diff --git a/Core/Code/Testing/mitkPlaneGeometryTest.cpp b/Core/Code/Testing/mitkPlaneGeometryTest.cpp
index 36f8d2130e..0e5ceef177 100644
--- a/Core/Code/Testing/mitkPlaneGeometryTest.cpp
+++ b/Core/Code/Testing/mitkPlaneGeometryTest.cpp
@@ -1,1023 +1,1025 @@
 /*===================================================================
 
 The Medical Imaging Interaction Toolkit (MITK)
 
 Copyright (c) German Cancer Research Center,
 Division of Medical and Biological Informatics.
 All rights reserved.
 
 This software is distributed WITHOUT ANY WARRANTY; without
 even the implied warranty of MERCHANTABILITY or FITNESS FOR
 A PARTICULAR PURPOSE.
 
 See LICENSE.txt or http://www.mitk.org for details.
 
 ===================================================================*/
 
 
 #include "mitkPlaneGeometry.h"
 #include "mitkRotationOperation.h"
 #include "mitkInteractionConst.h"
 #include "mitkLine.h"
 
 #include "mitkTestingMacros.h"
 
 #include <vnl/vnl_quaternion.h>
 #include <vnl/vnl_quaternion.txx>
 
 #include <fstream>
 #include <iomanip>
 
+static const mitk::ScalarType testEps = 1E-9; // the epsilon used in this test == at least float precision.
+
 int mappingTests2D(const mitk::PlaneGeometry* planegeometry, const mitk::ScalarType& width, const mitk::ScalarType& height, const mitk::ScalarType& widthInMM, const mitk::ScalarType& heightInMM, const mitk::Point3D& origin, const mitk::Vector3D& right, const mitk::Vector3D& bottom)
 {
 
   std::cout << "Testing mapping Map(pt2d_mm(x=widthInMM/2.3,y=heightInMM/2.5), pt3d_mm) and compare with expected: ";
   mitk::Point2D pt2d_mm;
   mitk::Point3D pt3d_mm, expected_pt3d_mm;
   pt2d_mm[0] = widthInMM/2.3; pt2d_mm[1] = heightInMM/2.5;
   expected_pt3d_mm = origin+right*(pt2d_mm[0]/right.GetNorm())+bottom*(pt2d_mm[1]/bottom.GetNorm());
   planegeometry->Map(pt2d_mm, pt3d_mm);
-  if(mitk::Equal(pt3d_mm, expected_pt3d_mm) == false)
+  if(mitk::Equal(pt3d_mm, expected_pt3d_mm, testEps) == false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing mapping Map(pt3d_mm, pt2d_mm) and compare with expected: ";
   mitk::Point2D testpt2d_mm;
   planegeometry->Map(pt3d_mm, testpt2d_mm);
   std::cout << std::setprecision(12) << "Expected pt2d_mm " << pt2d_mm << std::endl;
   std::cout << std::setprecision(12) << "Result testpt2d_mm " << testpt2d_mm << std::endl;
   std::cout << std::setprecision(12) << "10*mitk::eps " << 10*mitk::eps << std::endl;
   //This eps is temporarily set to 10*mitk::eps. See bug #15037 for details.
   if(mitk::Equal(pt2d_mm, testpt2d_mm, 10*mitk::eps) == false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing IndexToWorld(pt2d_units, pt2d_mm) and compare with expected: ";
   mitk::Point2D pt2d_units;
   pt2d_units[0] = width/2.0;     pt2d_units[1] = height/2.0;
   pt2d_mm[0]    = widthInMM/2.0; pt2d_mm[1]    = heightInMM/2.0;
   planegeometry->IndexToWorld(pt2d_units, testpt2d_mm);
 
   std::cout << std::setprecision(12) << "Expected pt2d_mm " << pt2d_mm << std::endl;
   std::cout << std::setprecision(12) << "Result testpt2d_mm " << testpt2d_mm << std::endl;
   std::cout << std::setprecision(12) << "10*mitk::eps " << 10*mitk::eps << std::endl;
   //This eps is temporarily set to 10*mitk::eps. See bug #15037 for details.
   if(mitk::Equal(pt2d_mm, testpt2d_mm, 10*mitk::eps) == false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing WorldToIndex(pt2d_mm, pt2d_units) and compare with expected: ";
   mitk::Point2D testpt2d_units;
   planegeometry->WorldToIndex(pt2d_mm, testpt2d_units);
 
   std::cout << std::setprecision(12) << "Expected pt2d_units " << pt2d_units << std::endl;
   std::cout << std::setprecision(12) << "Result testpt2d_units " << testpt2d_units << std::endl;
   std::cout << std::setprecision(12) << "10*mitk::eps " << 10*mitk::eps << std::endl;
   //This eps is temporarily set to 10*mitk::eps. See bug #15037 for details.
   if(mitk::Equal(pt2d_units, testpt2d_units, 10*mitk::eps) == false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   return EXIT_SUCCESS;
 }
 
 int TestCase1210()
 {
   mitk::PlaneGeometry::Pointer planegeometry = mitk::PlaneGeometry::New();
 
   mitk::Point3D origin;
   mitk::Vector3D right, down, spacing;
 
   mitk::FillVector3D(origin, 4.5,              7.3, 11.2);
   mitk::FillVector3D(right,
       1.015625, 1.015625, 1.1999969482421875
       );
 
   mitk::FillVector3D(down,
       1.4012984643248170709237295832899161312802619418765e-45, 0, 0
       );
   mitk::FillVector3D(spacing,
       0, 1.4713633875410579244699160624544119378442750389703e-43, 9.2806360452222355258639080851310540729807238879469e-32
       );
 
   std::cout << "Testing InitializeStandardPlane(rightVector, downVector, spacing = NULL): "<<std::endl;
   planegeometry->InitializeStandardPlane(right, down, &spacing);
 /*
   std::cout << "Testing width, height and thickness (in units): ";
   if((mitk::Equal(planegeometry->GetExtent(0),width)==false) ||
      (mitk::Equal(planegeometry->GetExtent(1),height)==false) ||
      (mitk::Equal(planegeometry->GetExtent(2),1)==false)
     )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in mm): ";
   if((mitk::Equal(planegeometry->GetExtentInMM(0),widthInMM)==false) ||
      (mitk::Equal(planegeometry->GetExtentInMM(1),heightInMM)==false) ||
      (mitk::Equal(planegeometry->GetExtentInMM(2),thicknessInMM)==false)
     )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
 */
   std::cout<<"[PASSED]"<<std::endl;
 
   return EXIT_SUCCESS;
 }
 
 
 
