subducting_plate.cc

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/*
  Copyright (C) 2018-2024 by the authors of the World Builder code.

  This file is part of the World Builder.

   This program is free software: you can redistribute it and/or modify
   it under the terms of the GNU Lesser General Public License as published
   by the Free Software Foundation, either version 2 of the License, or
   (at your option) any later version.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public License
   along with this program.  If not, see <https://www.gnu.org/licenses/>.
 */

#include "world_builder/features/subducting_plate.h"


#include "glm/glm.h"
#include "world_builder/types/array.h"
#include "world_builder/types/double.h"
#include "world_builder/types/object.h"
#include "world_builder/types/point.h"
#include "world_builder/types/segment.h"
#include "world_builder/types/unsigned_int.h"
#include "world_builder/world.h"
#include <algorithm>
#include <array>

using namespace std;

namespace WorldBuilder
{
  using namespace Utilities;

  namespace Features
  {
    SubductingPlate::SubductingPlate(WorldBuilder::World *world_)
      :
      reference_point(0,0,cartesian)
    {
      this->world = world_;
      this->name = "subducting plate";
    }

    SubductingPlate::~SubductingPlate()
      = default;



    void SubductingPlate::make_snippet(Parameters &prm)
    {
      using namespace rapidjson;
      Document &declarations = prm.declarations;

      const std::string path = prm.get_full_json_path();

      /*
      ideally:
       {
        "model": "fault",
        "name": "${1:default name}",
        "dip point":[0.0,0.0],
        "coordinates": [[0.0,0.0]],
        "segments": [],
        "sections": [],
        "temperature models":[{"model":"uniform", "temperature":600.0}],
        "composition models":[{"model":"uniform", "compositions": [0], "fractions":[1.0]}]
       }
       */

      Pointer((path + "/body").c_str()).Set(declarations,"object");
      Pointer((path + "/body/model").c_str()).Set(declarations,"subducting plate");
      Pointer((path + "/body/name").c_str()).Set(declarations,"${1:My Subducting Plate}");
      Pointer((path + "/body/coordinates").c_str()).Create(declarations).SetArray();
      Pointer((path + "/body/temperature models").c_str()).Create(declarations).SetArray();
      Pointer((path + "/body/composition models").c_str()).Create(declarations).SetArray();
    }



    void
    SubductingPlate::declare_entries(Parameters &prm,
                                     const std::string &parent_name,
                                     const std::vector<std::string> &required_entries)
    {
      // This statement is needed because of the recursion associated with
      // the sections entry.
      if (parent_name == "items")
        {
          prm.enter_subsection("properties");
        }
      else
        {
          prm.declare_entry("", Types::Object(required_entries), "Subducting slab object. Requires properties `model` and `coordinates`.");
        }


      prm.declare_entry("min depth", Types::Double(0),
                        "The depth to which this feature is present");
      prm.declare_entry("max depth", Types::Double(std::numeric_limits<double>::max()),
                        "The depth to which this feature is present");
      prm.declare_entry("dip point", Types::Point<2>(),
                        "The depth to which this feature is present");

      /*prm.declare_entry("segments", Types::Array(Types::Segment(0,Point<2>(0,0,invalid),Point<2>(0,0,invalid),Point<2>(0,0,invalid),
                                                                Types::PluginSystem("", Features::SubductingPlateModels::Temperature::Interface::declare_entries, {"model"}),
                                                                Types::PluginSystem("", Features::SubductingPlateModels::Composition::Interface::declare_entries, {"model"}),
                                                                Types::PluginSystem("", Features::SubductingPlateModels::Grains::Interface::declare_entries, {"model"}))),
                        "The depth to which this feature is present");*/
      prm.declare_entry("segments", Types::Array(Types::Segment(0,Point<2>(0,0,invalid),Point<2>(0,0,invalid),Point<2>(0,0,invalid),
                                                                Types::PluginSystem("", Features::SubductingPlateModels::Temperature::Interface::declare_entries, {"model"}),
                                                                Types::PluginSystem("", Features::SubductingPlateModels::Composition::Interface::declare_entries, {"model"}),
                                                                Types::PluginSystem("", Features::SubductingPlateModels::Grains::Interface::declare_entries, {"model"}),
                                                                Types::PluginSystem("", Features::SubductingPlateModels::Velocity::Interface::declare_entries, {"model"}))),
                        "The depth to which this feature is present");

