Current File : //backups/router/usr/local/include/boost/math/interpolators/detail/bezier_polynomial_detail.hpp
// Copyright Nick Thompson, 2021
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_INTERPOLATORS_BEZIER_POLYNOMIAL_DETAIL_HPP
#define BOOST_MATH_INTERPOLATORS_BEZIER_POLYNOMIAL_DETAIL_HPP
#include <stdexcept>
#include <iostream>
#include <string>
#include <limits>
namespace boost::math::interpolators::detail {
template <class RandomAccessContainer>
static inline RandomAccessContainer& get_bezier_storage()
{
static thread_local RandomAccessContainer the_storage;
return the_storage;
}
template <class RandomAccessContainer>
class bezier_polynomial_imp
{
public:
using Point = typename RandomAccessContainer::value_type;
using Real = typename Point::value_type;
using Z = typename RandomAccessContainer::size_type;
bezier_polynomial_imp(RandomAccessContainer && control_points)
{
using std::to_string;
if (control_points.size() < 2) {
std::string err = std::string(__FILE__) + ":" + to_string(__LINE__)
+ " At least two points are required to form a Bezier curve. Only " + to_string(control_points.size()) + " points have been provided.";
throw std::logic_error(err);
}
Z dimension = control_points[0].size();
for (Z i = 0; i < control_points.size(); ++i) {
if (control_points[i].size() != dimension) {
std::string err = std::string(__FILE__) + ":" + to_string(__LINE__)
+ " All points passed to the Bezier polynomial must have the same dimension.";
throw std::logic_error(err);
}
}
control_points_ = std::move(control_points);
auto & storage = get_bezier_storage<RandomAccessContainer>();
if (storage.size() < control_points_.size() -1) {
storage.resize(control_points_.size() -1);
}
}
inline Point operator()(Real t) const
{
if (t < 0 || t > 1) {
std::cerr << __FILE__ << ":" << __LINE__ << ":" << __func__ << "\n";
std::cerr << "Querying the Bezier curve interpolator at t = " << t << " is not allowed; t in [0,1] is required.\n";
Point p;
for (Z i = 0; i < p.size(); ++i) {
p[i] = std::numeric_limits<Real>::quiet_NaN();
}
return p;
}
auto & scratch_space = get_bezier_storage<RandomAccessContainer>();
for (Z i = 0; i < control_points_.size() - 1; ++i) {
for (Z j = 0; j < control_points_[0].size(); ++j) {
scratch_space[i][j] = (1-t)*control_points_[i][j] + t*control_points_[i+1][j];
}
}
decasteljau_recursion(scratch_space, control_points_.size() - 1, t);
return scratch_space[0];
}
Point prime(Real t) {
auto & scratch_space = get_bezier_storage<RandomAccessContainer>();
for (Z i = 0; i < control_points_.size() - 1; ++i) {
for (Z j = 0; j < control_points_[0].size(); ++j) {
scratch_space[i][j] = control_points_[i+1][j] - control_points_[i][j];
}
}
decasteljau_recursion(scratch_space, control_points_.size() - 1, t);
for (Z j = 0; j < control_points_[0].size(); ++j) {
scratch_space[0][j] *= (control_points_.size()-1);
}
return scratch_space[0];
}
void edit_control_point(Point const & p, Z index)
{
if (index >= control_points_.size()) {
std::cerr << __FILE__ << ":" << __LINE__ << ":" << __func__ << "\n";
std::cerr << "Attempting to edit a control point outside the bounds of the container; requested edit of index " << index << ", but there are only " << control_points_.size() << " control points.\n";
return;
}
control_points_[index] = p;
}
RandomAccessContainer const & control_points() const {
return control_points_;
}
// See "Bezier and B-spline techniques", section 2.7:
// I cannot figure out why this doesn't work.
/*RandomAccessContainer indefinite_integral() const {
using std::fma;
// control_points_.size() == n + 1
RandomAccessContainer c(control_points_.size() + 1);
// This is the constant of integration, chosen arbitrarily to be zero:
for (Z j = 0; j < control_points_[0].size(); ++j) {
c[0][j] = Real(0);
}
// Make the reciprocal approximation to unroll the iteration into a pile of fma's:
Real rnp1 = Real(1)/control_points_.size();
for (Z i = 1; i < c.size(); ++i) {
for (Z j = 0; j < control_points_[0].size(); ++j) {
//c[i][j] = c[i-1][j] + control_points_[i-1][j]*rnp1;
c[i][j] = fma(rnp1, control_points_[i-1][j], c[i-1][j]);
}
}
return c;
}*/
friend std::ostream& operator<<(std::ostream& out, bezier_polynomial_imp<RandomAccessContainer> const & bp) {
out << "{";
for (Z i = 0; i < bp.control_points_.size() - 1; ++i) {
out << "(";
for (Z j = 0; j < bp.control_points_[0].size() - 1; ++j) {
out << bp.control_points_[i][j] << ", ";
}
out << bp.control_points_[i][bp.control_points_[0].size() - 1] << "), ";
}
out << "(";
for (Z j = 0; j < bp.control_points_[0].size() - 1; ++j) {
out << bp.control_points_.back()[j] << ", ";
}
out << bp.control_points_.back()[bp.control_points_[0].size() - 1] << ")}";
return out;
}
private:
void decasteljau_recursion(RandomAccessContainer & points, Z n, Real t) const {
if (n <= 1) {
return;
}
for (Z i = 0; i < n - 1; ++i) {
for (Z j = 0; j < points[0].size(); ++j) {
points[i][j] = (1-t)*points[i][j] + t*points[i+1][j];
}
}
decasteljau_recursion(points, n - 1, t);
}
RandomAccessContainer control_points_;
};
}
#endif
Mini Shell