 /**
  * @brief This method tests method IntersectionPoint
  *
  * See also bug #7151. (ref 2 this test: iggy)
  * This test was written due to incorrect calculation of the intersection point
  * between a given line and plane. This only occured when the pointdistance of
  * the line was less than 1.
  * Test Behavour:
  * ==============
  * we have a given line and a given plane.
  * we let the line intersect the plane.
  * when testing several positions on the line the resulting intersection point must be the same
  * we test a position where the distance between the correspoinding points is < 0 and another position where the distance is > 0.
  *
  */
 int TestIntersectionPoint()
 {
     //init plane with its parameter
     mitk::PlaneGeometry::Pointer myPlaneGeometry = mitk::PlaneGeometry::New();
 
     mitk::Point3D origin;
     origin[0] = 0.0;
     origin[1] = 2.0;
     origin[2] = 0.0;
 
     mitk::Vector3D normal;
     normal[0] = 0.0;
     normal[1] = 1.0;
     normal[2] = 0.0;
 
     myPlaneGeometry->InitializePlane(origin,normal);
 
     //generate points and line for intersection testing
     //point distance of given line > 1
     mitk::Point3D pointP1;
     pointP1[0] = 2.0;
     pointP1[1] = 1.0;
     pointP1[2] = 0.0;
 
     mitk::Point3D pointP2;
     pointP2[0] = 2.0;
     pointP2[1] = 4.0;
     pointP2[2] = 0.0;
 
     mitk::Vector3D lineDirection;
     lineDirection[0] = pointP2[0] - pointP1[0];
     lineDirection[1] = pointP2[1] - pointP1[1];
     lineDirection[2] = pointP2[2] - pointP1[2];
 
     mitk::Line3D xingline( pointP1, lineDirection );
     mitk::Point3D calcXingPoint;
     myPlaneGeometry->IntersectionPoint(xingline, calcXingPoint);
 
     //point distance of given line < 1
     mitk::Point3D pointP3;
     pointP3[0] = 2.0;
     pointP3[1] = 2.2;
     pointP3[2] = 0.0;
 
     mitk::Point3D pointP4;
     pointP4[0] = 2.0;
     pointP4[1] = 1.7;
     pointP4[2] = 0.0;
 
     mitk::Vector3D lineDirection2;
     lineDirection2[0] = pointP4[0] - pointP3[0];
     lineDirection2[1] = pointP4[1] - pointP3[1];
     lineDirection2[2] = pointP4[2] - pointP3[2];
 
     mitk::Line3D xingline2( pointP3, lineDirection2 );
     mitk::Point3D calcXingPoint2;
     myPlaneGeometry->IntersectionPoint( xingline2, calcXingPoint2 );
 
     //intersection points must be the same
     if (calcXingPoint == calcXingPoint2) {
         return EXIT_SUCCESS;
 
     } else {
         return EXIT_FAILURE;
     }
 
 }
 
 
 /**
  * @brief This method tests method ProjectPointOntoPlane.
  *
  * See also bug #3409.
  */
 int TestProjectPointOntoPlane()
 {
   mitk::PlaneGeometry::Pointer myPlaneGeometry = mitk::PlaneGeometry::New();
 
   //create normal
   mitk::Vector3D normal;
   normal[0] = 0.0;
   normal[1] = 0.0;
   normal[2] = 1.0;
 
   //create origin
   mitk::Point3D origin;
   origin[0] = -27.582859;
   origin[1] = 50;
   origin[2] = 200.27742;
 
   //initialize plane geometry
   myPlaneGeometry->InitializePlane(origin,normal);
 
   //output to descripe the test
   std::cout << "Testing PlaneGeometry according to bug #3409" << std::endl;
   std::cout << "Our normal is: " << normal << std::endl;
   std::cout << "So ALL projected points should have exactly the same z-value!" << std::endl;
 
   //create a number of points
   mitk::Point3D myPoints[5];
   myPoints[0][0] = -27.582859;
   myPoints[0][1] = 50.00;
   myPoints[0][2] = 200.27742;
 
   myPoints[1][0] = -26.58662;
   myPoints[1][1] = 50.00;
   myPoints[1][2] = 200.19026;
 
   myPoints[2][0] = -26.58662;
   myPoints[2][1] = 50.00;
   myPoints[2][2] = 200.33124;
 
   myPoints[3][0] = 104.58662;
   myPoints[3][1] = 452.12313;
   myPoints[3][2] = 866.41236;
 
   myPoints[4][0] = -207.58662;
   myPoints[4][1] = 312.00;
   myPoints[4][2] = -300.12346;
 
   //project points onto plane
   mitk::Point3D myProjectedPoints[5];
   for ( unsigned int i = 0; i < 5; ++i )
   {
     myProjectedPoints[i] = myPlaneGeometry->ProjectPointOntoPlane( myPoints[i] );
   }
 
   //compare z-values with z-value of plane (should be equal)
   bool allPointsOnPlane = true;
   for ( unsigned int i = 0; i < 5; ++i )
   {
     if ( fabs(myProjectedPoints[i][2] - origin[2]) > mitk::sqrteps )
     {
       allPointsOnPlane = false;
     }
   }
   if (!allPointsOnPlane)
     {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
     }
   else
     {
     std::cout<<"[PASSED]"<<std::endl;
     return EXIT_SUCCESS;
     }
 }
 
 int mitkPlaneGeometryTest(int /*argc*/, char* /*argv*/[])
 {
   int result;
 