      prm.declare_entry("temperature models",
                        Types::PluginSystem("", Features::SubductingPlateModels::Temperature::Interface::declare_entries, {"model"}),
                        "A list of temperature models.");
      prm.declare_entry("composition models",
                        Types::PluginSystem("", Features::SubductingPlateModels::Composition::Interface::declare_entries, {"model"}),
                        "A list of composition models.");
      prm.declare_entry("grains models",
                        Types::PluginSystem("", Features::SubductingPlateModels::Grains::Interface::declare_entries, {"model"}),
                        "A list of grains models.");
      prm.declare_entry("velocity models",
                        Types::PluginSystem("", Features::SubductingPlateModels::Velocity::Interface::declare_entries, {"model"}),
                        "A list of velocity models.");

      if (parent_name != "items")
        {
          // This only happens if we are not in sections
          prm.declare_entry("sections", Types::Array(Types::PluginSystem("",Features::SubductingPlate::declare_entries, {"coordinate"}, false)),"A list of feature properties for a coordinate.");
        }
      else
        {

          // this only happens in sections
          prm.declare_entry("coordinate", Types::UnsignedInt(0),
                            "The coordinate which should be overwritten");

          prm.leave_subsection();
        }
    }

    void
    SubductingPlate::parse_entries(Parameters &prm)
    {
      const CoordinateSystem coordinate_system = prm.coordinate_system->natural_coordinate_system();

      this->name = prm.get<std::string>("name");

      std::string tag = prm.get<std::string>("tag");
      if (tag == "")
        {
          tag = "subducting plate";
        }
      this->tag_index = FeatureUtilities::add_vector_unique(this->world->feature_tags,tag);

      this->get_coordinates("coordinates", prm, coordinate_system);


      starting_depth = prm.get<double>("min depth");
      maximum_depth = prm.get<double>("max depth");

      const size_t n_sections = this->original_number_of_coordinates;

      reference_point = prm.get<Point<2> >("dip point");

      if (coordinate_system == spherical)
        {
          // When spherical, input is in degrees, so change to radians for internal use.
          reference_point *= (Consts::PI/180.);
        }

      default_temperature_models.resize(0);
      default_composition_models.resize(0);
      default_grains_models.resize(0);
      default_velocity_models.resize(0);
      prm.get_shared_pointers<Features::SubductingPlateModels::Temperature::Interface>("temperature models", default_temperature_models);
      prm.get_shared_pointers<Features::SubductingPlateModels::Composition::Interface>("composition models", default_composition_models);
      prm.get_shared_pointers<Features::SubductingPlateModels::Grains::Interface>("grains models", default_grains_models);
      prm.get_shared_pointers<Features::SubductingPlateModels::Velocity::Interface>("velocity models", default_velocity_models);

      // get the default segments.
      default_segment_vector = prm.get_vector<Objects::Segment<Features::SubductingPlateModels::Temperature::Interface,
      Features::SubductingPlateModels::Composition::Interface,
      Features::SubductingPlateModels::Grains::Interface,
      Features::SubductingPlateModels::Velocity::Interface> >("segments", default_temperature_models, default_composition_models, default_grains_models,default_velocity_models);


      // This vector stores segments to this coordinate/section.
      //First used (raw) pointers to the segment relevant to this coordinate/section,
      // but I do not trust it won't fail when memory is moved. So storing the all the data now.
      segment_vector.resize(0);
      segment_vector.resize(n_sections, default_segment_vector);


