framestest.cpp

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#include <math.h>
#include "framestest.hpp"
#include <frames_io.hpp>
CPPUNIT_TEST_SUITE_REGISTRATION( FramesTest );

using namespace KDL;

void FramesTest::setUp()
{
}

void FramesTest::tearDown()
{
}

void FramesTest::TestVector2(Vector& v) {
    Vector   v2;
    CPPUNIT_ASSERT_EQUAL(2*v-v,v);
        CPPUNIT_ASSERT_EQUAL(v*2-v,v);
        CPPUNIT_ASSERT_EQUAL(v+v+v-2*v,v);
        v2=v;
        CPPUNIT_ASSERT_EQUAL(v,v2);
        v2+=v;
        CPPUNIT_ASSERT_EQUAL(2*v,v2);
        v2-=v;
        CPPUNIT_ASSERT_EQUAL(v,v2);
        v2.ReverseSign();
        CPPUNIT_ASSERT_EQUAL(v,-v2);
}

void FramesTest::TestVector() {
        Vector   v(3,4,5);
        TestVector2(v);
        Vector   v2(0,0,0);
        TestVector2(v2);
        
        Vector nu(0,0,0);
        CPPUNIT_ASSERT_EQUAL(nu.Norm(),0.0);
        Vector nu2(10,0,0);
        CPPUNIT_ASSERT_EQUAL(nu2.Norm(),10.0);
}

void FramesTest::TestVector2DNorm() {
    Vector2 nu(0, 0);
        CPPUNIT_ASSERT_EQUAL(nu.Norm(), 0.0);
        
        CPPUNIT_ASSERT_EQUAL(Vector2(1, 0).Norm(), 1.0);
        CPPUNIT_ASSERT_EQUAL(Vector2(0, 1).Norm(), 1.0);
        CPPUNIT_ASSERT_EQUAL(Vector2(-1, 0).Norm(), 1.0);
        CPPUNIT_ASSERT_EQUAL(Vector2(0, -1).Norm(), 1.0);
}

void FramesTest::TestTwist2(Twist& t) {
        Twist t2(Vector(16,-3,5),Vector(-4,2,1));

        CPPUNIT_ASSERT_EQUAL(2*t-t,t);
        CPPUNIT_ASSERT_EQUAL(t*2-t,t);
        CPPUNIT_ASSERT_EQUAL(t+t+t-2*t,t);
        t2=t;
        CPPUNIT_ASSERT_EQUAL(t,t2);
        t2+=t;
        CPPUNIT_ASSERT_EQUAL(2*t,t2);
        t2-=t;
        CPPUNIT_ASSERT_EQUAL(t,t2);
        t.ReverseSign();
        CPPUNIT_ASSERT_EQUAL(t,-t2);
}

void FramesTest::TestTwist() {
        Twist    t(Vector(6,3,5),Vector(4,-2,7));
        TestTwist2(t);
        Twist    t2(Vector(0,0,0),Vector(0,0,0));
        TestTwist2(t2); 
        Twist    t3(Vector(0,-9,-3),Vector(1,-2,-4));
        TestTwist2(t3); 
}

void FramesTest::TestWrench2(Wrench& w) {
        // Wrench
        Wrench   w2;    
        CPPUNIT_ASSERT_EQUAL(2*w-w,w);
        CPPUNIT_ASSERT_EQUAL(w*2-w,w);
        CPPUNIT_ASSERT_EQUAL(w+w+w-2*w,w);
        w2=w;
        CPPUNIT_ASSERT_EQUAL(w,w2);
        w2+=w;
        CPPUNIT_ASSERT_EQUAL(2*w,w2);
        w2-=w;
        CPPUNIT_ASSERT_EQUAL(w,w2);
        w.ReverseSign();
        CPPUNIT_ASSERT_EQUAL(w,-w2);
}

void FramesTest::TestWrench() {
        Wrench   w(Vector(7,-1,3),Vector(2,-3,3));
        TestWrench2(w);
        Wrench   w2(Vector(0,0,0),Vector(0,0,0));
        TestWrench2(w2);
        Wrench   w3(Vector(2,1,4),Vector(5,3,1));
        TestWrench2(w3);                
}

void FramesTest::TestRotation2(const Vector& v,double a,double b,double c) {
        Vector   v2; 
        // Wrench
        Wrench   w(Vector(7,-1,3),Vector(2,-3,3));
        Twist    t(Vector(6,3,5),Vector(4,-2,7));
        // Rotation             
        Rotation R;
        Rotation R2;
        double ra;
        double rb;
        double rc;
    R = Rotation::RPY(a,b,c);