   /*
   // the following can be used to reproduce a bug in ITK matrix inversion
   // which was found while investigating bug #1210.
   result = TestCase1210();
   if(result!=EXIT_SUCCESS)
     return result;
   */
 
   mitk::PlaneGeometry::Pointer planegeometry = mitk::PlaneGeometry::New();
 
   mitk::Point3D origin;
   mitk::Vector3D right, bottom, normal;
   mitk::ScalarType width, height;
   mitk::ScalarType widthInMM, heightInMM, thicknessInMM;
 
   width  = 100;    widthInMM  = width;
   height = 200;    heightInMM = height;
   thicknessInMM = 1.0;
   mitk::FillVector3D(origin, 4.5,              7.3, 11.2);
   mitk::FillVector3D(right,  widthInMM,          0, 0);
   mitk::FillVector3D(bottom,         0, heightInMM, 0);
   mitk::FillVector3D(normal,         0,          0, thicknessInMM);
 
   std::cout << "Testing InitializeStandardPlane(rightVector, downVector, spacing = NULL): "<<std::endl;
   planegeometry->InitializeStandardPlane(right.GetVnlVector(), bottom.GetVnlVector());
 
   std::cout << "Testing width, height and thickness (in units): ";
-  if((mitk::Equal(planegeometry->GetExtent(0),width)==false) ||
-     (mitk::Equal(planegeometry->GetExtent(1),height)==false) ||
-     (mitk::Equal(planegeometry->GetExtent(2),1)==false)
+  if((mitk::Equal(planegeometry->GetExtent(0),width, testEps)==false) ||
+     (mitk::Equal(planegeometry->GetExtent(1),height, testEps)==false) ||
+     (mitk::Equal(planegeometry->GetExtent(2),1, testEps)==false)
     )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in mm): ";
-  if((mitk::Equal(planegeometry->GetExtentInMM(0),widthInMM)==false) ||
-     (mitk::Equal(planegeometry->GetExtentInMM(1),heightInMM)==false) ||
-     (mitk::Equal(planegeometry->GetExtentInMM(2),thicknessInMM)==false)
+  if((mitk::Equal(planegeometry->GetExtentInMM(0),widthInMM, testEps)==false) ||
+     (mitk::Equal(planegeometry->GetExtentInMM(1),heightInMM, testEps)==false) ||
+     (mitk::Equal(planegeometry->GetExtentInMM(2),thicknessInMM, testEps)==false)
     )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetAxisVector(): ";
-  if((mitk::Equal(planegeometry->GetAxisVector(0), right)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), bottom)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), normal)==false))
+  if((mitk::Equal(planegeometry->GetAxisVector(0), right, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), bottom, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), normal, testEps)==false))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
 
 
   std::cout << "Testing InitializeStandardPlane(rightVector, downVector, spacing = {1.0, 1.0, 1.5}): "<<std::endl;
   mitk::Vector3D spacing;
   thicknessInMM = 1.5;
   normal.Normalize(); normal *= thicknessInMM;
   mitk::FillVector3D(spacing, 1.0, 1.0, thicknessInMM);
   planegeometry->InitializeStandardPlane(right.GetVnlVector(), bottom.GetVnlVector(), &spacing);
 
   std::cout << "Testing width, height and thickness (in units): ";
-  if((mitk::Equal(planegeometry->GetExtent(0),width)==false) ||
-     (mitk::Equal(planegeometry->GetExtent(1),height)==false) ||
-     (mitk::Equal(planegeometry->GetExtent(2),1)==false)
+  if((mitk::Equal(planegeometry->GetExtent(0),width, testEps)==false) ||
+     (mitk::Equal(planegeometry->GetExtent(1),height, testEps)==false) ||
+     (mitk::Equal(planegeometry->GetExtent(2),1, testEps)==false)
     )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in mm): ";
-  if((mitk::Equal(planegeometry->GetExtentInMM(0),widthInMM)==false) ||
-     (mitk::Equal(planegeometry->GetExtentInMM(1),heightInMM)==false) ||
-     (mitk::Equal(planegeometry->GetExtentInMM(2),thicknessInMM)==false)
+  if((mitk::Equal(planegeometry->GetExtentInMM(0),widthInMM, testEps)==false) ||
+     (mitk::Equal(planegeometry->GetExtentInMM(1),heightInMM, testEps)==false) ||
+     (mitk::Equal(planegeometry->GetExtentInMM(2),thicknessInMM, testEps)==false)
     )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetAxisVector(): ";
-  if((mitk::Equal(planegeometry->GetAxisVector(0), right)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), bottom)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), normal)==false))
+  if((mitk::Equal(planegeometry->GetAxisVector(0), right, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), bottom, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), normal, testEps)==false))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
 
 
   std::cout << "Testing SetExtentInMM(2, ...), querying by GetExtentInMM(2): ";
   thicknessInMM = 3.5;
   normal.Normalize(); normal *= thicknessInMM;
   planegeometry->SetExtentInMM(2, thicknessInMM);
-  if(mitk::Equal(planegeometry->GetExtentInMM(2),thicknessInMM)==false)
+  if(mitk::Equal(planegeometry->GetExtentInMM(2),thicknessInMM, testEps)==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing SetExtentInMM(2, ...), querying by GetAxisVector(2) and comparing to normal: ";
-  if(mitk::Equal(planegeometry->GetAxisVector(2), normal)==false)
+  if(mitk::Equal(planegeometry->GetAxisVector(2), normal, testEps)==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing SetOrigin: ";
   planegeometry->SetOrigin(origin);
-  if(mitk::Equal(planegeometry->GetOrigin(), origin)==false)
+  if(mitk::Equal(planegeometry->GetOrigin(), origin, testEps)==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetAxisVector() after SetOrigin: ";
-  if((mitk::Equal(planegeometry->GetAxisVector(0), right)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), bottom)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), normal)==false))
+  if((mitk::Equal(planegeometry->GetAxisVector(0), right, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), bottom, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), normal, testEps)==false))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   result = mappingTests2D(planegeometry, width, height, widthInMM, heightInMM, origin, right, bottom);
   if(result!=EXIT_SUCCESS)
     return result;
 
