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testExtractSHRT.cpp

///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
// 
// All rights reserved.
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// modification, are permitted provided that the following conditions are
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// notice, this list of conditions and the following disclaimer.
// *       Redistributions in binary form must reproduce the above
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// in the documentation and/or other materials provided with the
// distribution.
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// its contributors may be used to endorse or promote products derived
// from this software without specific prior written permission. 
// 
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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///////////////////////////////////////////////////////////////////////////


#include <testExtractSHRT.h>
#include <ImathMatrixAlgo.h>
#include <ImathEuler.h>
#include <ImathRandom.h>
#include <ImathFun.h>
#include <iostream>
#include <exception>
#include <stdio.h>
#include <assert.h>


#if 0
    #define debug(x) (printf x, fflush (stdout))
#else
    #define debug(x)
#endif


using namespace std;
using namespace Imath;

namespace {

float rad (float deg) {return deg * (M_PI / 180);}
float deg (float rad) {return rad * (180 / M_PI);}


void
testMatrix (const M33f M)
{
    //
    // Extract the rotation angle from M, and convert the
    // angle back to a matrix, N.
    //

    V2f s, t;
    float h, r;
  
    extractSHRT (M, s, h, r, t, true);

    M33f N;

    N *= M33f().setScale (s);
    N *= M33f().setShear (h);
    N *= M33f().setRotation (r);
    N *= M33f().setTranslation (t);

    debug (("Re-scale: %f %f\n", s[0], s[1]));
    debug (("Re-shear: %f\n", h));
    debug (("Re-rot  : %f\n", r));
    debug (("Re-trans: %f %f\n", t[0], t[1]));

    //
    // Verify that the entries in M and N do not
    // differ too much.
    //

    M33f D (M - N);

    for (int j = 0; j < 3; ++j)
    {
      for (int k = 0; k < 3; ++k)
      {
          if (abs (D[j][k]) > 0.00001)
          {
            cout << "unexpectedly large matrix to "
                  "euler angles conversion error: " <<
                  D[j][k] << endl;

            cout << j << " " << k << endl;

            cout << "M\n" << M << endl;
            cout << "N\n" << N << endl;
            cout << "D\n" << D << endl;

            assert (false);
          }
      }
    }
}


void
testRandomAngles33 ()
{
    Rand48 random(0);

    for (int i = 0; i < 100000; ++i)
    {
      debug (("iteration: %d\n", i));

      M33f M;

      //
      // Scale M.
      //

      V2f s (random.nextf (0.000001, 2.0),
             random.nextf (0.000001, 2.0));

      for (int j=0; j < 2; j++)
          if (random.nextf (0.0, 1.0) >= 0.5)
            s[j] *= -1;

      M *= M33f().setScale (s);

      //
      // Shear M.
      //

      float h = random.nextf (0.000001, 2.);
      if (random.nextf (0.0, 1.0) >= 0.5)
          h *= -1;

      M *= M33f().setShear (h);

        //
      // Rotate M.
      //

      float r = rad (random.nextf (-180, 180));
      
      M *= M33f().setRotation (r);

      //
      // Translate M.
      //

      V2f t (random.nextf (-10, 10), 
             random.nextf (-10, 10));
      
      M *= M33f().setTranslation (t);

      //
      // Add a small random error to the elements of M
      //

      for (int j = 0; j < 3; ++j)
          for (int k = 0; k < 2; ++k)
            M[j][k] += random.nextf (-1e-7, 1e-7);


      debug (("Scale   : %f %f\n", s[0], s[1]));
      debug (("Shear   : %f\n", h));
      debug (("Rot     : %f\n", r));
      debug (("Trans   : %f %f\n", t[0], t[1]));


      //
      // Extract Euler angles from M, convert the Euler angles
      // back to a matrix, N, and verify that the entries in M
      // and N do not differ too much.
      //

      testMatrix (M);

      debug (("\n"));
    }
}


void
testAngles33 (float angle)
{
    M33f M;
    M.setRotation (rad (angle));

    //
    // With rounding errors from e.toMatrix.
    //

    testMatrix (M);

    //
    // Without rounding errors (assuming that
    // all angles are multiples of 90 degrees).
    //

    for (int i = 0; i < 2; ++i)
      for (int j = 0; j < 2; ++j)
          if (M[i][j] < -0.5)
            M[i][j] = -1;
          else if (M[i][j] > 0.5)
            M[i][j] = 1;
          else
            M[i][j] = 0;

    testMatrix (M);
}


void
testMatrix (const M44f M)
{
    //
    // Extract Euler angles from M, and convert the
    // Euler angles back to a matrix, N.
    //

    V3f s, h, r, t;
  
    extractSHRT (M, s, h, r, t, true);

    M44f N;

