1.m[i][j] * r;
   return result;
  }
 
 Mat3 operator * (const Mat3& c1, const Mat3& c2)
  {
   int i, j, k;
   double r;
   Mat3 result;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++)
     {
      r = 0;
      for (k=0; k<3; k++) r = r + c1.m[i][k] * c2.m[k][j];
      result.m[i][j] = r;
     };
 
   return result;
  }
 
 Mat3 operator / (const Mat3& c1, double r)
  {
   Mat3 result;
   int i, j;
   double q;
 
   if (r < 1E-100) q = 0.0;
   else q = 1.0 / r;
 
   for (i=0; i<3; i++)
    for (j=0; j<3; j++) result.m[i][j] = c1.m[i][j] * q;
   return result;
  }
 
 Vec3 mxvct (const Mat3& m1, Vec3& v1)
  {
   int i, j;
   double r;
   Vec3 result;
 
   for (i=0; i<3; i++)
    {
     r = 0;
     for (j=0; j<3; j++) r = r + m1.m[i][j] * v1[j];
     result[i] = r;
    };
   return result;
  }
 
 Mat3 xrot (double a)
  {
   //     Rotation matrix around x-axis with angle a (in radians).
   double c, s;
   Mat3 m1;
 
   c = cos (a);
   s = sin (a);
   m1.m[0][0] = 1.0;
   m1.m[0][1] = 0.0;
   m1.m[0][2] = 0.0;
   m1.m[1][0] = 0.0;
   m1.m[1][1] = c;
   m1.m[1][2] = s;
   m1.m[2][0] = 0.0;
   m1.m[2][1] = -s;
   m1.m[2][2] = c;
 
   return m1;
  }
 
 Mat3 yrot (double a)
  {
   //     Rotation matrix around y-axis with angle a (in radians).
   double c, s;
   Mat3 m1;
 
   c = cos (a);
   s = sin (a);
   m1.m[0][0] = c;
   m1.m[0][1] = 0.0;
   m1.m[0][2] = -s;
   m1.m[1][0] = 0.0;
   m1.m[1][1] = 1.0;
   m1.m[1][2] = 0.0;
   m1.m[2][0] = s;
   m1.m[2][1] = 0.0;
   m1.m[2][2] = c;
 
   return m1;
  }
 
 Mat3 zrot (double a)
  {
   //  Rotation matrix around z-axis with angle a (in radians).
   double c, s;
   Mat3 m1;
 
   c = cos (a);
   s = sin (a);
   m1.m[0][0] = c;
   m1.m[0][1] = s;
   m1.m[0][2] = 0.0;
   m1.m[1][0] = -s;
   m1.m[1][1] = c;
   m1.m[1][2] = 0.0;
   m1.m[2][0] = 0.0;
   m1.m[2][1] = 0.0;
   m1.m[2][2] = 1.0;
 
   return m1;
  }
 
 Mat3 csmx (double p, double y, double r)
  {
   // Form cosine matrix m from pitch p, yaw y and roll r angles.
   //      The angles are to be given in radians.
   //     Roll is rotation about the x-axis, pitch about y, yaw about z.
   //
   Mat3 pitch, yaw, roll, result;
 
   pitch = yrot (p);
   yaw =      zrot (y);
   roll =     xrot (r);
   result = yaw * pitch;
   result *= roll;
 
   return result;
  }
 
 void gpyr (const Mat3& m1, double& p, double& y, double& r)
  {
   // Get pitch p, yaw y and roll r angles (in radians) from
   // cosine matrix m1.
 
   y = asin (m1.m[0][1]);
   r = atan20 (-m1.m[2][1], m1.m[1][1]);
   p = atan20 (-m1.m[0][2], m1.m[0][0]);
  }
 
 void vcpy (Vec3& v, double& p, double& y)
  {
   // Convert direction given by cartesion vector v into a corresponding
   // pitch (p) / yaw (y) sequence. The angles are in radians.
 
   p = atan20 (-v[2], v[0]);
   y = atan20 (v[1], sqrt (v[0]*v[0] + v[2]*v[2]));
  }
 
 void vcrp (Vec3& v, double& p, double& r)
  {
   // Convert direction given by cartesian vector v into a corresponding
   // roll (r) / pitch (p) sequence. The angles are in radians.
 
   r = atan20 (v[1], -v[2]);
   p = M_PI / 2.0 - atan20 (v[0], sqrt (v[1]*v[1] + v[2]*v[2]));
  }
 
 void mxevc (const Mat3& m, double& a, Vec3& v)
  {
   // Get eigenvalue a and eigenvector v from cosine matrix m.
   // The eigenangle a is in radians.
 
   double ri, rj, rk, q1, q2, q3, q4;
 
   // using the 3-1-3 rotation matrix, first get the corresponding
   // angles ri, rj, rk of rotation about the x-, y-, z-axis.
   ri = atan20 (m.m[2][0], -m.m[2][1]);
   rj = 0.5 * acos (m.m[2][2]);
   rk = atan20 (m.m[0][2], m.m[1][2]);
 
   //  now convert to quaternions
   q4 = sin (rj);
   q1 = q4 * cos (0.5 * (ri - rk));
   q2 = q4 * sin (0.5 * (ri - rk));
   q4 = cos (rj);
   q3 = q4 * sin (0.5 * (ri + rk));
   q4 = q4 * cos (0.5 * (ri + rk));
 
   // now get the eigen angle and eigen vector
   v.assign(q1, q2, q3);
   ri = abs (v);
   if (ri == 0)
    {
     // treat singularity for 3-1-3 matrix
     v.assign (0.0, 0.0, 1.0);
     q4 = 0.5 * sqrt (1.0 + m.m[0][0] + m.m[1][1] + m.m[2][2]);
    }
   else v /= ri;
 
   a = 2.0 * acos (q4);
  }
 
 Mat3 mxrox (double& a, Vec3& v)
  {
   // Convert eigenvalue a (eigen angle in radians) and eigenvector v
   // into a corresponding cosine rotation matrix m.
 
   double q1, q2, q3, q4, q12, q22, q32, q42;
   Mat3 result;
 
   // calculate quaternions and their squares
   q4 = sin ( 0.5 * a);
   q1 = v[0] * q4;
   q2 = v[1] * q4;
   q3 = v[2] * q4;
   q4 = cos (0.5 * a);
   q12 = q1 * q1;
   q22 = q2 * q2;
   q32 = q3 * q3;
   q42 = q4 * q4;
 
   // now get the matrix elements
   result.assign ((q12 - q22 - q32 + q42), (2.0 * (q1*q2 + q3*q4)),
                  (2.0 * (q1*q3 - q2*q4)), (2.0 * (q1*q2 - q3*q4)),
                  (-q12 + q22 - q32 + q42),(2.0 * (q2*q3 + q1*q4)),
                  (2.0 * (q1*q3 + q2*q4)), (2.0 * (q2*q3 - q1*q4)),
                  (-q12 - q22 + q32 + q42));
 
   return result;
  }
 
 
 ostream& operator << (ostream& os, const Mat3& c)
  {
   os << "[" << c.m[0][0] << "," << c.m[0][1] << "," << c.m[0][2] << "]" << endl
      << "[" << c.m[1][0] << "," << c.m[1][1] << "," << c.m[1][2] << "]" << endl
      << "[" << c.m[2][0] << "," << c.m[2][1] << "," << c.m[2][2] << "]" << endl;
   return os;
  }