 
 
   std::cout << "Changing the IndexToWorldTransform to a rotated version by SetIndexToWorldTransform() (keep origin): "<<std::endl;
   mitk::AffineTransform3D::Pointer transform = mitk::AffineTransform3D::New();
   mitk::AffineTransform3D::MatrixType::InternalMatrixType vnlmatrix;
   vnlmatrix = planegeometry->GetIndexToWorldTransform()->GetMatrix().GetVnlMatrix();
   mitk::VnlVector axis(3);
   mitk::FillVector3D(axis, 1.0, 1.0, 1.0); axis.normalize();
   vnl_quaternion<mitk::ScalarType> rotation(axis, 0.223);
   vnlmatrix = rotation.rotation_matrix_transpose()*vnlmatrix;
   mitk::Matrix3D matrix;
   matrix = vnlmatrix;
   transform->SetMatrix(matrix);
   transform->SetOffset(planegeometry->GetIndexToWorldTransform()->GetOffset());
 
   right.SetVnlVector( rotation.rotation_matrix_transpose()*right.GetVnlVector() );
   bottom.SetVnlVector(rotation.rotation_matrix_transpose()*bottom.GetVnlVector());
   normal.SetVnlVector(rotation.rotation_matrix_transpose()*normal.GetVnlVector());
   planegeometry->SetIndexToWorldTransform(transform);
 
   //The origin changed,because m_Origin=m_IndexToWorldTransform->GetOffset()+GetAxisVector(2)*0.5
   //and the AxisVector changes due to the rotation. In other words: the rotation was done around
   //the corner of the box, not around the planes origin. Now change it to a rotation around
   //the origin, simply by re-setting the origin to the original one:
   planegeometry->SetOrigin(origin);
   mitk::Point3D cornerpoint0 = planegeometry->GetCornerPoint(0);
 
   std::cout << "Testing whether SetIndexToWorldTransform kept origin: ";
-  if(mitk::Equal(planegeometry->GetOrigin(), origin)==false)
+  if(mitk::Equal(planegeometry->GetOrigin(), origin, testEps)==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
 
   MITK_TEST_OUTPUT( << "Testing consistancy of index and world coordinates. ");
   mitk::Point2D point; point[0] = 4; point[1] = 3;
   mitk::Point2D dummy;
   planegeometry->WorldToIndex(point, dummy);
   planegeometry->IndexToWorld(dummy, dummy);
   MITK_TEST_CONDITION_REQUIRED(dummy == point, "");
 
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in mm) of rotated version: ";
-  if((mitk::Equal(planegeometry->GetExtentInMM(0),widthInMM)==false) ||
-     (mitk::Equal(planegeometry->GetExtentInMM(1),heightInMM)==false) ||
-     (mitk::Equal(planegeometry->GetExtentInMM(2),thicknessInMM)==false)
+  if((mitk::Equal(planegeometry->GetExtentInMM(0),widthInMM, testEps)==false) ||
+     (mitk::Equal(planegeometry->GetExtentInMM(1),heightInMM, testEps)==false) ||
+     (mitk::Equal(planegeometry->GetExtentInMM(2),thicknessInMM, testEps)==false)
     )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetAxisVector() of rotated version: ";
-  if((mitk::Equal(planegeometry->GetAxisVector(0), right)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), bottom)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), normal)==false))
+  if((mitk::Equal(planegeometry->GetAxisVector(0), right, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), bottom, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), normal, testEps)==false))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetAxisVector(direction).GetNorm() != planegeometry->GetExtentInMM(direction) of rotated version: ";
-  if((mitk::Equal(planegeometry->GetAxisVector(0).GetNorm(),planegeometry->GetExtentInMM(0))==false) ||
-     (mitk::Equal(planegeometry->GetAxisVector(1).GetNorm(),planegeometry->GetExtentInMM(1))==false) ||
-     (mitk::Equal(planegeometry->GetAxisVector(2).GetNorm(),planegeometry->GetExtentInMM(2))==false)
+  if((mitk::Equal(planegeometry->GetAxisVector(0).GetNorm(),planegeometry->GetExtentInMM(0), testEps)==false) ||
+     (mitk::Equal(planegeometry->GetAxisVector(1).GetNorm(),planegeometry->GetExtentInMM(1), testEps)==false) ||
+     (mitk::Equal(planegeometry->GetAxisVector(2).GetNorm(),planegeometry->GetExtentInMM(2), testEps)==false)
     )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   result = mappingTests2D(planegeometry, width, height, widthInMM, heightInMM, origin, right, bottom);
   if(result!=EXIT_SUCCESS)
     return result;
 
   std::cout << "Testing SetSizeInUnits() of rotated version: "<<std::endl;
   width  *= 2;
   height *= 3;
   planegeometry->SetSizeInUnits(width, height);
 