    CPPUNIT_ASSERT_DOUBLES_EQUAL(dot(R.UnitX(),R.UnitX()),1.0,epsilon);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(dot(R.UnitY(),R.UnitY()),1.0,epsilon);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(dot(R.UnitZ(),R.UnitZ()),1.0,epsilon);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(dot(R.UnitX(),R.UnitY()),0.0,epsilon);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(dot(R.UnitX(),R.UnitZ()),0.0,epsilon);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(dot(R.UnitY(),R.UnitZ()),0.0,epsilon);
        R2=R;
        CPPUNIT_ASSERT_EQUAL(R,R2);
        CPPUNIT_ASSERT_DOUBLES_EQUAL((R*v).Norm(),v.Norm(),epsilon);
        CPPUNIT_ASSERT_EQUAL(R.Inverse(R*v),v);
        CPPUNIT_ASSERT_EQUAL(R.Inverse(R*t),t);
        CPPUNIT_ASSERT_EQUAL(R.Inverse(R*w),w);
        CPPUNIT_ASSERT_EQUAL(R*R.Inverse(v),v);
        CPPUNIT_ASSERT_EQUAL(R*Rotation::Identity(),R);
        CPPUNIT_ASSERT_EQUAL(Rotation::Identity()*R,R);
        CPPUNIT_ASSERT_EQUAL(R*(R*(R*v)),(R*R*R)*v);
        CPPUNIT_ASSERT_EQUAL(R*(R*(R*t)),(R*R*R)*t);
        CPPUNIT_ASSERT_EQUAL(R*(R*(R*w)),(R*R*R)*w);
        CPPUNIT_ASSERT_EQUAL(R*R.Inverse(),Rotation::Identity());
        CPPUNIT_ASSERT_EQUAL(R.Inverse()*R,Rotation::Identity());
        CPPUNIT_ASSERT_EQUAL(R.Inverse()*v,R.Inverse(v));
        R.GetRPY(ra,rb,rc);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(ra,a,epsilon);
    CPPUNIT_ASSERT_DOUBLES_EQUAL(rb,b,epsilon);
    CPPUNIT_ASSERT_DOUBLES_EQUAL(rc,c,epsilon);
        R = Rotation::EulerZYX(a,b,c);
        R.GetEulerZYX(ra,rb,rc);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(ra,a,epsilon);
    CPPUNIT_ASSERT_DOUBLES_EQUAL(rb,b,epsilon);
    CPPUNIT_ASSERT_DOUBLES_EQUAL(rc,c,epsilon);
        R = Rotation::EulerZYZ(a,b,c);
        R.GetEulerZYZ(ra,rb,rc);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(ra,a,epsilon);
    CPPUNIT_ASSERT_DOUBLES_EQUAL(rb,b,epsilon);
    CPPUNIT_ASSERT_DOUBLES_EQUAL(rc,c,epsilon);
        double angle= R.GetRotAngle(v2);
        R2=Rotation::Rot2(v2,angle);
        CPPUNIT_ASSERT_EQUAL(R2,R);
        R2=Rotation::Rot(v2*1E20,angle);
        CPPUNIT_ASSERT_EQUAL(R,R2);
        v2=Vector(6,2,4);
        CPPUNIT_ASSERT_DOUBLES_EQUAL((v2).Norm(),::sqrt(dot(v2,v2)),epsilon);
}


// compare a rotation R with the expected angle and axis
void FramesTest::TestOneRotation(const std::string& msg,
                                                                 const KDL::Rotation& R,
                                                                 const double expectedAngle,
                                                                 const KDL::Vector& expectedAxis)
{
        double          angle =0;
        Vector          axis;

        angle = R.GetRotAngle(axis);
        CPPUNIT_ASSERT_DOUBLES_EQUAL_MESSAGE(msg, expectedAngle, angle, epsilon);
        CPPUNIT_ASSERT_EQUAL_MESSAGE(msg, expectedAxis, axis);
        CPPUNIT_ASSERT_EQUAL_MESSAGE(msg, expectedAngle * expectedAxis, R.GetRot());
        CPPUNIT_ASSERT_EQUAL_MESSAGE(msg, Rotation::Rot(axis, angle), R);
        (void)axis.Normalize();
        CPPUNIT_ASSERT_EQUAL_MESSAGE(msg, Rotation::Rot2(axis, angle), R);
}



void FramesTest::TestArbitraryRotation(const std::string& msg,
                                                                           const KDL::Vector& v,
                                                                           const double angle,
                                                                           const double expectedAngle,
                                                                           const KDL::Vector& expectedVector)
{
        std::stringstream       ss;
        ss << "rot(" << msg << "],(" << angle << ")";
        TestOneRotation(ss.str(), Rotation::Rot(v,angle*deg2rad), expectedAngle*deg2rad, expectedVector);
}


#define TESTEULERZYX(a,b,g) \
                {\
                        double eps=1E-14;\
                        Rotation R = Rotation::EulerZYX((a),(b),(g));\
                        double alpha,beta,gamma;\
                        R.GetEulerZYX(alpha,beta,gamma);\
                        CPPUNIT_ASSERT_DOUBLES_EQUAL((a),alpha,eps);\
                        CPPUNIT_ASSERT_DOUBLES_EQUAL((b),beta,eps);\
                        CPPUNIT_ASSERT_DOUBLES_EQUAL((g),gamma,eps);\
                }

