/
TestTransformations.hpp
605 lines (464 loc) · 21.5 KB
/
TestTransformations.hpp
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/*
Copyright (c) 2005-2024, University of Oxford.
All rights reserved.
University of Oxford means the Chancellor, Masters and Scholars of the
University of Oxford, having an administrative office at Wellington
Square, Oxford OX1 2JD, UK.
This file is part of Chaste.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
* Neither the name of the University of Oxford nor the names of 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 LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#ifndef TESTTRANSFORMATIONS_HPP_
#define TESTTRANSFORMATIONS_HPP_
#include <cxxtest/TestSuite.h>
#include "TetrahedralMesh.hpp"
#include "DistributedTetrahedralMesh.hpp"
#include "TrianglesMeshReader.hpp"
#include "TrianglesMeshWriter.hpp"
#include "PetscSetupAndFinalize.hpp"
#include <cmath>
/* HOW_TO_TAG Mesh
* Apply transformations to meshes
*/
class TestTransformations : public CxxTest::TestSuite
{
public:
void TestRefreshMeshByScaling()
{
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_136_elements");
TetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
TS_ASSERT_DELTA(mesh.GetVolume(), 1.0, 1e-6);
TS_ASSERT_DELTA(mesh.GetSurfaceArea(), 6.0, 1e-6);
// Change coordinates
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
Node<3>* p_node = mesh.GetNode(i);
ChastePoint<3> point = p_node->GetPoint();
point.SetCoordinate(0, point[0]*2.0);
point.SetCoordinate(1, point[1]*2.0);
point.SetCoordinate(2, point[2]*2.0);
p_node->SetPoint(point);
}
mesh.RefreshMesh();
TS_ASSERT_DELTA(mesh.GetVolume(), 8.0, 1e-6);
TS_ASSERT_DELTA(mesh.GetSurfaceArea(), 24.0, 1e-6);
}
void TestTranslation3DWithUblas()
{
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_136_elements");
TetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
double volume = mesh.GetVolume();
double surface_area = mesh.GetSurfaceArea();
Node<3>* p_node1 = mesh.GetNode(36);
ChastePoint<3> point1 = p_node1->GetPoint();
Node<3>* p_node2 = mesh.GetNode(23);
ChastePoint<3> point2 = p_node2->GetPoint();
c_vector<double, 3> old_location1 = point1.rGetLocation();
c_vector<double, 3> old_location2 = point2.rGetLocation();
// Set translation Vector
c_vector<double, 3> trans_vec;
trans_vec(0) = 2.0;
trans_vec(1) = 2.0;
trans_vec(2) = 2.0;
// Translate
mesh.Translate(trans_vec);
c_vector<double, 3> new_location1 = point1.rGetLocation();
c_vector<double, 3> new_location2 = point2.rGetLocation();
// Check Volume and Surface Area are invariant
TS_ASSERT_DELTA(mesh.GetVolume(), volume, 1e-6);
TS_ASSERT_DELTA(mesh.GetSurfaceArea(), surface_area, 1e-6);
// Spot check a couple of nodes
TS_ASSERT_DELTA(inner_prod(new_location1-old_location1, trans_vec), 0, 1e-6);
TS_ASSERT_DELTA(inner_prod(new_location2-old_location2, trans_vec), 0, 1e-6);
}
void TestTranslation2DWithUblas()
{
TrianglesMeshReader<2,2> mesh_reader("mesh/test/data/2D_0_to_1mm_200_elements");
TetrahedralMesh<2,2> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
double volume = mesh.GetVolume();
double surface_area = mesh.GetSurfaceArea();
Node<2>* p_node1 = mesh.GetNode(36);
ChastePoint<2> point1 = p_node1->GetPoint();
Node<2>* p_node2 = mesh.GetNode(23);
ChastePoint<2> point2 = p_node2->GetPoint();
c_vector<double, 2> old_location1 = point1.rGetLocation();
c_vector<double, 2> old_location2 = point2.rGetLocation();
// Set translation Vector
c_vector<double, 2> trans_vec;
trans_vec(0) = 2.0;
trans_vec(1) = 2.0;
// Translate
mesh.Translate(trans_vec);
c_vector<double, 2> new_location1 = point1.rGetLocation();