    N.translate (t); // ... matrix compositions
    N.rotate (r);
    N.shear (h);
    N.scale (s);

    debug (("Re-scale: %f %f %f\n", s[0], s[1], s[2]));
    debug (("Re-shear: %f %f %f\n", h[0], h[1], h[2]));
    debug (("Re-rot  : %f %f %f\n", r[0], r[1], r[2]));
    debug (("Re-trans: %f %f %f\n", t[0], t[1], t[2]));

    //
    // Verify that the entries in M and N do not
    // differ too much.
    //

    M44f D (M - N);

    for (int j = 0; j < 4; ++j)
    {
      for (int k = 0; k < 4; ++k)
      {
          if (abs (D[j][k]) > 0.00001)
          {
            cout << "unexpectedly large matrix to "
                  "euler angles conversion error: " <<
                  D[j][k] << endl;

            cout << j << " " << k << endl;

            cout << "M\n" << M << endl;
            cout << "N\n" << N << endl;
            cout << "D\n" << D << endl;

            assert (false);
          }
      }
    }
}


void
testRandomAngles44 ()
{
    Rand48 random(0);

    for (int i = 0; i < 100000; ++i)
    {
      debug (("iteration: %d\n", i));

      M44f M;

      //
      // Translate M.
      //

      V3f t (random.nextf (-10, 10), 
             random.nextf (-10, 10), 
             random.nextf (-10, 10));
      
      M.translate (t);

        //
      // Rotate M.
      //

      V3f r (rad (random.nextf (-180, 180)),
             rad (random.nextf (-180, 180)),
             rad (random.nextf (-180, 180)));
      
      M.rotate (r);

      //
      // Shear M.
      //

      V3f h (random.nextf (0.000001, 2.0), 
             random.nextf (0.000001, 2.0), 
             random.nextf (0.000001, 2.0));
      
      for (int j=0; j < 3; j++)
          if (random.nextf (0.0, 1.0) >= 0.5)
            h[j] *= -1;

      M.shear (h);

      //
      // Scale M.
      //

      V3f s (random.nextf (0.000001, 2.0),
             random.nextf (0.000001, 2.0),
             random.nextf (0.000001, 2.0));

      for (int j=0; j < 3; j++)
          if (random.nextf (0.0, 1.0) >= 0.5)
            s[j] *= -1;

      M.scale (s);

      //
      // Add a small random error to the elements of M
      //

      for (int j = 0; j < 4; ++j)
          for (int k = 0; k < 3; ++k)
            M[j][k] += random.nextf (-1e-7, 1e-7);


      debug (("Scale   : %f %f %f\n", s[0], s[1], s[2]));
      debug (("Shear   : %f %f %f\n", h[0], h[1], h[2]));
      debug (("Rot     : %f %f %f\n", r[0], r[1], r[2]));
      debug (("Trans   : %f %f %f\n", t[0], t[1], t[2]));


      //
      // Extract Euler angles from M, convert the Euler angles
      // back to a matrix, N, and verify that the entries in M
      // and N do not differ too much.
      //

      testMatrix (M);

      debug (("\n"));
    }
}


void
testAngles44 (V3f angles)
{
    Eulerf e (rad (angles.x),
            rad (angles.y),
            rad (angles.z));

    M44f M (e.toMatrix44());

    //
    // With rounding errors from e.toMatrix.
    //

    testMatrix (M);

    //
    // Without rounding errors (assuming that
    // all angles are multiples of 90 degrees).
    //

    for (int i = 0; i < 3; ++i)
      for (int j = 0; j < 3; ++j)
          if (M[i][j] < -0.5)
            M[i][j] = -1;
          else if (M[i][j] > 0.5)
            M[i][j] = 1;
          else
            M[i][j] = 0;

    testMatrix (M);
}


void
test ()
{
    cout << "  random angles" << endl;

    cout << "    3x3" << endl;
    testRandomAngles33 ();

    cout << "    4x4" << endl;
    testRandomAngles44 ();

    cout << "  special angles" << endl;

    cout << "    3x3" << endl;
    for (int i = 0; i < 360; i += 90)
      testAngles33 (float (i));

    cout << "    4x4" << endl;
    for (int i = 0; i < 360; i += 90)
      for (int j = 0; j < 360; j += 90)
          for (int k = 0; k < 360; k += 90)
            testAngles44 (V3f (i, j, k));
}


} // namespace


void
testExtractSHRT ()
{
    try
    {
      cout << "Testing extraction of scale, shear, rotation, translation " 
           << "from matrices" << endl;
      
      cout << "Imath::extractSHRT()" << endl;
      test ();
      
      cout << "ok\n" << endl;
    }
    catch (std::exception &e)
    {
      cerr << "  Caught exception: " << e.what () << endl;
    }
}


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