#define TESTEULERZYZ(a,b,g) \
                {\
                        double eps=1E-14;\
                        Rotation R = Rotation::EulerZYZ((a),(b),(g));\
                        double alpha,beta,gamma;\
                        R.GetEulerZYZ(alpha,beta,gamma);\
                        CPPUNIT_ASSERT_DOUBLES_EQUAL((a),alpha,eps);\
                        CPPUNIT_ASSERT_DOUBLES_EQUAL((b),beta,eps);\
                        CPPUNIT_ASSERT_DOUBLES_EQUAL((g),gamma,eps);\
                }
#define TESTEULERZYX_INVARIANT(a,b,g,a2,b2,g2)\
                {\
                        double eps=1E-14;\
                        Rotation R1=Rotation::EulerZYX(a,b,g);\
                        Rotation R2=Rotation::EulerZYX(a2,b2,g2);\
                        CPPUNIT_ASSERT_DOUBLES_EQUAL(0,diff(R2,R1).Norm(),eps);\
                }
#define TESTEULERZYZ_INVARIANT(a,b,g,a2,b2,g2)\
                {\
                        double eps=1E-14;\
                        Rotation R1=Rotation::EulerZYZ(a,b,g);\
                        Rotation R2=Rotation::EulerZYZ(a2,b2,g2);\
                        CPPUNIT_ASSERT_DOUBLES_EQUAL(0,diff(R2,R1).Norm(),eps);\
                }
void FramesTest::TestEuler() {
        using namespace KDL;
        TESTEULERZYX(0.1,0.2,0.3)
        TESTEULERZYX(-0.1,0.2,0.3)
        TESTEULERZYX(0.1,-0.2,0.3)
        TESTEULERZYX(0.1,0.2,-0.3)
        TESTEULERZYX(0,0.2,0.3)
        TESTEULERZYX(0.1,0.2,0)
        TESTEULERZYX(0.1,0,0.3)
        TESTEULERZYX(0.1,0,0)
        TESTEULERZYX(0,0,0.3)
        TESTEULERZYX(0,0,0)
        TESTEULERZYX(0.3,0.999*M_PI/2,0.1)
        // if beta== +/- M_PI/2 => multiple solutions available, gamma will be chosen to be zero !
        // so we test with gamma==0 !
        TESTEULERZYX(0.3,0.9999999999*M_PI/2,0)
        TESTEULERZYX(0.3,0.99999999*M_PI/2,0)
        TESTEULERZYX(0.3,0.999999*M_PI/2,0)
        TESTEULERZYX(0.3,0.9999*M_PI/2,0)
        TESTEULERZYX(0.3,0.99*M_PI/2,0)
        //TESTEULERZYX(0.1,-M_PI/2,0.3)
        TESTEULERZYX(0,M_PI/2,0)

        TESTEULERZYX(0.3,-M_PI/2,0)
        TESTEULERZYX(0.3,-0.9999999999*M_PI/2,0)
        TESTEULERZYX(0.3,-0.99999999*M_PI/2,0)
        TESTEULERZYX(0.3,-0.999999*M_PI/2,0)
        TESTEULERZYX(0.3,-0.9999*M_PI/2,0)
        TESTEULERZYX(0.3,-0.99*M_PI/2,0)
        TESTEULERZYX(0,-M_PI/2,0)

        // extremes of the range:
        TESTEULERZYX(M_PI,-M_PI/2,0)
        TESTEULERZYX(-M_PI,-M_PI/2,0)
        TESTEULERZYX(M_PI,1,0)
        TESTEULERZYX(-M_PI,1,0)
        //TESTEULERZYX(0,-M_PI/2,M_PI)  gamma will be chosen zero
        //TESTEULERZYX(0,M_PI/2,-M_PI)  gamma will be chosen zero
        TESTEULERZYX(0,1,M_PI)

        TESTEULERZYZ(0.1,0.2,0.3)
        TESTEULERZYZ(-0.1,0.2,0.3)
        TESTEULERZYZ(0.1,0.9*M_PI,0.3)
        TESTEULERZYZ(0.1,0.2,-0.3)
        TESTEULERZYZ(0,0,0)
        TESTEULERZYZ(0,0,0)
        TESTEULERZYZ(0,0,0)
        TESTEULERZYZ(PI,0,0)
        TESTEULERZYZ(0,0.2,PI)
        TESTEULERZYZ(0.4,PI,0)
        TESTEULERZYZ(0,PI,0)
        TESTEULERZYZ(PI,PI,0)
        TESTEULERZYX(0.3,M_PI/2,0)
        TESTEULERZYZ(0.3,0.9999999999*M_PI/2,0)
        TESTEULERZYZ(0.3,0.99999999*M_PI/2,0)
        TESTEULERZYZ(0.3,0.999999*M_PI/2,0)
        TESTEULERZYZ(0.3,0.9999*M_PI/2,0)
        TESTEULERZYZ(0.3,0.99*M_PI/2,0)

        TESTEULERZYX_INVARIANT(0.1,0.2,0.3,   0.1+M_PI,  M_PI-0.2, 0.3+M_PI);
        TESTEULERZYX_INVARIANT(0.1,0.2,0.3,   0.1-M_PI,  M_PI-0.2, 0.3-M_PI);
        TESTEULERZYX_INVARIANT(0.1,0.2,0.3,   0.1-M_PI,  M_PI-0.2, 0.3+M_PI);
        TESTEULERZYX_INVARIANT(0.1,0.2,0.3,   0.1+M_PI,  M_PI-0.2, 0.3-M_PI);