   std::cout << "Testing width, height and thickness (in units): ";
-  if((mitk::Equal(planegeometry->GetExtent(0),width)==false) ||
-     (mitk::Equal(planegeometry->GetExtent(1),height)==false) ||
-     (mitk::Equal(planegeometry->GetExtent(2),1)==false)
+  if((mitk::Equal(planegeometry->GetExtent(0),width, testEps)==false) ||
+     (mitk::Equal(planegeometry->GetExtent(1),height, testEps)==false) ||
+     (mitk::Equal(planegeometry->GetExtent(2),1, testEps)==false)
     )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in mm) of version with changed size in units: ";
-  if(!mitk::Equal(planegeometry->GetExtentInMM(0), widthInMM) || !mitk::Equal(planegeometry->GetExtentInMM(1), heightInMM) || !mitk::Equal(planegeometry->GetExtentInMM(2), thicknessInMM))
+  if(!mitk::Equal(planegeometry->GetExtentInMM(0), widthInMM, testEps) || !mitk::Equal(planegeometry->GetExtentInMM(1), heightInMM, testEps) || !mitk::Equal(planegeometry->GetExtentInMM(2), thicknessInMM, testEps))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetAxisVector() of version with changed size in units: ";
-  if((mitk::Equal(planegeometry->GetAxisVector(0), right)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), bottom)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), normal)==false))
+  if((mitk::Equal(planegeometry->GetAxisVector(0), right, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), bottom, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), normal, testEps)==false))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetAxisVector(direction).GetNorm() != planegeometry->GetExtentInMM(direction) of rotated version: ";
-  if((mitk::Equal(planegeometry->GetAxisVector(0).GetNorm(),planegeometry->GetExtentInMM(0))==false) ||
-     (mitk::Equal(planegeometry->GetAxisVector(1).GetNorm(),planegeometry->GetExtentInMM(1))==false) ||
-     (mitk::Equal(planegeometry->GetAxisVector(2).GetNorm(),planegeometry->GetExtentInMM(2))==false)
+  if((mitk::Equal(planegeometry->GetAxisVector(0).GetNorm(),planegeometry->GetExtentInMM(0), testEps)==false) ||
+     (mitk::Equal(planegeometry->GetAxisVector(1).GetNorm(),planegeometry->GetExtentInMM(1), testEps)==false) ||
+     (mitk::Equal(planegeometry->GetAxisVector(2).GetNorm(),planegeometry->GetExtentInMM(2), testEps)==false)
     )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   result = mappingTests2D(planegeometry, width, height, widthInMM, heightInMM, origin, right, bottom);
   if(result!=EXIT_SUCCESS)
     return result;
 
 
 
   std::cout << "Testing Clone(): ";
   mitk::PlaneGeometry::Pointer clonedplanegeometry = dynamic_cast<mitk::PlaneGeometry*>(planegeometry->Clone().GetPointer());
   if((clonedplanegeometry.IsNull()) || (clonedplanegeometry->GetReferenceCount()!=1))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing origin of cloned version: ";
-  if(mitk::Equal(clonedplanegeometry->GetOrigin(), origin)==false)
+  if(mitk::Equal(clonedplanegeometry->GetOrigin(), origin, testEps)==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in units) of cloned version: ";
-  if((mitk::Equal(clonedplanegeometry->GetExtent(0),width)==false) ||
-     (mitk::Equal(clonedplanegeometry->GetExtent(1),height)==false) ||
-     (mitk::Equal(clonedplanegeometry->GetExtent(2),1)==false)
+  if((mitk::Equal(clonedplanegeometry->GetExtent(0),width, testEps)==false) ||
+     (mitk::Equal(clonedplanegeometry->GetExtent(1),height, testEps)==false) ||
+     (mitk::Equal(clonedplanegeometry->GetExtent(2),1, testEps)==false)
     )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in mm) of cloned version: ";
-  if(!mitk::Equal(clonedplanegeometry->GetExtentInMM(0), widthInMM) || !mitk::Equal(clonedplanegeometry->GetExtentInMM(1), heightInMM) || !mitk::Equal(clonedplanegeometry->GetExtentInMM(2), thicknessInMM))
+  if(!mitk::Equal(clonedplanegeometry->GetExtentInMM(0), widthInMM, testEps) || !mitk::Equal(clonedplanegeometry->GetExtentInMM(1), heightInMM, testEps) || !mitk::Equal(clonedplanegeometry->GetExtentInMM(2), thicknessInMM, testEps))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetAxisVector() of cloned version: ";
-  if((mitk::Equal(clonedplanegeometry->GetAxisVector(0), right)==false) || (mitk::Equal(clonedplanegeometry->GetAxisVector(1), bottom)==false) || (mitk::Equal(clonedplanegeometry->GetAxisVector(2), normal)==false))
+  if((mitk::Equal(clonedplanegeometry->GetAxisVector(0), right, testEps)==false) || (mitk::Equal(clonedplanegeometry->GetAxisVector(1), bottom, testEps)==false) || (mitk::Equal(clonedplanegeometry->GetAxisVector(2), normal, testEps)==false))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   result = mappingTests2D(clonedplanegeometry, width, height, widthInMM, heightInMM, origin, right, bottom);
   if(result!=EXIT_SUCCESS)
     return result;
 
 
   // Clone, move, rotate and test for 'IsParallel' and 'IsOnPlane'
   std::cout << "Testing Clone(): ";
   mitk::PlaneGeometry::Pointer clonedplanegeometry2 = dynamic_cast<mitk::PlaneGeometry*>(planegeometry->Clone().GetPointer());
   if((clonedplanegeometry2.IsNull()) || (clonedplanegeometry2->GetReferenceCount()!=1))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout << "Testing if cloned and original version are at the same place: ";
   if(mitk::Equal(clonedplanegeometry2->IsOnPlane(planegeometry), true) ==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing if the origin is on the plane: ";
   if(mitk::Equal(clonedplanegeometry2->IsOnPlane(origin), true)==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   mitk::VnlVector newaxis(3);
   mitk::FillVector3D(newaxis, 1.0, 1.0, 1.0); newaxis.normalize();
   vnl_quaternion<mitk::ScalarType> rotation2(newaxis, 0.0);
 
   mitk::Vector3D clonednormal = clonedplanegeometry2->GetNormal();
   mitk::Point3D clonedorigin = clonedplanegeometry2->GetOrigin();
 
   mitk::RotationOperation* planerot = new mitk::RotationOperation( mitk::OpROTATE, origin, clonedplanegeometry2->GetAxisVector( 0 ), 180.0 );
 
   clonedplanegeometry2->ExecuteOperation( planerot );
 