c_vector<double, 2> new_location2 = point2.rGetLocation();
// Check Volume and Surface Area are invariant
TS_ASSERT_DELTA(mesh.GetVolume(), volume, 1e-6);
TS_ASSERT_DELTA(mesh.GetSurfaceArea(), surface_area, 1e-6);
// Spot check a couple of nodes
TS_ASSERT_DELTA(inner_prod(new_location1-old_location1, trans_vec), 0, 1e-6);
TS_ASSERT_DELTA(inner_prod(new_location2-old_location2, trans_vec), 0, 1e-6);
}
void TestTranslationMethod()
{
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_136_elements");
TetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
// Pick a random node and store spatial position
Node<3>* p_node = mesh.GetNode(10);
ChastePoint<3> original_coordinate = p_node->GetPoint();
double mesh_volume = mesh.GetVolume();
const double x_movement = 1.0;
const double y_movement = 2.5;
const double z_movement = -3.75;
mesh.Translate(x_movement, y_movement, z_movement);
ChastePoint<3> new_coordinate = p_node->GetPoint();
double new_mesh_volume = mesh.GetVolume();
TS_ASSERT_DELTA(mesh_volume, new_mesh_volume, 1e-6);
TS_ASSERT_DELTA(original_coordinate[0], new_coordinate[0]-x_movement, 1e-6);
TS_ASSERT_DELTA(original_coordinate[1], new_coordinate[1]-y_movement, 1e-6);
TS_ASSERT_DELTA(original_coordinate[2], new_coordinate[2]-z_movement, 1e-6);
}
void Test3DMeshTranslationWithUblasMethod()
{
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_136_elements");
TetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
// Translations - add a constant vector to each node
c_vector<double,3> displacement;
displacement(0) = 1;
displacement(1) = 1;
displacement(2) = 1;
// Translate the mesh along the vector displacement
mesh.Translate(displacement);
TetrahedralMesh<3,3> original_mesh;
original_mesh.ConstructFromMeshReader(mesh_reader);
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
// Find new coordinates of the translated node
Node<3>* p_node = mesh.GetNode(i);
ChastePoint<3> new_coordinate = p_node->GetPoint();
// Get original node
Node<3>* p_original_node = original_mesh.GetNode(i);
ChastePoint<3> original_coordinate = p_original_node->GetPoint();
// Run a test to make sure the node has gone to the correct place
TS_ASSERT_DELTA(original_coordinate[0] + displacement[0], new_coordinate[0], 1e-5);
TS_ASSERT_DELTA(original_coordinate[1] + displacement[1], new_coordinate[1], 1e-5);
TS_ASSERT_DELTA(original_coordinate[2] + displacement[2], new_coordinate[2], 1e-5);
}
// Check volume conservation
double mesh_volume = mesh.GetVolume();
double original_mesh_volume = original_mesh.GetVolume();
TS_ASSERT_DELTA(mesh_volume, original_mesh_volume, 1e-5);
}
void TestXaxisRotation3DWithHomogeneousUblas()
{
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_136_elements");
TetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
TS_ASSERT_DELTA(mesh.GetVolume(), 1.0, 1e-6);
TS_ASSERT_DELTA(mesh.GetSurfaceArea(), 6.0, 1e-6);
// Change coordinates
c_matrix<double, 4, 4> x_rotation_matrix = identity_matrix<double>(4);
double theta = M_PI/2;
x_rotation_matrix(1,1) = cos(theta);
x_rotation_matrix(1,2) = sin(theta);
x_rotation_matrix(2,1) = -sin(theta);
x_rotation_matrix(2,2) = cos(theta);
ChastePoint<3> corner_before = mesh.GetNode(6)->GetPoint();
TS_ASSERT_EQUALS(corner_before[0], 1.0);
TS_ASSERT_EQUALS(corner_before[1], 1.0);
TS_ASSERT_EQUALS(corner_before[2], 1.0);
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
Node<3>* p_node = mesh.GetNode(i);
ChastePoint<3> point = p_node->GetPoint();
c_vector<double, 4> point_location;
point_location[0] = point[0];
point_location[1] = point[1];
point_location[2] = point[2];
point_location[3] = 1.0;
c_vector<double, 4> new_point_location = prod(x_rotation_matrix, point_location);
