//-----------------------------------------------------------------------------
//  tbezier.h: contains useful function to manipulate bezier polynomious
//-----------------------------------------------------------------------------
#ifndef TBEZIER_H
#define TBEZIER_H
#include <iterator>

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

/*!
  Compute the forward differences.  
 */
template <class T>
void forwardDifferences(
	const std::vector<T> &coeff,
	std::vector<T> &diffs)
{
	diffs.clear();

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

	typename std::vector<T>::iterator vectIt;

	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>
void bezier2poly(const std::vector<T> &bez,
				 std::vector<T> &coeff)
{
	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>
void poly2bezier(const std::vector<T> &poly,
				 std::vector<T> &bez)
{
	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
//-----------------------------------------------------------------------------