2016-05-17 03:04:11 +12:00
|
|
|
#pragma once
|
2016-03-19 06:57:51 +13:00
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
// tbezier.h: contains useful function to manipulate bezier polynomious
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
#ifndef TBEZIER_H
|
|
|
|
#define TBEZIER_H
|
|
|
|
#include <iterator>
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
|
|
|
/*!
|
2016-06-15 18:43:10 +12:00
|
|
|
Compute the forward differences.
|
2016-03-19 06:57:51 +13:00
|
|
|
*/
|
|
|
|
template <class T>
|
2016-06-15 18:43:10 +12:00
|
|
|
void forwardDifferences(const std::vector<T> &coeff, std::vector<T> &diffs) {
|
|
|
|
diffs.clear();
|
2016-03-19 06:57:51 +13:00
|
|
|
|
2016-06-15 18:43:10 +12:00
|
|
|
std::copy(coeff.begin(), coeff.end(), std::back_inserter(diffs));
|
2016-03-19 06:57:51 +13:00
|
|
|
|
2016-06-15 18:43:10 +12:00
|
|
|
typename std::vector<T>::iterator vectIt;
|
2016-03-19 06:57:51 +13:00
|
|
|
|
2016-06-15 18:43:10 +12:00
|
|
|
const UINT degree = coeff.size();
|
2016-03-19 06:57:51 +13:00
|
|
|
|
2016-06-15 18:43:10 +12:00
|
|
|
for (UINT r = 0; r < degree; ++r) {
|
|
|
|
vectIt = diffs.begin();
|
|
|
|
std::advance(vectIt, r);
|
|
|
|
std::adjacent_difference(vectIt, diffs.end(), vectIt);
|
|
|
|
}
|
2016-03-19 06:57:51 +13:00
|
|
|
}
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
|
|
|
/*!
|
2016-06-15 18:43:10 +12:00
|
|
|
Converts Bezier form to power (polynomial) form.
|
2016-03-19 06:57:51 +13:00
|
|
|
\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>
|
2016-06-15 18:43:10 +12:00
|
|
|
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];
|
|
|
|
}
|
2016-03-19 06:57:51 +13:00
|
|
|
}
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
|
|
|
/*!
|
2016-06-15 18:43:10 +12:00
|
|
|
Converts power (polynomial) form to Bezier form.
|
2016-03-19 06:57:51 +13:00
|
|
|
\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>
|
2016-06-15 18:43:10 +12:00
|
|
|
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;
|
|
|
|
}
|
|
|
|
}
|
2016-03-19 06:57:51 +13:00
|
|
|
}
|
|
|
|
|
2016-06-15 18:43:10 +12:00
|
|
|
#endif // TBEZIER_H
|
2016-03-19 06:57:51 +13:00
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
// End Of File
|
|
|
|
//-----------------------------------------------------------------------------
|