        TESTEULERZYZ_INVARIANT(0.1,0.2,0.3,   0.1+M_PI,  -0.2, 0.3+M_PI);
        TESTEULERZYZ_INVARIANT(0.1,0.2,0.3,   0.1-M_PI,  -0.2, 0.3+M_PI);
        TESTEULERZYZ_INVARIANT(0.1,0.2,0.3,   0.1+M_PI,  -0.2, 0.3-M_PI);
        TESTEULERZYZ_INVARIANT(0.1,0.2,0.3,   0.1-M_PI,  -0.2, 0.3-M_PI);
}

void FramesTest::TestRangeArbitraryRotation(const std::string& msg,
                                                                                        const KDL::Vector& v,
                                                                                        const KDL::Vector& expectedVector)
{
        TestArbitraryRotation(msg, v, 0,     0, Vector(0,0,1));         // no rotation
        TestArbitraryRotation(msg, v, 45,   45, expectedVector);
        TestArbitraryRotation(msg, v, 90,   90, expectedVector);
        TestArbitraryRotation(msg, v, 179, 179, expectedVector);
//      TestArbitraryRotation(msg, v, 180, 180, expectedVector);        // sign VARIES by case because 180 degrees not
                                                                // full determined: it can return +/- the axis
                                                                // depending on what the original axis was.
                                                                // BOTH RESULTS ARE CORRECT.
        TestArbitraryRotation(msg, v, 181, 179, -expectedVector);       // >+180 rotation => <+180 + negative axis
        TestArbitraryRotation(msg, v, 270,  90, -expectedVector);
        TestArbitraryRotation(msg, v, 359,   1, -expectedVector);
        TestArbitraryRotation(msg, v, 360,   0, Vector(0,0,1));         // no rotation
        TestArbitraryRotation(msg, v, 361,   1, expectedVector);
        TestArbitraryRotation(msg, v, 450,  90, expectedVector);
        TestArbitraryRotation(msg, v, 539, 179, expectedVector);
//      TestArbitraryRotation(msg, v, 540, 180, expectedVector);        // see above 
        TestArbitraryRotation(msg, v, 541, 179, -expectedVector);       // like 181
        TestArbitraryRotation(msg, v, 630,  90, -expectedVector);       // like 270
        TestArbitraryRotation(msg, v, 719,   1, -expectedVector);       // like 259
        TestArbitraryRotation(msg, v, 720,   0, Vector(0,0,1));         // no rotation

        TestArbitraryRotation(msg, v, -45,   45, -expectedVector);
        TestArbitraryRotation(msg, v, -90,   90, -expectedVector);
        TestArbitraryRotation(msg, v, -179, 179, -expectedVector);
//      TestArbitraryRotation(msg, v, -180, 180, expectedVector);       // see above 
        TestArbitraryRotation(msg, v, -181, 179, expectedVector);
        TestArbitraryRotation(msg, v, -270,  90, expectedVector);
        TestArbitraryRotation(msg, v, -359,   1, expectedVector);
        TestArbitraryRotation(msg, v, -360,   0, Vector(0,0,1));        // no rotation
        TestArbitraryRotation(msg, v, -361,   1, -expectedVector);
        TestArbitraryRotation(msg, v, -450,  90, -expectedVector);
        TestArbitraryRotation(msg, v, -539, 179, -expectedVector);
//      TestArbitraryRotation(msg, v, -540, 180, -expectedVector);      // see above 
        TestArbitraryRotation(msg, v, -541, 179, expectedVector);
        TestArbitraryRotation(msg, v, -630,  90, expectedVector);
        TestArbitraryRotation(msg, v, -719,   1, expectedVector);
        TestArbitraryRotation(msg, v, -720,   0, Vector(0,0,1));        // no rotation
}

void FramesTest::TestRotation() {
        TestRotation2(Vector(3,4,5),10*deg2rad,20*deg2rad,30*deg2rad);

        // X axis
        TestRangeArbitraryRotation("[1,0,0]", Vector(1,0,0), Vector(1,0,0));
        TestRangeArbitraryRotation("[-1,0,0]", Vector(-1,0,0), Vector(-1,0,0));
        // Y axis
        TestRangeArbitraryRotation("[0,1,0]", Vector(0,1,0), Vector(0,1,0));
        TestRangeArbitraryRotation("[0,-1,0]", Vector(0,-1,0), Vector(0,-1,0));
        // Z axis
        TestRangeArbitraryRotation("[0,0,1]", Vector(0,0,1), Vector(0,0,1));
        TestRangeArbitraryRotation("[0,0,-1]", Vector(0,0,-1), Vector(0,0,-1));
        // X,Y axes
        TestRangeArbitraryRotation("[1,1,0]", Vector(1,1,0), Vector(1,1,0)/sqrt(2.0));
        TestRangeArbitraryRotation("[-1,-1,0]", Vector(-1,-1,0), Vector(-1,-1,0)/sqrt(2.0));
        // X,Z axes
        TestRangeArbitraryRotation("[1,0,1]", Vector(1,0,1), Vector(1,0,1)/sqrt(2.0));
        TestRangeArbitraryRotation("[-1,0,-1]", Vector(-1,0,-1), Vector(-1,0,-1)/sqrt(2.0));
        // Y,Z axes
        TestRangeArbitraryRotation("[0,1,1]", Vector(0,1,1), Vector(0,1,1)/sqrt(2.0));
        TestRangeArbitraryRotation("[0,-1,-1]", Vector(0,-1,-1), Vector(0,-1,-1)/sqrt(2.0));
        // X,Y,Z axes
        TestRangeArbitraryRotation("[1,1,1]", Vector(1,1,1), Vector(1,1,1)/sqrt(3.0));
        TestRangeArbitraryRotation("[-1,-1,-1]", Vector(-1,-1,-1), Vector(-1,-1,-1)/sqrt(3.0));

