text: // This file is part of libigl, a simple c++ geometry processing library.
  // 
  // Copyright (C) 2020 Alec Jacobson <alecjacobson@gmail.com>
  // 
  // This Source Code Form is subject to the terms of the Mozilla Public License 
  // v. 2.0. If a copy of the MPL was not distributed with this file, You can 
  // obtain one at http://mozilla.org/MPL/2.0/.
  #ifndef FIT_CUBIC_BEZIER_H
  #define FIT_CUBIC_BEZIER_H
  #include "igl_inline.h"
  #include <Eigen/Core>
  #include <vector>
  namespace igl
  {
    // Fit a cubic bezier spline (G1 continuous) to an ordered list of input
    // points in any dimension, according to "An algorithm for automatically
    // fitting digitized curves" [Schneider 1990].
    //
    // Inputs:
    //   d  #d by dim list of points along a curve to be fit with a cubic bezier
    //     spline (should probably be roughly uniformly spaced). If d(0)==d(end),
    //     then will treat as a closed curve.
    //   error  maximum squared distance allowed
    // Output:
    //   cubics #cubics list of 4 by dim lists of cubic control points
    IGL_INLINE void fit_cubic_bezier(
      const Eigen::MatrixXd & d,
      const double error,
      std::vector<Eigen::MatrixXd> & cubics);
    // Recursive helper function. 
    //
    // Inputs:
    //    first  index of first point in d of substring
    //    last  index of last point in d of substring
    //    tHat1  tangent to use at beginning of spline
    //    tHat2  tangent to use at end of spline
    //    error  see above
    //    force_split  whether to force a split (i.e., force a recursive call)
    //    cubics  running list of cubics so far
    // Outputs
    //    cubics  running list of cubics so far (new cubics appended)
    IGL_INLINE void fit_cubic_bezier_substring(
      const Eigen::MatrixXd & d,
      const int first,
      const int last,
      const Eigen::RowVectorXd & tHat1,
      const Eigen::RowVectorXd & tHat2,
      const double error,
      const bool force_split, 
      std::vector<Eigen::MatrixXd> & cubics);
  }
  
  #ifndef IGL_STATIC_LIBRARY
  #include "fit_cubic_bezier.cpp"
  #endif
  
  #endif 
  