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//  tbezier.h: contains useful function to manipulate bezier polynomious

//-----------------------------------------------------------------------------

#ifndef TBEZIER_H

#define TBEZIER_H

#include <iterator></iterator>

//-----------------------------------------------------------------------------

/*!

  Compute the forward differences.  

 */

template <class t=""></class>

void forwardDifferences(

	const std::vector<t> &coeff,</t>

	std::vector<t> &diffs)</t>

{

	diffs.clear();

	std::copy(coeff.begin(), coeff.end(), std::back_inserter(diffs));

	typename std::vector<t>::iterator vectIt;</t>

	const UINT degree = coeff.size();

	for (UINT r = 0; r < degree; ++r) {

		vectIt = diffs.begin();

		std::advance(vectIt, r);

		std::adjacent_difference(vectIt, diffs.end(), vectIt);

	}

}

//-----------------------------------------------------------------------------

/*!

  Converts Bezier form to power (polynomial) form. 

  \par  bez coefficients in Bezier form.

  \ret  coeff coefficients of power form.

  \note coeffs are ordered from smaller b[0] to greater b[size-1] .

 */

template <class t=""></class>

void bezier2poly(const std::vector<t> &bez,</t>

				 std::vector<t> &coeff)</t>

{

	forwardDifferences(bez, coeff); // compute forward differences

									// and store them in coeff.

	int

		degree = bez.size() - 1;

	double

		i_factorial = 1,

		n_r = 1;

	coeff[0] = bez[0];

	for (int i = 1; i < degree; i++) {

		i_factorial = i_factorial * i;

		n_r = n_r * (degree - i + 1);

		i_factorial = 1.0 / i_factorial;

		coeff[i] = (n_r * i_factorial) * coeff[i];

	}

}

//-----------------------------------------------------------------------------

/*!

  Converts power (polynomial) form to Bezier form. 

  \par  coeff coefficients of power form.

  \ret  bez coefficients in Bezier form.

  \note coeffs are ordered from smaller b[0] to greater b[size-1].

 */

template <class t=""></class>

void poly2bezier(const std::vector<t> &poly,</t>

				 std::vector<t> &bez)</t>

{

	UINT n = poly.size();

	bez.clear();

	std::copy(poly.begin(), poly.end(), std::back_inserter(bez));

	double c, d, e;

	for (UINT j = 1; j < n; j++) {

		c = 1.0 / (n - j);

		d = 1;

		e = c;

		for (UINT i = n - 1; i >= j; i--) {

			bez[i] = d * bez[i] + e * bez[i - 1];

			d -= c;

			e += c;

		}

	}

}

#endif // TBEZIER_H

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//  End Of File

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