        // these change ... some of the -180 are the same as the +180, and some
        // results are the opposite sign.
        TestOneRotation("rot([1,0,0],180)", KDL::Rotation::Rot(KDL::Vector(1,0,0),180*deg2rad), 180*deg2rad, Vector(1,0,0));
        // same as +180
        TestOneRotation("rot([-1,0,0],180)", KDL::Rotation::Rot(KDL::Vector(-1,0,0),180*deg2rad), 180*deg2rad, Vector(1,0,0));
        TestOneRotation("rot([0,1,0],180)", KDL::Rotation::Rot(KDL::Vector(0,1,0),180*deg2rad), 180*deg2rad, Vector(0,1,0));
        // same as +180
        TestOneRotation("rot([0,-1,0],180)", KDL::Rotation::Rot(KDL::Vector(0,-1,0),180*deg2rad), 180*deg2rad, Vector(0,1,0));

        TestOneRotation("rot([0,0,1],180)", KDL::Rotation::Rot(KDL::Vector(0,0,1),180*deg2rad), 180*deg2rad, Vector(0,0,1));
        // same as +180
        TestOneRotation("rot([0,0,-1],180)", KDL::Rotation::Rot(KDL::Vector(0,0,-1),180*deg2rad), 180*deg2rad, Vector(0,0,1));

        TestOneRotation("rot([1,0,1],180)", KDL::Rotation::Rot(KDL::Vector(1,0,1),180*deg2rad), 180*deg2rad, Vector(1,0,1)/sqrt(2.0));
        // same as +180
        TestOneRotation("rot([1,0,1],-180)", KDL::Rotation::Rot(KDL::Vector(1,0,1),-180*deg2rad), 180*deg2rad, Vector(1,0,1)/sqrt(2.0));
        TestOneRotation("rot([-1,0,-1],180)", KDL::Rotation::Rot(KDL::Vector(-1,0,-1),180*deg2rad), 180*deg2rad, Vector(1,0,1)/sqrt(2.0));
        // same as +180
        TestOneRotation("rot([-1,0,-1],-180)", KDL::Rotation::Rot(KDL::Vector(-1,0,-1),-180*deg2rad), 180*deg2rad, Vector(1,0,1)/sqrt(2.0));

        TestOneRotation("rot([1,1,0],180)", KDL::Rotation::Rot(KDL::Vector(1,1,0),180*deg2rad), 180*deg2rad, Vector(1,1,0)/sqrt(2.0));
        // opposite of +180
        TestOneRotation("rot([1,1,0],-180)", KDL::Rotation::Rot(KDL::Vector(1,1,0),-180*deg2rad), 180*deg2rad, Vector(1,1,0)/sqrt(2.0));
        TestOneRotation("rot([-1,-1,0],180)", KDL::Rotation::Rot(KDL::Vector(-1,-1,0),180*deg2rad), 180*deg2rad, Vector(1,1,0)/sqrt(2.0));
        // opposite of +180
        TestOneRotation("rot([-1,-1,0],-180)", KDL::Rotation::Rot(KDL::Vector(-1,-1,0),-180*deg2rad), 180*deg2rad, Vector(1,1,0)/sqrt(2.0));

        TestOneRotation("rot([0,1,1],180)", KDL::Rotation::Rot(KDL::Vector(0,1,1),180*deg2rad), 180*deg2rad, Vector(0,1,1)/sqrt(2.0));
        // same as +180
        TestOneRotation("rot([0,1,1],-180)", KDL::Rotation::Rot(KDL::Vector(0,1,1),-180*deg2rad), 180*deg2rad, Vector(0,1,1)/sqrt(2.0));
        TestOneRotation("rot([0,-1,-1],180)", KDL::Rotation::Rot(KDL::Vector(0,-1,-1),180*deg2rad), 180*deg2rad, Vector(0,1,1)/sqrt(2.0));
        // same as +180
        TestOneRotation("rot([0,-1,-1],-180)", KDL::Rotation::Rot(KDL::Vector(0,-1,-1),-180*deg2rad), 180*deg2rad, Vector(0,1,1)/sqrt(2.0));

        TestOneRotation("rot([1,1,1],180)", KDL::Rotation::Rot(KDL::Vector(1,1,1),180*deg2rad), 180*deg2rad, Vector(1,1,1)/sqrt(3.0));
        // same as +180
        TestOneRotation("rot([1,1,1],-180)", KDL::Rotation::Rot(KDL::Vector(1,1,1),-180*deg2rad), 180*deg2rad, Vector(1,1,1)/sqrt(3.0));
        TestOneRotation("rot([-1,-1,-1],180)", KDL::Rotation::Rot(KDL::Vector(-1,-1,-1),180*deg2rad), 180*deg2rad, Vector(1,1,1)/sqrt(3.0));
        // same as +180
        TestOneRotation("rot([-1,-1,-1],-180)", KDL::Rotation::Rot(KDL::Vector(-1,-1,-1),-180*deg2rad), 180*deg2rad, Vector(1,1,1)/sqrt(3.0));

