// sv-6.cc
// 		A ZOOM PhysicsVectors tutorial example
//
// 		Tutorial example 6 for the SpaceVector and UnitVector class:
//
// 		Rotating SpaceVectors and UnitVectors
//
// * Rotating around a given axis
// * Rotating around a coordinate axis
// * Rotations by Euler Angles
//
//   This example shows how to do "direct" rotations.
//   The PhysicsVectors package also supports Rotation objects which
//     may be manipulated and applied to vectors.
//   To see how the sames things can be done with the Rotation class, look
//     at tutorial example ro-1 for construction and access, and ro-3 for
//     application to vectors. Bear in mind that you need not use Rotation
//     if all that is needed is to rotate vectors by some given amount.

// Key lines are marked by 				    // <-------------

	// Get the UnitVector and SpaceVector classes

#include "ZMutility/ZMenvironment.h"
#include "ZMutility/FixedTypes.h"
#include "PhysicsVectors/SpaceVector.h"
#include "PhysicsVectors/UnitVector.h"
ZM_USING_NAMESPACE( zmpv )
USING( std::cout )
USING( std::endl )

	// These classes themselves pull in FixedTypes, but just to
	// remind ourselves that we are using Float8, not double, for
	// 64-bit floats...

#include "ZMutility/FixedTypes.h"
ZM_USING_NAMESPACE( zmfxt )

	// This example will use iostream output, so get that --
	// in a portable way.

#include "ZMutility/iostream"
using std::cout;
using std::endl;

const Float8 PI =  3.1415926535897931;


int main() {

// ***** Rotating around a given axis

	// Here is how to rotate a vector about a UnitVector axis
	//-------------------------------------------------------

  Float8 theta = 45;
  Float8 phi   = 30;
  UnitVector u1 ( theta, DEGREES, phi, DEGREES );
  cout << "axis =" << u1 << endl;

  SpaceVector v1 ( 12, -16, 48 );
  cout << "Before rotation vector is " << v1 << endl;
  cout << "Magnitude is " << v1.mag() << endl;

  v1.rotate ( u1, PI/3 );				    // <-------------
  cout << "After PI/3 rotation vector is " << v1 << endl;
  cout << "Magnitude is " << v1.mag() << endl;

  UnitVector u2 = Y_HAT;
  cout << "Before rotation unit vector is " << u2 << endl;

  u2.rotate ( u1, PI/2 );				    // <-------------
  cout << "After PI/2 rotation unit vector is " << u2 << endl;

  	// Here is how to supply a non-zero SpaceVector axis
	//--------------------------------------------------

  SpaceVector v2 = 20 * u1;
  cout << "axis =" << v2 << endl;

  v1.rotate ( v2, -PI/3 );				    // <-------------
  cout << "After -PI/3 rotation vector is " << v1 << endl;

	// Here is how to form a new vector by rotating an existing vector
	//----------------------------------------------------------------

  SpaceVector v3 = rotationOf (v1, u1, PI/4);		    // <-------------
  cout << "After PI/ rotation new vector is " << v3 << endl;
  cout << "Old vector remains " << v1 << endl;



// ***** Rotating around a coordinate axis

	// Here is how to rotate around Z with a minimal amount of computation
	//--------------------------------------------------------------------

  v3.rotateZ ( PI/2 );					    // <-------------
  cout << "After rotating by PI/2 about Z axis this is " << v3 << endl;

	// This is equivalent to, but much faster than:

  v3.rotate ( Z_HAT, PI/2 );
  cout << "After another PI/2 about Z axis this is " << v3 << endl;

	// Similarly,
  v1.rotateX (PI/3);					    // <-------------
  v2.rotateY (PI);					    // <-------------

  	// And the analog to rotationOf is also there:

  v1 = rotationZOf (v3, PI/2);				    // <-------------
  cout << "After yet another PI/2 about Z axis, " << v1 << endl;

// ***** Rotations by Euler Angles

	// Here is how to rotate a vector using Euler Angles
	//--------------------------------------------------

  phi   =  PI/6;
  theta =  PI/4;
  Float8 psi   = -PI/3;
  cout << "Vector is " << v3 << endl;

  v3.rotate ( phi, theta, psi );			    // <-------------
  cout << "Now vector is " << v3 << endl;
	// The Euler angles definition is that of
	// Goldstein Classical Mechanics, page 109

  v2 = rotationOf ( v3, PI/3, PI/4, -PI/6 );		    // <-------------
  cout << "New vector is " << v2 << endl;

  return 0;

} /* end of main */