/******************************************
 * C++ Spherical Splines
 * Version: 1.0.9
 * Author:  Douglas Wilhelm Harder
 * Date:    2008/03/03
 *
 * Copyright (c) 2007-8 by Douglas Wilhelm Harder.
 * All rights reserved.
 *
 * References:
 *    Ken Shoemake, 'Animating Rotation with Quatenrion Curves', SIGGRAPH 95.
 *    Erik B. Dam, Martin Koch, Martin Lillholm,
 *      'Quaternions, Interpolation and Animation', Technical Report DIKU-TR-98/5.
 ******************************************/

#include "Spline.h"
#include "Complex.h"
#include "Quaternion.h"
#include "Octonion.h"
#include "Sedenion.h"
#include "Trigintaduonion.h"

template<typename T, typename S>
Spline<T, S>::Spline( T * q, unsigned int N ):n(N), slerpq( new Slerp<T, S>[n - 1] ), slerpa( new Slerp<T, S>[n - 1] ) {
	T * a = new T[n];

	q0 = q[0];
	qn = q[n - 1];

	a[0] = q[0];

	for ( unsigned int i = 1; i < n - 1; ++i ) {
		T invqi = inverse(q[i]);

		a[i] = q[i] * exp( -static_cast<S>(0.25)*(
			log(invqi*q[i + 1]) + log(invqi*q[i - 1])
		) );
	}

	a[n - 1] = q[n - 1];

	for ( unsigned int i = 0; i < n - 1; ++i ) {
		slerpq[i] = Slerp<T, S>( q[i], q[i + 1] );
		slerpa[i] = Slerp<T, S>( a[i], a[i + 1] );
	}

	delete [] a;
}

template<typename T, typename S>
Spline<T, S>::~Spline() {
	delete [] slerpq;
	delete [] slerpa;
}

template<typename T, typename S>
T Spline<T, S>::value( S t ) const {
	if ( t <= 0 ) {
		return q0;
	}

	if ( t >= n - 1 ) {
		return qn;
	}

	int m = static_cast<int>( std::floor( t ) );
	S ft = t - static_cast<S>( m ); 

	return Slerp<T, S>( slerpq[m].value(ft), slerpa[m].value(ft) ).value( 2*ft*(1 - ft) );
}

template class Spline< Quaternion<long double>, long double >;
template class Spline< Quaternion<double>, double >;
template class Spline< Quaternion<float>, float >;
template class Spline< Octonion<long double>, long double >;
template class Spline< Octonion<double>, double >;
template class Spline< Octonion<float>, float >;
template class Spline< Sedenion<long double>, long double >;
template class Spline< Sedenion<double>, double >;
template class Spline< Sedenion<float>, float >;
template class Spline< Trigintaduonion<long double>, long double >;
template class Spline< Trigintaduonion<double>, double >;
template class Spline< Trigintaduonion<float>, float >;