TS_ASSERT_EQUALS(new_point_location[3], 1.0);
point.SetCoordinate(0, new_point_location[0]);
point.SetCoordinate(1, new_point_location[1]);
point.SetCoordinate(2, new_point_location[2]);
p_node->SetPoint(point);
}
ChastePoint<3> corner_after = mesh.GetNode(6)->GetPoint();
TS_ASSERT_EQUALS(corner_after[0], 1.0);
TS_ASSERT_EQUALS(corner_after[1], 1.0);
TS_ASSERT_DELTA(corner_after[2], -1.0, 1e-7);
mesh.RefreshMesh();
TS_ASSERT_DELTA(mesh.GetVolume(), 1.0, 1e-6);
TS_ASSERT_DELTA(mesh.GetSurfaceArea(), 6.0, 1e-6);
}
void TestXaxisRotation3DWithMethod()
{
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_136_elements");
TetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
ChastePoint<3> corner_before = mesh.GetNode(6)->GetPoint();
TS_ASSERT_EQUALS(corner_before[0], 1.0);
TS_ASSERT_EQUALS(corner_before[1], 1.0);
TS_ASSERT_EQUALS(corner_before[2], 1.0);
double mesh_volume = mesh.GetVolume();
mesh.RotateX(M_PI/2.0);
double new_mesh_volume = mesh.GetVolume();
TS_ASSERT_DELTA(mesh_volume,new_mesh_volume,1e-6);
ChastePoint<3> corner_after = mesh.GetNode(6)->GetPoint();
TS_ASSERT_DELTA(corner_after[0], 1.0, 1e-7);
TS_ASSERT_DELTA(corner_after[1], 1.0, 1e-7);
TS_ASSERT_DELTA(corner_after[2], -1.0, 1e-7);
}
void TestYaxisRotation3DWithMethod()
{
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_136_elements");
TetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
double mesh_volume = mesh.GetVolume();
mesh.RotateY(M_PI/2.0);
double new_mesh_volume = mesh.GetVolume();
TS_ASSERT_DELTA(mesh_volume, new_mesh_volume, 1e-6);
ChastePoint<3> corner_after = mesh.GetNode(6)->GetPoint();
TS_ASSERT_DELTA(corner_after[0], -1.0, 1e-7);
TS_ASSERT_DELTA(corner_after[1], 1.0, 1e-7);
TS_ASSERT_DELTA(corner_after[2], 1.0, 1e-7);
}
void TestZaxisRotation3DWithMethod()
{
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_136_elements");
TetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
double mesh_volume = mesh.GetVolume();
mesh.RotateZ(M_PI/2.0);
double new_mesh_volume = mesh.GetVolume();
TS_ASSERT_DELTA(mesh_volume, new_mesh_volume, 1e-6);
ChastePoint<3> corner_after = mesh.GetNode(6)->GetPoint();
TS_ASSERT_DELTA(corner_after[0], 1.0, 1e-7);
TS_ASSERT_DELTA(corner_after[1], -1.0, 1e-7);
TS_ASSERT_DELTA(corner_after[2], 1.0, 1e-7);
}
void TestGeneralConvolution3DWithHomogeneousUblas()
{
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_136_elements");
TetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
TS_ASSERT_DELTA(mesh.GetVolume(), 1.0, 1e-6);
TS_ASSERT_DELTA(mesh.GetSurfaceArea(), 6.0, 1e-6);
// Change coordinates
c_matrix<double, 4, 4> x_rotation_matrix = identity_matrix<double>(4);
c_matrix<double, 4, 4> y_rotation_matrix = identity_matrix<double>(4);
c_matrix<double, 4, 4> z_rotation_matrix = identity_matrix<double>(4);
c_matrix<double, 4, 4> translation_matrix = identity_matrix<double>(4);
double theta = 0.7;
double phi = 0.3;
double psi = 1.4;
x_rotation_matrix(1,1) = cos(theta);
x_rotation_matrix(1,2) = sin(theta);
x_rotation_matrix(2,1) = -sin(theta);
x_rotation_matrix(2,2) = cos(theta);
y_rotation_matrix(0,0) = cos(phi);
y_rotation_matrix(0,2) = -sin(phi);
y_rotation_matrix(2,0) = sin(phi);
y_rotation_matrix(2,2) = cos(phi);
z_rotation_matrix(0,0) = cos(psi);
z_rotation_matrix(0,1) = sin(psi);
z_rotation_matrix(1,0) = -sin(psi);
z_rotation_matrix(1,1) = cos(psi);
translation_matrix(0,3) = 2.3;
translation_matrix(1,3) = 3.1;
translation_matrix(2,3) = 1.7;
/*
Note: because we are using column-major vectors this tranformation:
RotX(theta) . RotY(phi) . RotZ(psi) . Trans(...)
is actually being applied right-to-left
See test below.