        TestOneRotation("rot([0.707107, 0, 0.707107", KDL::Rotation::RPY(-2.9811968953315162, -atan(1)*2, -0.1603957582582825), 180*deg2rad, Vector(0.707107,0,0.707107) );
}

void FramesTest::TestGetRotAngle() {
    static const double pi = atan(1)*4;
    double roll = -2.9811968953315162;
    double pitch = -pi/2;
    double yaw = -0.1603957582582825;

    // rpy -> rotation
    KDL::Rotation kdlRotation1 = KDL::Rotation::RPY(roll, pitch, yaw);

    // rotation -> angle-axis (with KDL::GetRotAngle)
    KDL::Vector kdlAxis;
    double theta = kdlRotation1.GetRotAngle(kdlAxis);


    CPPUNIT_ASSERT(0==isnan(theta));
    CPPUNIT_ASSERT(0==isnan(kdlAxis[0]));
    CPPUNIT_ASSERT(0==isnan(kdlAxis[1]));
    CPPUNIT_ASSERT(0==isnan(kdlAxis[2]));

  // Test GetRotAngle on slightly non-orthogonal rotation matrices
  {
    Vector axis;
    double angle = KDL::Rotation( 1, 0, 0 + 1e-6, 0, 1, 0, 0, 0,  1 + 1e-6).GetRotAngle(axis);
    CPPUNIT_ASSERT_DOUBLES_EQUAL_MESSAGE("rot(NON-ORTHOGONAL, 0)", 0.0, angle, epsilon);
  }

  {
    Vector axis;
    double angle = KDL::Rotation(-1, 0, 0 + 1e-6, 0, 1, 0, 0, 0, -1 - 1e-6).GetRotAngle(axis);
    CPPUNIT_ASSERT_DOUBLES_EQUAL_MESSAGE("rot(NON-ORTHOGONAL, PI)", M_PI, angle, epsilon);
  }

  // Tests to show that GetRotAngle does not work for an improper rotation matrix which has a determinant of -1;
  // an improper rotation matrix corresponds to a rotation between a right-hand and left-hand coordinate system
  {
    Vector axis;
    double angle;
    Rotation R, Rout;
    double det;
    // Improper Rotation Matrix for 120 deg rotation
    R = KDL::Rotation( 0, -1, 0, 0, 0, -1, -1, 0, 0);
    det = +R(0,0)*(R(1,1)*R(2,2)-R(2,1)*R(1,2))-R(0,1)*(R(1,0)*R(2,2)-R(2,0)*R(1,2))+R(0,2)*(R(1,0)*R(2,1)-R(2,0)*R(1,1));
    CPPUNIT_ASSERT_EQUAL(det,-1.0);
    angle = R.GetRotAngle(axis);
    Rout = KDL::Rotation::Rot(axis, angle);
    CPPUNIT_ASSERT_ASSERTION_FAIL(CPPUNIT_ASSERT_EQUAL(R,Rout));
    // Improper Rotation matrix for 180 deg rotation (singular)
    R = KDL::Rotation( -1, 0, 0, 0, -1, 0, 0, 0, -1);
    det = +R(0,0)*(R(1,1)*R(2,2)-R(2,1)*R(1,2))-R(0,1)*(R(1,0)*R(2,2)-R(2,0)*R(1,2))+R(0,2)*(R(1,0)*R(2,1)-R(2,0)*R(1,1));
    CPPUNIT_ASSERT_EQUAL(det,-1.0);
    angle = R.GetRotAngle(axis);
    Rout = KDL::Rotation::Rot(axis, angle);
    CPPUNIT_ASSERT_ASSERTION_FAIL(CPPUNIT_ASSERT_EQUAL(R,Rout));
  }

}

void FramesTest::TestQuaternion() {
    Rotation    R;
    Rotation    R2;
    double      x,y,z,w;
    double      x2,y2,z2,w2;

    // identity R -> quat -> R2
    R.GetQuaternion(x,y,z,w);
    R2.Quaternion(x,y,z,w);
        CPPUNIT_ASSERT_EQUAL(R,R2);

    // 45 deg rotation in X
    R = Rotation::EulerZYX(0,0,45*deg2rad);
    R.GetQuaternion(x,y,z,w);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(x, sin((45*deg2rad)/2), epsilon);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(y, 0, epsilon);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(z, 0, epsilon);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(w, cos((45*deg2rad)/2), epsilon);
    R2 = Rotation::Quaternion(x,y,z,w);
        CPPUNIT_ASSERT_EQUAL(R,R2);    

    // direct 45 deg rotation in X
    R2 = Rotation::Quaternion(sin((45*deg2rad)/2), 0, 0, cos((45*deg2rad)/2));
        CPPUNIT_ASSERT_EQUAL(R,R2);
    R2.GetQuaternion(x2,y2,z2,w2);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(x, x2, epsilon);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(y, y2, epsilon);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(z, z2, epsilon);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(w, w2, epsilon);
    
