shape_spherical_harmonics.hpp

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#pragma once
 
#include "shape.hpp"
#include "stl_model.hpp"
#include "stl_reader.hpp"
#include <cmath>
#include <iostream>
#include <string>
 
namespace netdem {
 
class SphericalHarmonics : public Shape {
public:
  int degree{8};      
  VecXT<double> a_nm; 
 
  SphericalHarmonics();
 
  SphericalHarmonics(int n);
 
  nlohmann::json PackJson() override;
 
  void InitFromJson(nlohmann::json const &js) override;
 
  void InitFromSTL(std::string const &file);
 
  void InitFromSTL(STLModel const &stl_model);
 
  void InitFromSurfacePoints(VecXT<Vec3d> const surf_points);
 
  void Init();
 
  void UpdateSurfaceNodes() override;
 
  void UpdateShapeProperties() override;
 
  void SetSize(double d) override;
 
  STLModel GetSTLModel(int num_nodes = 200) override;
 
  Shape *Clone() const override;
 
  double SignedDistance(Vec3d const &pos) const override;
 
  Vec3d SurfacePoint(Vec3d const &pos) override;
 
  Vec3d SurfaceNormal(Vec3d const &pos);
 
  Vec2d SurfaceCurvature(Vec3d const &pos);
 
  Vec3d SurfaceNormal(double theta, double phi);
 
  Vec2d SurfaceCurvature(double theta, double phi);
 
  static VecXT<double> CalculateYnm(double theta, double phi, int deg);
 
  static VecXT<VecXT<double>> CalculateYnm(const VecXT<double> &theta,
                                           const VecXT<double> &phi, int deg);
 
  static VecXT<double> CalculateYnm_Fast(double theta, double phi, int deg);
 
  static VecXT<VecXT<double>> CalculateYnm_Fast(const VecXT<double> &theta,
                                                const VecXT<double> &phi,
                                                int deg);
 
  double CalculateRho(double theta, double phi) const;
 
  // another fast option by using unit VecXT as direction (thus to avoid sin
  // and cos)
  static VecXT<double> CalculateYnm_Fast(Vec3d const &dir, int deg);
  static VecXT<VecXT<double>> CalculateYnm_Fast(const VecXT<Vec3d> &dir_list,
                                                int deg);
 
  double CalculateRho(Vec3d const &dir) const;
 
private:
  static VecXT<VecXT<double>> sph_legendre_fast(double theta, int deg);
 
  static VecXT<VecXT<double>> sph_legendre_fast(Vec3d const &dir, int deg);
 
  double d_rho_d_theta(double theta, double phi);
 
  double d_rho_d_phi(double theta, double phi);
 
  Vec3d d_xyz_d_theta(double theta, double phi);
 
  Vec3d d_xyz_d_phi(double theta, double phi);
 
  Vec3d d_normal_d_theta(double theta, double phi);
 
  Vec3d d_normal_d_phi(double theta, double phi);
};
 
} // namespace netdem