height_map.h

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#ifndef TOWR_HEIGHT_MAP_H_
#define TOWR_HEIGHT_MAP_H_

#include <memory>
#include <vector>
#include <map>
#include <string>

#include <Eigen/Dense>

#include <towr/variables/cartesian_dimensions.h>

namespace towr {

class HeightMap {
public:
  using Ptr      = std::shared_ptr<HeightMap>;
  using Vector3d = Eigen::Vector3d;

  enum TerrainID { FlatID,
                   BlockID,
                   StairsID,
                   GapID,
                   SlopeID,
                   ChimneyID,
                   ChimneyLRID,
                   TERRAIN_COUNT };

  static HeightMap::Ptr MakeTerrain(TerrainID type);

  enum Direction { Normal, Tangent1, Tangent2 };

  HeightMap() = default;
  virtual ~HeightMap () = default;

  virtual double GetHeight(double x, double y) const = 0;

  double GetDerivativeOfHeightWrt(Dim2D dim, double x, double y) const;

  Vector3d GetNormalizedBasis(Direction direction, double x, double y) const;

  Vector3d GetDerivativeOfNormalizedBasisWrt(Direction direction, Dim2D dim,
                                             double x, double y) const;
  double GetFrictionCoeff() const { return friction_coeff_; };

protected:
  double friction_coeff_ = 0.5;

private:
  using DimDerivs = std::vector<Dim2D>; 

  Vector3d GetBasis(Direction direction, double x, double y,
                    const DimDerivs& dim_deriv= {}) const;

  Vector3d GetNormal(double x,   double y, const DimDerivs& = {}) const;
  Vector3d GetTangent1(double x, double y, const DimDerivs& = {}) const;
  Vector3d GetTangent2(double x, double y, const DimDerivs& = {}) const;

  double GetSecondDerivativeOfHeightWrt(Dim2D dim1, Dim2D dim2,
                                        double x, double y) const;

  Vector3d GetDerivativeOfNormalizedVectorWrtNonNormalizedIndex(
      const Vector3d& non_normalized, int index) const;

  // first derivatives that must be implemented by the user
  virtual double GetHeightDerivWrtX(double x, double y) const { return 0.0; };
  virtual double GetHeightDerivWrtY(double x, double y) const { return 0.0; };

  // second derivatives with respect to first letter, then second
  virtual double GetHeightDerivWrtXX(double x, double y) const { return 0.0; };
  virtual double GetHeightDerivWrtXY(double x, double y) const { return 0.0; };
  virtual double GetHeightDerivWrtYX(double x, double y) const { return 0.0; };
  virtual double GetHeightDerivWrtYY(double x, double y) const { return 0.0; };
};


const static std::map<HeightMap::TerrainID, std::string> terrain_names =
{
  {HeightMap::FlatID,        "Flat"       },
  {HeightMap::BlockID,       "Block"      },
  {HeightMap::StairsID,      "Stairs"     },
  {HeightMap::GapID,         "Gap"        },
  {HeightMap::SlopeID,       "Slope"      },
  {HeightMap::ChimneyID,     "Chimney"    },
  {HeightMap::ChimneyLRID,   "ChimenyLR"  }
};

} /* namespace towr */

#endif /* TOWR_HEIGHT_MAP_H_ */