   std::cout << "Testing whether the flipped plane is still the original plane: ";
   if( mitk::Equal( clonedplanegeometry2->IsOnPlane(planegeometry), true )==false )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   clonedorigin += clonednormal;
   clonedplanegeometry2->SetOrigin( clonedorigin );
 
   std::cout << "Testing if the translated (cloned, flipped) plane is parallel to its origin plane: ";
   if( mitk::Equal( clonedplanegeometry2->IsParallel(planegeometry), true )==false )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
 
   delete planerot;
 
   planerot = new mitk::RotationOperation( mitk::OpROTATE, origin, clonedplanegeometry2->GetAxisVector( 0 ), 0.5 );
   clonedplanegeometry2->ExecuteOperation( planerot );
 
   std::cout << "Testing if a non-paralell plane gets recognized as not paralell  [rotation +0.5 degree] : ";
   if( mitk::Equal( clonedplanegeometry2->IsParallel(planegeometry), false )==false )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   delete planerot;
 
   planerot = new mitk::RotationOperation( mitk::OpROTATE, origin, clonedplanegeometry2->GetAxisVector( 0 ), -1.0 );
   clonedplanegeometry2->ExecuteOperation( planerot );
 
   std::cout << "Testing if a non-paralell plane gets recognized as not paralell  [rotation -0.5 degree] : ";
   if( mitk::Equal( clonedplanegeometry2->IsParallel(planegeometry), false )==false )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   delete planerot;
 
   planerot = new mitk::RotationOperation( mitk::OpROTATE, origin, clonedplanegeometry2->GetAxisVector( 0 ), 360.5 );
   clonedplanegeometry2->ExecuteOperation( planerot );
 
   std::cout << "Testing if a non-paralell plane gets recognized as not paralell  [rotation 360 degree] : ";
   if( mitk::Equal( clonedplanegeometry2->IsParallel(planegeometry), true )==false )
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
 
   std::cout << "Testing InitializeStandardPlane(clonedplanegeometry, planeorientation = Axial, zPosition = 0, frontside=true): " <<std::endl;
   planegeometry->InitializeStandardPlane(clonedplanegeometry);
 
   std::cout << "Testing origin of axially initialized version: ";
   if(mitk::Equal(planegeometry->GetOrigin(), origin)==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetCornerPoint(0) of axially initialized version: ";
   if(mitk::Equal(planegeometry->GetCornerPoint(0), cornerpoint0)==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in units) of axially initialized version (should be same as in mm due to unit spacing, except for thickness, which is always 1): ";
-  if(!mitk::Equal(planegeometry->GetExtent(0), width) || !mitk::Equal(planegeometry->GetExtent(1), height) || !mitk::Equal(planegeometry->GetExtent(2), 1))
+  if(!mitk::Equal(planegeometry->GetExtent(0), width, testEps) || !mitk::Equal(planegeometry->GetExtent(1), height, testEps) || !mitk::Equal(planegeometry->GetExtent(2), 1, testEps))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in mm) of axially initialized version: ";
-  if(!mitk::Equal(planegeometry->GetExtentInMM(0), widthInMM) || !mitk::Equal(planegeometry->GetExtentInMM(1), heightInMM) || !mitk::Equal(planegeometry->GetExtentInMM(2), thicknessInMM))
+  if(!mitk::Equal(planegeometry->GetExtentInMM(0), widthInMM, testEps) || !mitk::Equal(planegeometry->GetExtentInMM(1), heightInMM, testEps) || !mitk::Equal(planegeometry->GetExtentInMM(2), thicknessInMM, testEps))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetAxisVector() of axially initialized version: ";
-  if((mitk::Equal(planegeometry->GetAxisVector(0), right)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), bottom)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), normal)==false))
+  if((mitk::Equal(planegeometry->GetAxisVector(0), right, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), bottom, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), normal, testEps)==false))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   result = mappingTests2D(planegeometry, width, height, widthInMM, heightInMM, origin, right, bottom);
   if(result!=EXIT_SUCCESS)
     return result;
 
 
 
   mitk::Vector3D newright, newbottom, newnormal;
   mitk::ScalarType newthicknessInMM;
   std::cout << "Testing InitializeStandardPlane(clonedplanegeometry, planeorientation = Frontal, zPosition = 0, frontside=true): " <<std::endl;
   planegeometry->InitializeStandardPlane(clonedplanegeometry, mitk::PlaneGeometry::Frontal);
   newright = right;
   newbottom = normal; newbottom.Normalize();  newbottom *= thicknessInMM;
   newthicknessInMM = heightInMM/height*1.0/*extent in normal direction is 1*/;
   newnormal = -bottom; newnormal.Normalize(); newnormal *= newthicknessInMM;
 
   std::cout << "Testing GetCornerPoint(0) of frontally initialized version: ";
-  if(mitk::Equal(planegeometry->GetCornerPoint(0), cornerpoint0)==false)
+  if(mitk::Equal(planegeometry->GetCornerPoint(0), cornerpoint0, testEps)==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
   //ok, corner was fine, so we can dare to believe the origin is ok.
   origin = planegeometry->GetOrigin();
 
   std::cout << "Testing width, height and thickness (in units) of frontally initialized version: ";
-  if(!mitk::Equal(planegeometry->GetExtent(0), width) || !mitk::Equal(planegeometry->GetExtent(1), 1) || !mitk::Equal(planegeometry->GetExtent(2), 1))
+  if(!mitk::Equal(planegeometry->GetExtent(0), width, testEps) || !mitk::Equal(planegeometry->GetExtent(1), 1, testEps) || !mitk::Equal(planegeometry->GetExtent(2), 1, testEps))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in mm) of frontally initialized version: ";
-  if(!mitk::Equal(planegeometry->GetExtentInMM(0), widthInMM) || !mitk::Equal(planegeometry->GetExtentInMM(1), thicknessInMM) || !mitk::Equal(planegeometry->GetExtentInMM(2), newthicknessInMM))
+  if(!mitk::Equal(planegeometry->GetExtentInMM(0), widthInMM, testEps) || !mitk::Equal(planegeometry->GetExtentInMM(1), thicknessInMM, testEps) || !mitk::Equal(planegeometry->GetExtentInMM(2), newthicknessInMM, testEps))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetAxisVector() of frontally initialized version: ";
-  if((mitk::Equal(planegeometry->GetAxisVector(0), newright)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), newbottom)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), newnormal)==false))
+  if((mitk::Equal(planegeometry->GetAxisVector(0), newright, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), newbottom, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), newnormal, testEps)==false))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   result = mappingTests2D(planegeometry, width, 1, widthInMM, thicknessInMM, origin, newright, newbottom);
   if(result!=EXIT_SUCCESS)
     return result;
 