    // 45 deg rotation in X and in Z
    R = Rotation::EulerZYX(45*deg2rad,0,45*deg2rad);
    R.GetQuaternion(x,y,z,w);
    R2 = Rotation::Quaternion(x,y,z,w);
        CPPUNIT_ASSERT_EQUAL(R,R2);    
    R2.GetQuaternion(x2,y2,z2,w2);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(x, x2, epsilon);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(y, y2, epsilon);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(z, z2, epsilon);
        CPPUNIT_ASSERT_DOUBLES_EQUAL(w, w2, epsilon);
}


void FramesTest::TestRotationDiff() {

        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotX(0*deg2rad), Rotation::RotX(0*deg2rad)), Vector(0,0,0));           // no rotation
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotX(0*deg2rad), Rotation::RotX(90*deg2rad)), Vector(M_PI/2,0,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotX(0*deg2rad), Rotation::RotX(180*deg2rad)), Vector(M_PI,0,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotX(0*deg2rad), Rotation::RotX(270*deg2rad)), Vector(-M_PI/2,0,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotX(0*deg2rad), Rotation::RotX(360*deg2rad)), Vector(0,0,0));         // no rotation
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotX(0*deg2rad), Rotation::RotX(-360*deg2rad)), Vector(0,0,0));        // no rotation
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotX(0*deg2rad), Rotation::RotX(-270*deg2rad)), Vector(M_PI/2,0,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotX(0*deg2rad), Rotation::RotX(-180*deg2rad)), Vector(M_PI,0,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotX(0*deg2rad), Rotation::RotX(-90*deg2rad)), Vector(-M_PI/2,0,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotX(0*deg2rad), Rotation::RotX(-0*deg2rad)), Vector(0,0,0));          // no rotation

        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotY(0*deg2rad), Rotation::RotY(0*deg2rad)), Vector(0,0,0));           // no rotation
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotY(0*deg2rad), Rotation::RotY(90*deg2rad)), Vector(0,M_PI/2,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotY(0*deg2rad), Rotation::RotY(180*deg2rad)), Vector(0,M_PI,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotY(0*deg2rad), Rotation::RotY(270*deg2rad)), Vector(0,-M_PI/2,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotY(0*deg2rad), Rotation::RotY(360*deg2rad)), Vector(0,0,0));         // no rotation
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotY(0*deg2rad), Rotation::RotY(-360*deg2rad)), Vector(0,0,0));        // no rotation
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotY(0*deg2rad), Rotation::RotY(-270*deg2rad)), Vector(0,M_PI/2,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotY(0*deg2rad), Rotation::RotY(-180*deg2rad)), Vector(0,M_PI,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotY(0*deg2rad), Rotation::RotY(-90*deg2rad)), Vector(0,-M_PI/2,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotY(0*deg2rad), Rotation::RotY(-0*deg2rad)), Vector(0,0,0));          // no rotation

        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotZ(0*deg2rad), Rotation::RotZ(0*deg2rad)), Vector(0,0,0));           // no rotation
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotZ(0*deg2rad), Rotation::RotZ(90*deg2rad)), Vector(0,0,M_PI/2));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotZ(0*deg2rad), Rotation::RotZ(180*deg2rad)), Vector(0,0,M_PI));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotZ(0*deg2rad), Rotation::RotZ(270*deg2rad)), Vector(0,0,-M_PI/2));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotZ(0*deg2rad), Rotation::RotZ(360*deg2rad)), Vector(0,0,0));         // no rotation
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotZ(0*deg2rad), Rotation::RotZ(-360*deg2rad)), Vector(0,0,0));        // no rotation
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotZ(0*deg2rad), Rotation::RotZ(-270*deg2rad)), Vector(0,0,M_PI/2));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotZ(0*deg2rad), Rotation::RotZ(-180*deg2rad)), Vector(0,0,M_PI));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotZ(0*deg2rad), Rotation::RotZ(-90*deg2rad)), Vector(0,0,-M_PI/2));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotZ(0*deg2rad), Rotation::RotZ(-0*deg2rad)), Vector(0,0,0));          // no rotation

        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotX(0*deg2rad), Rotation::RotZ(90*deg2rad)), Vector(0,0,M_PI/2));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotX(0*deg2rad), Rotation::RotY(90*deg2rad)), Vector(0,M_PI/2,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RotY(0*deg2rad), Rotation::RotZ(90*deg2rad)), Vector(0,0,M_PI/2));

        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::Identity(), Rotation::RotX(90*deg2rad)), Vector(M_PI/2,0,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::Identity(), Rotation::RotY(90*deg2rad)), Vector(0,M_PI/2,0));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::Identity(), Rotation::RotZ(90*deg2rad)), Vector(0,0,M_PI/2));

        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RPY(+0*deg2rad,0,-90*deg2rad),
                                                                   Rotation::RPY(-0*deg2rad,0,+90*deg2rad)),
                                                 Vector(0,0,M_PI));
        CPPUNIT_ASSERT_EQUAL(KDL::diff(Rotation::RPY(+5*deg2rad,0,-0*deg2rad),
                                                                   Rotation::RPY(-5*deg2rad,0,+0*deg2rad)),
                                                 Vector(-10*deg2rad,0,0));

