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// Copyright (c) 2008 Max-Planck-Institute Saarbruecken (Germany) // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Polynomial/include/CGAL/Polynomial/Interpolator.h $ // $Id: include/CGAL/Polynomial/Interpolator.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Michael Hemmer #ifndef CGAL_POLYNOMIAL_INTERPOLATE_H #define CGAL_POLYNOMIAL_INTERPOLATE_H namespace CGAL { namespace internal { // Class for interpolation of univariate or multivariate polynomials. // The template argument must be a model of concept Polynomial_d // // template class Interpolator{ typedef CGAL::Polynomial_traits_d PT; public: typedef typename PT::Polynomial_d Polynomial_d; typedef typename PT::Coefficient_type Coeff; typedef typename PT::Innermost_coefficient_type IC; private: typedef typename CGAL::Coercion_traits::Cast IC2Coeff; typedef typename PT::Construct_polynomial Construct; std::vector xvals; std::vector yvals; std::vector b; bool valid; Polynomial_d interpolant; Coeff eval_newton(int n, IC z) { Coeff p(b[n]); for (int i = n-1; i >=0; i--){ Coeff tmp(IC2Coeff()((z - xvals[i]))); p = p * tmp + b[i]; } return p; } Polynomial_d eval_newton_poly(int n) { CGAL_precondition(n >=0); Polynomial_d p(Construct()(b[n])); for (int i = n-1; i >=0; i--) { Polynomial_d tmp = Construct()(IC2Coeff()(-xvals[i]),Coeff(1)); p = (p * tmp) + b[i]; } return p; } public: Interpolator(){}; // constructor from an InputIterator range with value type std::pair template Interpolator(InputIterator begin, InputIterator end){ for(InputIterator it = begin; it != end; it++){ add_interpolation_point(*it); } } /* Interpolator(std::vector xvals_, std::vector yvals_) : valid(false) { CGAL_precondition(xvals_.size() != 0); CGAL_precondition(xvals_.size() == yvals_.size()); for(unsigned i = 0; i < xvals_.size(); i++){ add_interpolation_point(xvals_[i],yvals_[i]); } } */ // void add_interpolation_point(std::pair point){ // add_interpolation_point(point.first, point.second); // } // void add_interpolation_point(IC xval, Coeff yval){ void add_interpolation_point(std::pair point){ valid = false; // CGAL_precondition(0 == std::count(xval, xvals.begin(), yvals.end())); xvals.push_back(point.first); yvals.push_back(point.second); Coeff num, den; int k = static_cast(xvals.size()) - 1; if(k == 0){ b.push_back(yvals[0]); }else{ num = yvals[k] - eval_newton(k-1,xvals[k]); den = Coeff(1); for (int j = 0; j < k; j++) { // (k-j) if xvals's are sequential den *= (xvals[k] - xvals[j]); } b.push_back(num / den); } } Polynomial_d get_interpolant(){ if (xvals.size() == 0) return Polynomial_d(0); // TODO: compute new interpolant from old interpolant ? if(!valid) interpolant = eval_newton_poly(static_cast(xvals.size())-1); return interpolant; } }; } // namespace internal } //namespace CGAL #endif // CGAL_POLYNOMIAL_INTERPOLATE_H