GeneralizedBezierCurve.h

#ifndef GENERALIZED_BEZIER_CURVE_H
#define GENERALIZED_BEZIER_CURVE_H

#include "CSpace.h"
#include "GeodesicSpace.h"
#include <iosfwd>
#include <vector>

class GeneralizedCubicBezierCurve
{
 public:
  GeneralizedCubicBezierCurve(CSpace* space=NULL,GeodesicSpace* manifold=NULL);
  void Eval(Real u,Config& x) const;
  void Deriv(Real u,Config& dx) const;
  void Accel(Real u,Config& ddx) const;
  Real OuterLength() const;

  void GetBounds(Vector& xmin,Vector& xmax) const;
  void GetDerivBounds(Vector& vmin,Vector& vmax,Vector& amin,Vector& amax) const;
  void GetDerivBounds(Real u1,Real u2,Vector& vmin,Vector& vmax,Vector& amin,Vector& amax) const;

  void SetSmoothTangents(const Config* prev=NULL,const Config* next=NULL);
  void SetSmoothTangents(const Config* prev,const Config* next,Real dtprev,Real dtnext);
  void SetNaturalTangents(const Vector& dx0,const Vector& dx1);

  void Midpoint(Vector& x) const;
  void MidpointDeriv(Vector& v) const;
  void MidpointTimeDeriv(Real duration,Vector& v) const;

  void Bisect(GeneralizedCubicBezierCurve& c1,GeneralizedCubicBezierCurve& c2) const;

  CSpace* space;
  GeodesicSpace* manifold;
  Config x0,x1,x2,x3;
};


class GeneralizedCubicBezierSpline
{
public:
  int ParamToSegment(Real u,Real* segparam=NULL) const;
  int Eval(Real u,Vector& x) const;
  int Deriv(Real u,Vector& dx) const;
  int Accel(Real u,Vector& ddx) const;
  Real TotalTime() const;
  const Config& Start() const { return segments.front().x0; }
  const Config& End() const { return segments.back().x3; }
  void Append(const GeneralizedCubicBezierCurve& seg,Real duration);
  void Concat(const GeneralizedCubicBezierSpline& s);
  void TimeScale(Real scale);
  //gets the piecewise linear path corresponding to each segment endpoint
  void GetPiecewiseLinear(std::vector<Real>& times,std::vector<Config>& milestones) const;
  //bisects every segment (O(n) cost)
  void Bisect();
  //bisects one segment at the parameter u (O(n-seg) cost)
  void Bisect(int seg,Real u=0.5);
  bool Save(std::ostream& out) const;
  bool Load(std::istream& in);

  std::vector<GeneralizedCubicBezierCurve> segments;
  std::vector<Real> durations;
};

#endif