polynomial.h

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#ifndef TOWR_VARIABLES_POLYNOMIAL_H_
#define TOWR_VARIABLES_POLYNOMIAL_H_

#include <string>
#include <vector>

#include <Eigen/Dense>

#include "state.h"

namespace towr {

class Polynomial {
public:
  enum Coefficients { A=0, B, C, D, E, F, G, H, I, J};
  using CoeffIDVec = std::vector<Coefficients>;
  using VectorXd   = Eigen::VectorXd;

public:
  explicit Polynomial(int poly_order, int poly_dim);
  virtual ~Polynomial() = default;

  State GetPoint(double t) const;

  double GetDerivativeWrtCoeff(double t, Dx poly_deriv, Coefficients coeff) const;

protected:
  std::vector<VectorXd> coeff_;

private:
  CoeffIDVec coeff_ids_;
};


class CubicHermitePolynomial : public Polynomial {
public:
  CubicHermitePolynomial(int dim);
  virtual ~CubicHermitePolynomial() = default;


  void SetDuration(double duration);

  void SetNodes(const Node& n0, const Node& n1);

  void UpdateCoeff();

  VectorXd GetDerivativeOfPosWrtDuration(double t) const;

  double GetDerivativeWrtStartNode(Dx dfdt, Dx node_deriv, double t) const;

  double GetDerivativeWrtEndNode(Dx dfdt, Dx node_deriv, double t) const;

  const double GetDuration() const { return T_; };

private:
  double T_;     
  Node n0_, n1_; 

  // see matlab/cubic_hermite_polynomial.m script for derivation
  double GetDerivativeOfPosWrtStartNode(Dx node_deriv, double t_local) const;
  double GetDerivativeOfVelWrtStartNode(Dx node_deriv, double t_local) const;
  double GetDerivativeOfAccWrtStartNode(Dx node_deriv, double t_local) const;

  double GetDerivativeOfPosWrtEndNode(Dx node_deriv, double t_local) const;
  double GetDerivativeOfVelWrtEndNode(Dx node_deriv, double t_local) const;
  double GetDerivativeOfAccWrtEndNode(Dx node_deriv, double t_local) const;
};

} // namespace towr

#endif // TOWR_VARIABLES_POLYNOMIAL_H_