*/
c_matrix<double, 4, 4> transformation_matrix = prod (x_rotation_matrix, y_rotation_matrix);
transformation_matrix = prod (transformation_matrix, z_rotation_matrix);
transformation_matrix = prod (transformation_matrix, translation_matrix);
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
Node<3>* p_node = mesh.GetNode(i);
ChastePoint<3> point = p_node->GetPoint();
c_vector<double, 4> point_location;
point_location[0] = point[0];
point_location[1] = point[1];
point_location[2] = point[2];
point_location[3] = 1.0;
c_vector<double, 4> new_point_location = prod(transformation_matrix, point_location);
TS_ASSERT_EQUALS(new_point_location[3], 1.0);
point.SetCoordinate(0,new_point_location[0]);
point.SetCoordinate(1,new_point_location[1]);
point.SetCoordinate(2,new_point_location[2]);
p_node->SetPoint(point);
}
mesh.RefreshMesh();
TS_ASSERT_DELTA(mesh.GetVolume(), 1.0, 1e-6);
TS_ASSERT_DELTA(mesh.GetSurfaceArea(), 6.0, 1e-6);
ChastePoint<3> corner_after = mesh.GetNode(6)->GetPoint();
TS_ASSERT_DELTA(corner_after[0], 3.59782, 5e-5);
TS_ASSERT_DELTA(corner_after[1], 0.583418, 5e-5);
TS_ASSERT_DELTA(corner_after[2], 4.65889, 5e-5);
// Write to file
TrianglesMeshWriter<3,3> mesh_writer("","TransformedMesh");
mesh_writer.WriteFilesUsingMesh(mesh);
/*
* Now try
tetview /tmp/chaste/testoutput/TransformedMesh
*/
}
void TestGeneralConvolution3DWithMethod()
{
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_136_elements");
TetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
double mesh_volume = mesh.GetVolume();
mesh.Translate(2.3, 3.1, 1.7);
mesh.RotateZ(1.4);
mesh.RotateY(0.3);
mesh.RotateX(0.7);
double new_mesh_volume = mesh.GetVolume();
TS_ASSERT_DELTA(mesh_volume, new_mesh_volume, 1e-6);
ChastePoint<3> corner_after = mesh.GetNode(6)->GetPoint();
TS_ASSERT_DELTA(corner_after[0], 3.59782, 5e-5);
TS_ASSERT_DELTA(corner_after[1], 0.583418, 5e-5);
TS_ASSERT_DELTA(corner_after[2], 4.65889, 5e-5);
}
void Test3DAngleAxisRotation()
{
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_136_elements");
TetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
c_vector<double,3> axis;
axis(0) = 1;
axis(1) = 0;
axis(2) = 0;
double angle = M_PI;
mesh.Rotate(axis, angle);
TetrahedralMesh<3,3> original_mesh;
original_mesh.ConstructFromMeshReader(mesh_reader);
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
Node<3>* p_node = mesh.GetNode(i);
ChastePoint<3> new_coordinate = p_node->GetPoint();
// Get original node
Node<3>* p_original_node = original_mesh.GetNode(i);
ChastePoint<3> original_coordinate = p_original_node->GetPoint();
// Run a test to make sure the node has gone to the correct place
TS_ASSERT_DELTA(original_coordinate[0], new_coordinate[0], 1e-5);
TS_ASSERT_DELTA(original_coordinate[1], -new_coordinate[1], 1e-5);
TS_ASSERT_DELTA(original_coordinate[2], -new_coordinate[2], 1e-5);
}
// Check volume conservation
double mesh_volume = mesh.GetVolume();
double original_mesh_volume = original_mesh.GetVolume();
TS_ASSERT_DELTA(mesh_volume, original_mesh_volume, 1e-5);
}
void Test2DMeshRotation()
{
TrianglesMeshReader<2,2> mesh_reader("mesh/test/data/2D_0_to_1mm_200_elements");