 
 
   std::cout << "Changing plane to in-plane unit spacing using SetSizeInUnits: " <<std::endl;
   planegeometry->SetSizeInUnits(planegeometry->GetExtentInMM(0), planegeometry->GetExtentInMM(1));
 
   std::cout << "Testing origin of unit spaced, frontally initialized version: ";
-  if(mitk::Equal(planegeometry->GetOrigin(), origin)==false)
+  if(mitk::Equal(planegeometry->GetOrigin(), origin, testEps)==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in units) of unit spaced, frontally initialized version: ";
-  if(!mitk::Equal(planegeometry->GetExtent(0), widthInMM) || !mitk::Equal(planegeometry->GetExtent(1), thicknessInMM) || !mitk::Equal(planegeometry->GetExtent(2), 1))
+  if(!mitk::Equal(planegeometry->GetExtent(0), widthInMM, testEps) || !mitk::Equal(planegeometry->GetExtent(1), thicknessInMM, testEps) || !mitk::Equal(planegeometry->GetExtent(2), 1, testEps))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in mm) of unit spaced, frontally initialized version: ";
-  if(!mitk::Equal(planegeometry->GetExtentInMM(0), widthInMM) || !mitk::Equal(planegeometry->GetExtentInMM(1), thicknessInMM) || !mitk::Equal(planegeometry->GetExtentInMM(2), newthicknessInMM))
+  if(!mitk::Equal(planegeometry->GetExtentInMM(0), widthInMM, testEps) || !mitk::Equal(planegeometry->GetExtentInMM(1), thicknessInMM, testEps) || !mitk::Equal(planegeometry->GetExtentInMM(2), newthicknessInMM, testEps))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetAxisVector() of unit spaced, frontally initialized version: ";
-  if((mitk::Equal(planegeometry->GetAxisVector(0), newright)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), newbottom)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), newnormal)==false))
+  if((mitk::Equal(planegeometry->GetAxisVector(0), newright, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), newbottom, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), newnormal, testEps)==false))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   result = mappingTests2D(planegeometry, widthInMM, thicknessInMM, widthInMM, thicknessInMM, origin, newright, newbottom);
   if(result!=EXIT_SUCCESS)
     return result;
 
 
 
   std::cout << "Changing plane to unit spacing also in normal direction using SetExtentInMM(2, 1.0): " <<std::endl;
   planegeometry->SetExtentInMM(2, 1.0);
   newnormal.Normalize();
 
   std::cout << "Testing origin of unit spaced, frontally initialized version: ";
-  if(mitk::Equal(planegeometry->GetOrigin(), origin)==false)
+  if(mitk::Equal(planegeometry->GetOrigin(), origin, testEps)==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in units) of unit spaced, frontally initialized version: ";
-  if(!mitk::Equal(planegeometry->GetExtent(0), widthInMM) || !mitk::Equal(planegeometry->GetExtent(1), thicknessInMM) || !mitk::Equal(planegeometry->GetExtent(2), 1))
+  if(!mitk::Equal(planegeometry->GetExtent(0), widthInMM, testEps) || !mitk::Equal(planegeometry->GetExtent(1), thicknessInMM, testEps) || !mitk::Equal(planegeometry->GetExtent(2), 1, testEps))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in mm) of unit spaced, frontally initialized version: ";
-  if(!mitk::Equal(planegeometry->GetExtentInMM(0), widthInMM) || !mitk::Equal(planegeometry->GetExtentInMM(1), thicknessInMM) || !mitk::Equal(planegeometry->GetExtentInMM(2), 1.0))
+  if(!mitk::Equal(planegeometry->GetExtentInMM(0), widthInMM, testEps) || !mitk::Equal(planegeometry->GetExtentInMM(1), thicknessInMM, testEps) || !mitk::Equal(planegeometry->GetExtentInMM(2), 1.0, testEps))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetAxisVector() of unit spaced, frontally initialized version: ";
-  if((mitk::Equal(planegeometry->GetAxisVector(0), newright)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), newbottom)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), newnormal)==false))
+  if((mitk::Equal(planegeometry->GetAxisVector(0), newright, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), newbottom, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), newnormal, testEps)==false))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   result = mappingTests2D(planegeometry, widthInMM, thicknessInMM, widthInMM, thicknessInMM, origin, newright, newbottom);
   if(result!=EXIT_SUCCESS)
     return result;
 