      // now search whether a section is present, if so, replace the default segments.
      std::vector<std::unique_ptr<Features::SubductingPlate> > sections_vector;
      prm.get_unique_pointers("sections", sections_vector);

      prm.enter_subsection("sections");
      for (unsigned int i_section = 0; i_section < n_sections; ++i_section)
        {
          // first check whether this section/coordinate has a a special overwrite
          for (unsigned int i_sector = 0; i_sector < sections_vector.size(); ++i_sector)
            {
              prm.enter_subsection(std::to_string(i_sector));
              {
                const unsigned int change_coord_number = prm.get<unsigned int>("coordinate");

                WBAssertThrow(segment_vector.size() > change_coord_number, "Error: for subducting plate with name: '" << this->name
                              << "', trying to change the section of coordinate " << change_coord_number
                              << " while only " << segment_vector.size() << " coordinates are defined.");

                std::vector<std::shared_ptr<Features::SubductingPlateModels::Temperature::Interface> > local_default_temperature_models;
                std::vector<std::shared_ptr<Features::SubductingPlateModels::Composition::Interface>  > local_default_composition_models;
                std::vector<std::shared_ptr<Features::SubductingPlateModels::Grains::Interface>  > local_default_grains_models;
                std::vector<std::shared_ptr<Features::SubductingPlateModels::Velocity::Interface>  > local_default_velocity_models;

                if (!prm.get_shared_pointers<Features::SubductingPlateModels::Temperature::Interface>("temperature models", local_default_temperature_models))
                  {
                    // no local temperature model, use global default
                    local_default_temperature_models = default_temperature_models;
                  }

                if (!prm.get_shared_pointers<Features::SubductingPlateModels::Composition::Interface>("composition models", local_default_composition_models))
                  {
                    // no local composition model, use global default
                    local_default_composition_models = default_composition_models;
                  }

                if (!prm.get_shared_pointers<Features::SubductingPlateModels::Grains::Interface>("grains models", local_default_grains_models))
                  {
                    // no local composition model, use global default
                    local_default_grains_models = default_grains_models;
                  }

                if (!prm.get_shared_pointers<Features::SubductingPlateModels::Velocity::Interface>("velocity models", local_default_velocity_models))
                  {
                    // no local composition model, use global default
                    local_default_velocity_models = default_velocity_models;
                  }

                segment_vector[change_coord_number] = prm.get_vector<Objects::Segment<Features::SubductingPlateModels::Temperature::Interface,
                                                      Features::SubductingPlateModels::Composition::Interface,
                                                      Features::SubductingPlateModels::Grains::Interface,
                                                      Features::SubductingPlateModels::Velocity::Interface> >("segments", local_default_temperature_models, local_default_composition_models, local_default_grains_models, local_default_velocity_models);


                WBAssertThrow(segment_vector[change_coord_number].size() == default_segment_vector.size(),
                              "Error: There are not the same amount of segments in section with coordinate " << change_coord_number
                              << " (" << segment_vector[change_coord_number].size() << " segments) as in the default segment ("
                              << default_segment_vector.size() << " segments). This is not allowed.");

                prm.enter_subsection("segments");
                {
                  for (unsigned int i = 0; i < segment_vector[change_coord_number].size(); ++i)
                    {
                      prm.enter_subsection(std::to_string(i));
                      {
                        prm.enter_subsection("temperature models");
                        {
                          for (unsigned int j = 0; j < segment_vector[change_coord_number][i].temperature_systems.size(); ++j)
                            {
                              prm.enter_subsection(std::to_string(j));
                              {
                                segment_vector[change_coord_number][i].temperature_systems[j]->parse_entries(prm);
                              }
                              prm.leave_subsection();
                            }
                        }
                        prm.leave_subsection();


                        prm.enter_subsection("composition models");
                        {
                          for (unsigned int j = 0; j < segment_vector[change_coord_number][i].composition_systems.size(); ++j)
                            {
                              prm.enter_subsection(std::to_string(j));
                              {
                                segment_vector[change_coord_number][i].composition_systems[j]->parse_entries(prm);
                              }
                              prm.leave_subsection();
                            }
                        }
                        prm.leave_subsection();

