/**
default constructor
*/
vectorBasisNode::vectorBasisNode()
: pv_v1( aVector(1.0, 0.0, 0.0) ),
pv_v2( aVector(0.0, 1.0, 0.0) ),
pv_v3( aVector(0.0, 0.0, 1.0) )
{
// empty
}
/**
this function transforms a given vector in the new basis
to the old basis
*/
aVector vectorBasisNode::ToOld(const aVector& v_new) const
{
double p0, p1, p2;
p0 = v_new(0) * pv_v1(0) + v_new(1) * pv_v2(0) + v_new(2) * pv_v3(0);
p1 = v_new(0) * pv_v1(1) + v_new(1) * pv_v2(1) + v_new(2) * pv_v3(1);
p2 = v_new(0) * pv_v1(2) + v_new(1) * pv_v2(2) + v_new(2) * pv_v3(2);
return aVector(p0, p1, p2);
}
CSuffixTrie::StringsSet CSuffixTrie::GetAllStringsSet()const
{
//We will convert the vector
StringsVector aVector(GetAllStringsVector());
//Our set
StringsSet aSet;
//Iterate it
for (int iCount=0;
iCount<aVector.size();
++iCount)
//Insert to the set
aSet.insert(aVector[iCount]);
//Done
return aSet;
}
/**
this function transforms a given vector in the old basis
to the new basis
*/
aVector vectorBasisNode::ToNew(const aVector& v_old) const
{
return aVector( v_old * pv_v1, v_old * pv_v2, v_old * pv_v3 );
}
/**
computes the cross product of a vector. this
operator has a very low precedence and care must be
taken while using it.
*/
aVector operator^(const aVector& v1, const aVector& v2)
{
return aVector( (v1.pv_p[1]*v2.pv_p[2] - v2.pv_p[1]*v1.pv_p[2]),
(v1.pv_p[2]*v2.pv_p[0] - v2.pv_p[2]*v1.pv_p[0]),
(v1.pv_p[0]*v2.pv_p[1] - v2.pv_p[0]*v1.pv_p[1]) );
}
/**
computes the scalar product of a vector (returns
a vector)
*/
aVector operator*(double alpha, const aVector& v1)
{
return aVector( alpha*v1.pv_p[0],
alpha*v1.pv_p[1],
alpha*v1.pv_p[2] );
}
/**
adds two vectors
*/
aVector operator+(const aVector& v1, const aVector& v2)
{
return aVector( (v1.pv_p[0] + v2.pv_p[0]),
(v1.pv_p[1] + v2.pv_p[1]),
(v1.pv_p[2] + v2.pv_p[2]) );
}
int main(int argc, char* argv[])
{
// store the invoking program name
char* prg_name = argv[0];
// create an object of cpuClock and start it
cpuClock clock;
clock.Start();
//
int i;
// declare an object of the test class
aVectorBasis vb;
std::cout << "Default basis constructed (vb): " << vb << std::endl;
aVector v1, v2, v3;
v1 = aVector(5.23, 1.34, 1.45);
v2 = aVector(2.23, 2.34, 2.45);
// v3 = aVector(3.23, 3.34, 3.45);
v3 = v1^v2;
v2 = v3^v1;
std::cout << "Coplanarity: " << v1*(v2^v3) << std::endl;
try
{
vb.Set(v1, v2, v3);
std::cout << "Basis set to three new vectors (vb): " << vb << std::endl;
aVectorBasis vb2 = vb;
std::cout << "This basis (vb2): " << std::endl
<< vb2 << " is a copy of" << std::endl
<< " (vb ): " << std::endl
<< vb << std::endl;
v1 = aVector(22.23, 22.34, 22.45);
std::cout << "v1 and v2 are: " << std::endl
<< v1 << std::endl
<< v2 << std::endl;
v3 = v1^v2;
v2 = v3^v1;
std::cout.precision(16);
std::cout << "v1, v2 and v3 are: " << std::endl
<< v1 << std::endl
<< v2 << std::endl
<< v3 << std::endl;
vb2.Set(v1, v2, v3);
std::cout << "vb2 is set to: " << std::endl
<< vb2 << std::endl
<< "vb is unchanged: " << std::endl
<< vb << std::endl;
// now try some transformation (rotate by 45 degrees about z axis
v1 = aVector( 1.0, 1.0, 0.0);
v2 = aVector(-1.0, 1.0, 0.0);
v3 = aVector( 0.0, 0.0, 1.0);
aVectorBasis vb2d(v1, v2, v3);
v1 = aVector(0.0, 1.0, 0.0); // the old y axis
v2 = vb2d.ToLocal(v1); // vb2d.ToNew(v1);
std::cout << "on transformation: " << v2 << std::endl;
v2 = vb2d.ToWorld(v2); // ToOld(v2);
std::cout << "on transforming back: " << v2 << std::endl;
// now take a random vector. a random basis and transform
// the random vector to and fro and check
// take an orthogonal system
v1 = aVector( 1.0, 25., 0.52 );
v2 = aVector( 893.15, 420.35, 35.525);
// v3 = aVector(40.5, 1200.25, 0040.125);
v3 = v1^v2;
v2 = v3^v1;
aVector v4(1.225, 0.255, 0.224);
vb.Set(v1, v2, v3);
std::cout << "vector before transformation is: " << std::endl
<< " " << v4 << std::endl;
v4 = vb.ToLocal(v4); // ToNew(v4);
std::cout << "vector after transformation is: " << std::endl
<< " " << v4 << std::endl;
// transform back the same vector
v4 = vb.ToWorld(v4); // ToOld(v4);
std::cout << "vector after inverse transformation is: " << std::endl
<< " " << v4 << std::endl;
// now take e1, e2 and e3 and transform them into the new basis
// this gives us three new vectors (as seen from the new basis).
// let this form a newer basis. dump the new basis and the newer
// basis and see what they are. note that newer basis is the
// OLD basis
// first dump the new basis
std::cout << std::endl
<< "The new basis is" << std::endl
<< vb << std::endl;
// now get the newer basis
v1 = vb.ToLocal( aVector( 1.0, 0.0, 0.0 ) ); // ToNew( aVector( 1.0, 0.0, 0.0 ) ); // e1
v2 = vb.ToLocal( aVector( 0.0, 1.0, 0.0 ) ); // ToNew( aVector( 0.0, 1.0, 0.0 ) ); // e2
v3 = vb.ToLocal( aVector( 0.0, 0.0, 1.0 ) ); // ToNew( aVector( 0.0, 0.0, 1.0 ) ); // e3
vb.Set(v1, v2, v3);
std::cout << std::endl
<< "The newer basis is" << std::endl
<< vb << std::endl;
}
catch (char* s)
{
std::cout << s << std::endl;
}
// stop the clock and display cpu time
clock.Stop();
clock.Display();
// write a closure message and finish the program
std::cout << "Program <"
<< prg_name
<< "> completed successfully :-)"
<< std::endl;
return 0;
}