TetrahedralMesh<2,2> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
double angle = M_PI;
mesh.Rotate(angle);
TetrahedralMesh<2,2> original_mesh;
original_mesh.ConstructFromMeshReader(mesh_reader);
for (unsigned i=0; i<mesh.GetNumNodes(); i++)
{
// Find new coordinates of the translated node
Node<2>* p_node = mesh.GetNode(i);
ChastePoint<2> new_coordinate = p_node->GetPoint();
// Get original node
Node<2>* p_original_node = original_mesh.GetNode(i);
ChastePoint<2> original_coordinate = p_original_node->GetPoint();
// Run a test to make sure the node has gone to the correct place
TS_ASSERT_DELTA(original_coordinate[0], -new_coordinate[0], 1e-5);
TS_ASSERT_DELTA(original_coordinate[1], -new_coordinate[1], 1e-5);
}
// Check volume conservation
double mesh_volume = mesh.GetVolume();
double original_mesh_volume = original_mesh.GetVolume();
TS_ASSERT_DELTA(mesh_volume, original_mesh_volume, 1e-5);
}
void TestScalingWithMethod()
{
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_136_elements");
TetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
double mesh_volume = mesh.GetVolume();
mesh.Scale(1.0);
TS_ASSERT_DELTA(mesh_volume, mesh.GetVolume(), 1e-6);
mesh.Scale(2.0, 3.0, 4.0);
TS_ASSERT_DELTA(24.0*mesh_volume, mesh.GetVolume(), 1e-6);
ChastePoint<3> corner_after = mesh.GetNode(6)->GetPoint();
TS_ASSERT_DELTA(corner_after[0], 2.0, 1e-7);
TS_ASSERT_DELTA(corner_after[1], 3.0, 1e-7);
TS_ASSERT_DELTA(corner_after[2], 4.0, 1e-7);
mesh.Scale(0.5, 1.0/3.0, 0.25);
TS_ASSERT_DELTA(mesh_volume,mesh.GetVolume(),1e-6);
corner_after = mesh.GetNode(6)->GetPoint();
TS_ASSERT_DELTA(corner_after[0], 1.0, 1e-7);
TS_ASSERT_DELTA(corner_after[1], 1.0, 1e-7);
TS_ASSERT_DELTA(corner_after[2], 1.0, 1e-7);
}
void failsInParallelTestDistributedRigidBodyMethods()
{
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_136_elements");
DistributedTetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
c_matrix<double, 3, 3> dummy;
double jacobian_det = 0.0;
double scaled_volume = 0.0;
for (AbstractTetrahedralMesh<3, 3>::ElementIterator iter = mesh.GetElementIteratorBegin();
iter != mesh.GetElementIteratorEnd();
++iter)
{
iter->CalculateJacobian(dummy, jacobian_det);
scaled_volume += jacobian_det;
}
TS_ASSERT_DELTA(scaled_volume, 1.0*6, 1e-6);
mesh.RotateX(M_PI);
//mesh.Translate(100.0, 0.0, 0.0);
double scaled_volume_after = 0.0;
for (AbstractTetrahedralMesh<3, 3>::ElementIterator iter = mesh.GetElementIteratorBegin();
iter != mesh.GetElementIteratorEnd();
++iter)
{
iter->CalculateJacobian(dummy, jacobian_det);
scaled_volume_after += jacobian_det;
}
TS_ASSERT_DELTA(scaled_volume_after, 1.0*6, 1e-6);
}
void TestExceptions()
{
TrianglesMeshReader<1,1> mesh_reader("mesh/test/data/1D_0_to_10_100_elements");
TetrahedralMesh<1,1> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
TS_ASSERT_THROWS_THIS(mesh.RotateZ(1.4),"This rotation is not valid in less than 2D");
TS_ASSERT_THROWS_THIS(mesh.RotateY(0.3),"This rotation is only valid in 3D");
TS_ASSERT_THROWS_THIS(mesh.RotateX(0.7),"This rotation is only valid in 3D");
}
};
#endif /*TESTTRANSFORMATIONS_HPP_*/