bernstein.h

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#ifndef _CLASS_BERNSTEIN
#define _CLASS_BERNSTEIN
 
#include <math.h>
 
#include <stdexcept>
#include <vector>
 
#include "MathDefs.h"
#include "curve_abc.h"
 
namespace spline {
unsigned int fact(const unsigned int n) {
  assert(n >= 0);
  int res = 1;
  for (int i = 2; i <= n; ++i) res *= i;
  return res;
}
 
unsigned int bin(const unsigned int n, const unsigned int k) {
  return fact(n) / (fact(k) * fact(n - k));
}
 
template <typename Numeric = double>
struct Bern {
  Bern(const unsigned int m, const unsigned int i)
      : m_minus_i(m - i), i_(i), bin_m_i_(bin(m, i)) {}
 
  ~Bern() {}
 
  Numeric operator()(const Numeric u) const {
    assert(u >= 0. && u <= 1.);
    return bin_m_i_ * (pow(u, i_)) * pow((1 - u), m_minus_i);
  }
 
  Numeric m_minus_i;
  Numeric i_;
  Numeric bin_m_i_;
};
 
template <typename Numeric>
std::vector<Bern<Numeric> > makeBernstein(const unsigned int n) {
  std::vector<Bern<Numeric> > res;
  for (unsigned int i = 0; i <= n; ++i) res.push_back(Bern<Numeric>(n, i));
  return res;
}
}  // namespace spline
#endif  //_CLASS_BERNSTEIN