                        prm.enter_subsection("grains models");
                        {
                          for (unsigned int j = 0; j < segment_vector[change_coord_number][i].grains_systems.size(); ++j)
                            {
                              prm.enter_subsection(std::to_string(j));
                              {
                                segment_vector[change_coord_number][i].grains_systems[j]->parse_entries(prm);
                              }
                              prm.leave_subsection();
                            }
                        }
                        prm.leave_subsection();

                        prm.enter_subsection("velocity models");
                        {
                          for (unsigned int j = 0; j < segment_vector[change_coord_number][i].velocity_systems.size(); ++j)
                            {
                              prm.enter_subsection(std::to_string(j));
                              {
                                segment_vector[change_coord_number][i].velocity_systems[j]->parse_entries(prm);
                              }
                              prm.leave_subsection();
                            }
                        }
                        prm.leave_subsection();
                      }
                      prm.leave_subsection();
                    }
                }
                prm.leave_subsection();

              }
              prm.leave_subsection();
            }

        }
      prm.leave_subsection();


      prm.enter_subsection("segments");
      {
        for (unsigned int i = 0; i < default_segment_vector.size(); ++i)
          {
            prm.enter_subsection(std::to_string(i));
            {
              prm.enter_subsection("temperature models");
              {
                for (unsigned int j = 0; j < default_segment_vector[i].temperature_systems.size(); ++j)
                  {
                    prm.enter_subsection(std::to_string(j));
                    {
                      default_segment_vector[i].temperature_systems[j]->parse_entries(prm);
                    }
                    prm.leave_subsection();
                  }
              }
              prm.leave_subsection();


              prm.enter_subsection("composition models");
              {
                for (unsigned int j = 0; j < default_segment_vector[i].composition_systems.size(); ++j)
                  {
                    prm.enter_subsection(std::to_string(j));
                    {
                      default_segment_vector[i].composition_systems[j]->parse_entries(prm);
                    }
                    prm.leave_subsection();
                  }
              }
              prm.leave_subsection();


              prm.enter_subsection("grains models");
              {
                for (unsigned int j = 0; j < default_segment_vector[i].grains_systems.size(); ++j)
                  {
                    prm.enter_subsection(std::to_string(j));
                    {
                      default_segment_vector[i].grains_systems[j]->parse_entries(prm);
                    }
                    prm.leave_subsection();
                  }
              }
              prm.leave_subsection();

              prm.enter_subsection("velocity models");
              {
                for (unsigned int j = 0; j < default_segment_vector[i].velocity_systems.size(); ++j)
                  {
                    prm.enter_subsection(std::to_string(j));
                    {
                      default_segment_vector[i].velocity_systems[j]->parse_entries(prm);
                    }
                    prm.leave_subsection();
                  }
              }
              prm.leave_subsection();
            }
            prm.leave_subsection();
          }
      }
      prm.leave_subsection();

      maximum_slab_thickness = 0;
      maximum_total_slab_length = 0;
      total_slab_length.resize(original_number_of_coordinates);
      slab_segment_lengths.resize(original_number_of_coordinates);
      slab_segment_thickness.resize(original_number_of_coordinates);
      slab_segment_top_truncation.resize(original_number_of_coordinates);
      slab_segment_angles.resize(original_number_of_coordinates);

      for (unsigned int i = 0; i < segment_vector.size(); ++i)
        {
          double local_total_slab_length = 0;
          slab_segment_lengths[i].resize(segment_vector[i].size());
          slab_segment_thickness[i].resize(segment_vector[i].size(), Point<2>(invalid));
          slab_segment_top_truncation[i].resize(segment_vector[i].size(), Point<2>(invalid));
          slab_segment_angles[i].resize(segment_vector[i].size(), Point<2>(invalid));
          for (unsigned int j = 0; j < segment_vector[i].size(); ++j)
            {
              slab_segment_lengths[i][j] = segment_vector[i][j].value_length;
              local_total_slab_length += segment_vector[i][j].value_length;

