I found a bug when we do matrix inverse calculation by vtkTransform object. The version 8.2.0 and 9.1.0 of VTK has the same potential risk in vtkMatrix4x4::Invert(const double inElements[16], double outElements[16]).
Let’s see the source code, it judges whether the determinant value is zero by ==. The equal comparison operation for float data type in C++ is not reliable. It can be dangerous if the zero value cheats the judgment expression. So my program go in an infinite loop after it.

//------------------------------------------------------------------------------
// Matrix Inversion (adapted from Richard Carling in "Graphics Gems,"
// Academic Press, 1990).
void vtkMatrix4x4::Invert(const double inElements[16], double outElements[16])
{
  // inverse( original_matrix, inverse_matrix )
  // calculate the inverse of a 4x4 matrix
  //
  //     -1
  //     A  = ___1__ adjoint A
  //         det A
  //

  // calculate the 4x4 determinent
  // if the determinent is zero,
  // then the inverse matrix is not unique.

  double det = vtkMatrix4x4::Determinant(inElements);
  if (det == 0.0)
  {
    return;
  }

  // calculate the adjoint matrix
  vtkMatrix4x4::Adjoint(inElements, outElements);

  // scale the adjoint matrix to get the inverse
  for (int i = 0; i < 16; i++)
  {
    outElements[i] /= det;
  }
}

Rewrite it to fix the potential bug.

bool Invert(const vtkSmartPointer<vtkMatrix4x4> inMatrix, double outElements[])
{
    // calculate the inverse of a 4x4 matrix
    //
    //     -1
    //     A  = ___1__ adjoint A
    //         det A
    //
    double det = inMatrix->Determinant();
    if( fabs( det ) < 1e-5 )
    {
        LOG( ERR, "jump: zero det!" );
        return false;
    }

    double inElements[16];
    for( int i = 0; i < 4; ++i )
    {
        for( int j = 0; j < 4; ++j )
        {
            inElements[i*4+j] = inMatrix->GetElement( i, j );
        }
    }
    // calculate the adjoint matrix
    vtkMatrix4x4::Adjoint(inElements, outElements);

    // scale the adjoint matrix to get the inverse
    for (int i = 0; i < 16; i++)
    {
        outElements[i] /= det;
    }
    return true;
}
Categories: MathVTK

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