    KDL::Rotation R1 = Rotation::RPY(+5*deg2rad,0,-90*deg2rad);
        CPPUNIT_ASSERT_EQUAL(KDL::diff(R1, Rotation::RPY(-5*deg2rad,0,+90*deg2rad)),
                                                           R1*Vector(0, 0, 180*deg2rad));
}

void FramesTest::TestFrame() {
        Vector   v(3,4,5);
        Wrench   w(Vector(7,-1,3),Vector(2,-3,3)) ;
        Twist    t(Vector(6,3,5),Vector(4,-2,7)) ;
        Rotation R ;
        Frame F;
        Frame F2 ;
        F = Frame(Rotation::EulerZYX(10*deg2rad,20*deg2rad,-10*deg2rad),Vector(4,-2,1));
        F2=F   ;
        CPPUNIT_ASSERT_EQUAL(F,F2);
        CPPUNIT_ASSERT_EQUAL(F.Inverse(F*v),v);
        CPPUNIT_ASSERT_EQUAL(F.Inverse(F*t),t);
        CPPUNIT_ASSERT_EQUAL(F.Inverse(F*w),w);
        CPPUNIT_ASSERT_EQUAL(F*F.Inverse(v),v);
        CPPUNIT_ASSERT_EQUAL(F*F.Inverse(t),t);
        CPPUNIT_ASSERT_EQUAL(F*F.Inverse(w),w);
        CPPUNIT_ASSERT_EQUAL(F*Frame::Identity(),F);
        CPPUNIT_ASSERT_EQUAL(Frame::Identity()*F,F);
        CPPUNIT_ASSERT_EQUAL(F*(F*(F*v)),(F*F*F)*v);
        CPPUNIT_ASSERT_EQUAL(F*(F*(F*t)),(F*F*F)*t);
        CPPUNIT_ASSERT_EQUAL(F*(F*(F*w)),(F*F*F)*w);
        CPPUNIT_ASSERT_EQUAL(F*F.Inverse(),Frame::Identity());
        CPPUNIT_ASSERT_EQUAL(F.Inverse()*F,Frame::Identity());
        CPPUNIT_ASSERT_EQUAL(F.Inverse()*v,F.Inverse(v));
}

void FramesTest::TestJntArray()
{
    JntArray a1(4);
    random(a1(0));
    random(a1(1));
    random(a1(2));
    random(a1(3));
    JntArray a2(a1);
    CPPUNIT_ASSERT(Equal(a2,a1));

    SetToZero(a2);
    CPPUNIT_ASSERT(!Equal(a1,a2));
    
    JntArray a3(4);
    CPPUNIT_ASSERT(Equal(a2,a3));
    
    a1=a2;
    CPPUNIT_ASSERT(Equal(a1,a3));

    random(a1(0));
    random(a1(1));
    random(a1(2));
    random(a1(3));
    
    Add(a1,a2,a3);
    CPPUNIT_ASSERT(Equal(a1,a3));
    
    random(a2(0));
    random(a2(1));
    random(a2(2));
    random(a2(3));
    Add(a1,a2,a3);
    Subtract(a3,a2,a3);
    CPPUNIT_ASSERT(Equal(a1,a3));
    
    Multiply(a1,2,a3);
    Add(a1,a1,a2);
    CPPUNIT_ASSERT(Equal(a2,a3));
    
    double a;
    random(a);
    Multiply(a1,a,a3);
    Divide(a3,a,a2);
    CPPUNIT_ASSERT(Equal(a2,a1));
}

 
void FramesTest::TestJntArrayWhenEmpty()
{
    JntArray a1;
    JntArray a2;
    JntArray a3(a2);
    
        // won't assert()
    CPPUNIT_ASSERT_EQUAL((unsigned int)0,a1.rows());
    CPPUNIT_ASSERT(Equal(a2,a1));
    
        a2 = a1;
    CPPUNIT_ASSERT(Equal(a2,a1));
    
        SetToZero(a2);
    CPPUNIT_ASSERT(Equal(a2,a1));
    
    Add(a1,a2,a3);
    CPPUNIT_ASSERT(Equal(a1,a3));
    
    Subtract(a1,a2,a3);
    CPPUNIT_ASSERT(Equal(a1,a3));
        
    Multiply(a1,3.1,a3);
    CPPUNIT_ASSERT(Equal(a1,a3));
        
    Divide(a1,3.1,a3);
    CPPUNIT_ASSERT(Equal(a1,a3));
        
        // MultiplyJacobian() - not tested here
    
    
        /* will assert() - not tested here
       double j1 = a1(0);
        */      
    
        // and now resize, and do just a few tests
    a1.resize(3);
    a2.resize(3);
    CPPUNIT_ASSERT_EQUAL((unsigned int)3,a1.rows());
    CPPUNIT_ASSERT(Equal(a2,a1));
    
    random(a1(0));
    random(a1(1));
    random(a1(2));
    a1 = a2;
    CPPUNIT_ASSERT(Equal(a1,a2));
    CPPUNIT_ASSERT_EQUAL(a1(1),a2(1));
    
    a3.resize(3);
    Subtract(a1,a2,a3); // a3 = a2 - a1 = {0}
    SetToZero(a1);
    CPPUNIT_ASSERT(Equal(a1,a3));
}