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testExtractEuler.cpp

///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
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// *       Redistributions in binary form must reproduce the above
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// its contributors may be used to endorse or promote products derived
// from this software without specific prior written permission. 
// 
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#include <testExtractEuler.h>
#include <ImathMatrixAlgo.h>
#include <ImathEuler.h>
#include <ImathRandom.h>
#include <ImathFun.h>
#include <iostream>
#include <assert.h>


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);}


M44f
matrixEulerMatrix_1 (const M44f &M, Eulerf::Order order)
{
    V3f f;

    if (order == Eulerf::XYZ)
      extractEulerXYZ (M, f);
    else
      extractEulerZYX (M, f);

    return Eulerf(f, order).toMatrix44();
}


M44f
matrixEulerMatrix_2 (const M44f &M, Eulerf::Order order)
{
    Eulerf f (order);
    f.extract (M);
    return f.toMatrix44();
}


void
testMatrix (const M44f M,
          M44f (*matrixEulerMatrix)(const M44f &, Eulerf::Order),
          Eulerf::Order order)
{
    //
    // Extract Euler angles from M, and convert the
    // Euler angles back to a matrix, N.
    //

    M44f N = matrixEulerMatrix (M, order);

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

    M44f D (M - N);

    for (int j = 0; j < 3; ++j)
    {
      for (int k = 0; k < 3; ++k)
      {
            if (abs (D[j][k]) > 0.000002)
          {
            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
testRandomAngles (M44f (*matrixEulerMatrix)(const M44f &, Eulerf::Order),
              Eulerf::Order order)
{
    Rand48 r(0);

    for (int i = 0; i < 100000; ++i)
    {
      //
      // Create a rotation matrix, M
      //

      Eulerf e (rad (r.nextf (-180, 180)),
              rad (r.nextf (-180, 180)),
              rad (r.nextf (-180, 180)),
              Eulerf::XYZ);

      M44f M (e.toMatrix44());

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

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

      //
      // 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, matrixEulerMatrix, order);
    }
}


void
testAngles (V3f angles,
          M44f (*matrixEulerMatrix)(const M44f &, Eulerf::Order),
          Eulerf::Order order)
{
    Eulerf e (rad (angles.x),
            rad (angles.y),
            rad (angles.z),
            order);

    M44f M (e.toMatrix44());

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

    testMatrix (M, matrixEulerMatrix, order);

    //
    // 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, matrixEulerMatrix, order);
}


void
test (M44f (*matrixEulerMatrix)(const M44f &, Eulerf::Order),
      Eulerf::Order order)
{
    cout << "order = " << setbase (16) << int (order) << setbase (10) << endl;

    // cout << "random angles" << endl;

    testRandomAngles (matrixEulerMatrix, order);

    // cout << "special angles" << 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)
            testAngles (V3f (i, j, k), matrixEulerMatrix, order);
}


void
testRandomAngles33 ()
{
    Rand48 r(0);

    float eps = 8.0 * limits<float>::epsilon();

    for (int i = 0; i < 100000; ++i)
    {
      float angle = rad (r.nextf (-180, 180));

      M33f M;
      M.setRotation (angle);

      float angleEx;
      extractEuler (M, angleEx);

      assert (Imath::equal (angle, angleEx, eps));
    }
}


} // namespace


void
testExtractEuler ()
{
#if defined PLATFORM_WINDOWS && _MSC_VER >= 1300
    cout << "testExtractEuler disabled on this compiler due to bugs" << endl;
#else
    cout << "Testing extraction of rotation angle from 3x3 matrices" << endl;
    testRandomAngles33 ();
    
    cout << "Testing extraction of Euler angles from matrices" << endl;

    cout << "extractEulerXYZ()" << endl;
    test (matrixEulerMatrix_1, Eulerf::XYZ);

    cout << "extractEulerZYX()" << endl;
    test (matrixEulerMatrix_1, Eulerf::ZYX);

    cout << "Eulerf::extract()" << endl;
    test (matrixEulerMatrix_2, Eulerf::XYZ);
    test (matrixEulerMatrix_2, Eulerf::XZY);
    test (matrixEulerMatrix_2, Eulerf::YZX);
    test (matrixEulerMatrix_2, Eulerf::YXZ);
    test (matrixEulerMatrix_2, Eulerf::ZXY);
    test (matrixEulerMatrix_2, Eulerf::ZYX);
    
    test (matrixEulerMatrix_2, Eulerf::XZX);
    test (matrixEulerMatrix_2, Eulerf::XYX);
    test (matrixEulerMatrix_2, Eulerf::YXY);
    test (matrixEulerMatrix_2, Eulerf::YZY);
    test (matrixEulerMatrix_2, Eulerf::ZYZ);
    test (matrixEulerMatrix_2, Eulerf::ZXZ);

    test (matrixEulerMatrix_2, Eulerf::XYZr);
    test (matrixEulerMatrix_2, Eulerf::XZYr);
    test (matrixEulerMatrix_2, Eulerf::YZXr);
    test (matrixEulerMatrix_2, Eulerf::YXZr);
    test (matrixEulerMatrix_2, Eulerf::ZXYr);
    test (matrixEulerMatrix_2, Eulerf::ZYXr);
    
    test (matrixEulerMatrix_2, Eulerf::XZXr);
    test (matrixEulerMatrix_2, Eulerf::XYXr);
    test (matrixEulerMatrix_2, Eulerf::YXYr);
    test (matrixEulerMatrix_2, Eulerf::YZYr);
    test (matrixEulerMatrix_2, Eulerf::ZYZr);
    test (matrixEulerMatrix_2, Eulerf::ZXZr);

    cout << "ok\n" << endl;
#endif
}

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