 
 
   std::cout << "Testing InitializeStandardPlane(clonedplanegeometry, planeorientation = Sagittal, zPosition = 0, frontside=true): " <<std::endl;
   planegeometry->InitializeStandardPlane(clonedplanegeometry, mitk::PlaneGeometry::Sagittal);
   newright = bottom;
   newthicknessInMM = widthInMM/width*1.0/*extent in normal direction is 1*/;
   newnormal = right; newnormal.Normalize(); newnormal *= newthicknessInMM;
 
   std::cout << "Testing GetCornerPoint(0) of sagitally initialized version: ";
-  if(mitk::Equal(planegeometry->GetCornerPoint(0), cornerpoint0)==false)
+  if(mitk::Equal(planegeometry->GetCornerPoint(0), cornerpoint0, testEps)==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
   //ok, corner was fine, so we can dare to believe the origin is ok.
   origin = planegeometry->GetOrigin();
 
   std::cout << "Testing width, height and thickness (in units) of sagitally initialized version: ";
-  if(!mitk::Equal(planegeometry->GetExtent(0), height) || !mitk::Equal(planegeometry->GetExtent(1), 1) || !mitk::Equal(planegeometry->GetExtent(2), 1))
+  if(!mitk::Equal(planegeometry->GetExtent(0), height, testEps) || !mitk::Equal(planegeometry->GetExtent(1), 1, testEps) || !mitk::Equal(planegeometry->GetExtent(2), 1, testEps))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in mm) of sagitally initialized version: ";
-  if(!mitk::Equal(planegeometry->GetExtentInMM(0), heightInMM) || !mitk::Equal(planegeometry->GetExtentInMM(1), thicknessInMM) || !mitk::Equal(planegeometry->GetExtentInMM(2), newthicknessInMM))
+  if(!mitk::Equal(planegeometry->GetExtentInMM(0), heightInMM, testEps) || !mitk::Equal(planegeometry->GetExtentInMM(1), thicknessInMM, testEps) || !mitk::Equal(planegeometry->GetExtentInMM(2), newthicknessInMM, testEps))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetAxisVector() of sagitally initialized version: ";
-  if((mitk::Equal(planegeometry->GetAxisVector(0), newright)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), newbottom)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), newnormal)==false))
+  if((mitk::Equal(planegeometry->GetAxisVector(0), newright, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), newbottom, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), newnormal, testEps)==false))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   result = mappingTests2D(planegeometry, height, 1, heightInMM, thicknessInMM, origin, newright, newbottom);
   if(result!=EXIT_SUCCESS)
     return result;
 
 
 
   //set origin back to the one of the axial slice:
   origin = clonedplanegeometry->GetOrigin();
   std::cout << "Testing backside initialization: InitializeStandardPlane(clonedplanegeometry, planeorientation = Axial, zPosition = 0, frontside=false, rotated=true): " <<std::endl;
   planegeometry->InitializeStandardPlane(clonedplanegeometry, mitk::PlaneGeometry::Axial, 0, false, true);
   mitk::Point3D backsideorigin;
   backsideorigin=origin+clonedplanegeometry->GetAxisVector(1);//+clonedplanegeometry->GetAxisVector(2);
 
   std::cout << "Testing origin of backsidedly, axially initialized version: ";
-  if(mitk::Equal(planegeometry->GetOrigin(), backsideorigin)==false)
+  if(mitk::Equal(planegeometry->GetOrigin(), backsideorigin, testEps)==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetCornerPoint(0) of sagitally initialized version: ";
   mitk::Point3D backsidecornerpoint0;
   backsidecornerpoint0 = cornerpoint0+clonedplanegeometry->GetAxisVector(1);//+clonedplanegeometry->GetAxisVector(2);
-  if(mitk::Equal(planegeometry->GetCornerPoint(0), backsidecornerpoint0)==false)
+  if(mitk::Equal(planegeometry->GetCornerPoint(0), backsidecornerpoint0, testEps)==false)
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in units) of backsidedly, axially initialized version (should be same as in mm due to unit spacing, except for thickness, which is always 1): ";
-  if(!mitk::Equal(planegeometry->GetExtent(0), width) || !mitk::Equal(planegeometry->GetExtent(1), height) || !mitk::Equal(planegeometry->GetExtent(2), 1))
+  if(!mitk::Equal(planegeometry->GetExtent(0), width, testEps) || !mitk::Equal(planegeometry->GetExtent(1), height, testEps) || !mitk::Equal(planegeometry->GetExtent(2), 1, testEps))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing width, height and thickness (in mm) of backsidedly, axially initialized version: ";
-  if(!mitk::Equal(planegeometry->GetExtentInMM(0), widthInMM) || !mitk::Equal(planegeometry->GetExtentInMM(1), heightInMM) || !mitk::Equal(planegeometry->GetExtentInMM(2), thicknessInMM))
+  if(!mitk::Equal(planegeometry->GetExtentInMM(0), widthInMM, testEps) || !mitk::Equal(planegeometry->GetExtentInMM(1), heightInMM, testEps) || !mitk::Equal(planegeometry->GetExtentInMM(2), thicknessInMM, testEps))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   std::cout << "Testing GetAxisVector() of backsidedly, axially initialized version: ";
-  if((mitk::Equal(planegeometry->GetAxisVector(0), right)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), -bottom)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), -normal)==false))
+  if((mitk::Equal(planegeometry->GetAxisVector(0), right, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(1), -bottom, testEps)==false) || (mitk::Equal(planegeometry->GetAxisVector(2), -normal, testEps)==false))
   {
     std::cout<<"[FAILED]"<<std::endl;
     return EXIT_FAILURE;
   }
   std::cout<<"[PASSED]"<<std::endl;
 
   result = mappingTests2D(planegeometry, width, height, widthInMM, heightInMM, backsideorigin, right, -bottom);
   if(result!=EXIT_SUCCESS)
     return result;
 
 
   // test method mitk::PlaneGeometry::ProjectPointOntoPlane()
   // (see also bug #3409)
   result = TestProjectPointOntoPlane();
   if(result!=EXIT_SUCCESS)
     return result;
 
 
   // testing mitk::PlaneGeometry::IntersectionPoint()
   std::cout << std::endl;
   std::cout << "Testing IntersectionPoint using given plane and given line:  ";
     result = TestIntersectionPoint();
     if (result != EXIT_SUCCESS) {
         std::cout << "[FAILED]" << std::endl;
         return result;
     }
 
   std::cout<<"[PASSED]"<<std::endl<<std::endl;
 
 
 
   std::cout<<"[TEST DONE]"<<std::endl;
   return EXIT_SUCCESS;
 }