              slab_segment_thickness[i][j] = segment_vector[i][j].value_thickness;
              maximum_slab_thickness = std::max(maximum_slab_thickness, slab_segment_thickness[i][j][0]);
              maximum_slab_thickness = std::max(maximum_slab_thickness, slab_segment_thickness[i][j][1]);
              slab_segment_top_truncation[i][j] = segment_vector[i][j].value_top_truncation;

              slab_segment_angles[i][j] = segment_vector[i][j].value_angle * (Consts::PI/180);
            }
          total_slab_length[i] = local_total_slab_length;
          maximum_total_slab_length = std::max(maximum_total_slab_length, local_total_slab_length);
        }

      // Here, we compute the spherical bounding box using the two extreme points of the box containing all the surface
      // coordinates and an additional buffer zone that accounts for the slab thickness and length. The first and second
      // points correspond to the lower left and the upper right corners of the bounding box, respectively (see the
      // documentation in include/bounding_box.h).
      // For the spherical system, the buffer zone along the longitudal direction is calculated using the
      // corresponding latitude points.

      // Find minimal and maximal coordinates. Do this by finding the
      // leftmost/rightmost point with regard to either the [0] or [1]
      // coordinate, and then takes its [0] or [1] element.
      auto compare_x_coordinate = [](auto p1, auto p2)
      {
        return p1[0]<p2[0];
      };

      min_along_x = (*std::min_element(coordinates.begin(), coordinates.end(), compare_x_coordinate)) [0];
      max_along_x = (*std::max_element(coordinates.begin(), coordinates.end(), compare_x_coordinate)) [0];


      auto compare_y_coordinate = [](auto p1, auto p2)
      {
        return p1[1]<p2[1];
      };

      min_along_y = (*std::min_element(coordinates.begin(), coordinates.end(), compare_y_coordinate)) [1];
      max_along_y = (*std::max_element(coordinates.begin(), coordinates.end(), compare_y_coordinate)) [1];

      min_lat_cos_inv = 1. / std::cos(min_along_y);
      max_lat_cos_inv = 1. / std::cos(max_along_y);

      buffer_around_slab_cartesian = (maximum_slab_thickness + maximum_total_slab_length);

      // Compute the surface bounding box
      buffer_around_slab_cartesian = (maximum_slab_thickness + maximum_total_slab_length);
      if (world->parameters.coordinate_system->natural_coordinate_system() == CoordinateSystem::spherical)
        {
          const double starting_radius_inv = 1 / (world->parameters.coordinate_system->max_model_depth());
          std::pair<Point<2>, Point<2> > &spherical_bounding_box = surface_bounding_box.get_boundary_points();

          const double buffer_around_slab_spherical = 2 * Consts::PI * buffer_around_slab_cartesian * starting_radius_inv;

          spherical_bounding_box.first = {(min_along_x - buffer_around_slab_spherical * min_lat_cos_inv) ,
                                          (min_along_y - buffer_around_slab_spherical), spherical
                                         } ;

          spherical_bounding_box.second = {(max_along_x + buffer_around_slab_spherical * max_lat_cos_inv) ,
                                           (max_along_y + buffer_around_slab_spherical), spherical
                                          };
        }
      else if (world->parameters.coordinate_system->natural_coordinate_system() == CoordinateSystem::cartesian)
        {
          std::pair<Point<2>, Point<2> > &bounding_box = surface_bounding_box.get_boundary_points();
          bounding_box.first = {min_along_x, min_along_y, cartesian};
          bounding_box.second = {max_along_x, max_along_y, cartesian};
          surface_bounding_box.extend(buffer_around_slab_cartesian);
        }
    }



    const BoundingBox<2> &
    SubductingPlate::get_surface_bounding_box () const
    {
      return surface_bounding_box;
    }


    void
    SubductingPlate::properties(const Point<3> &position_in_cartesian_coordinates,
                                const Objects::NaturalCoordinate &position_in_natural_coordinates,
                                const double depth,
                                const std::vector<std::array<unsigned int,3>> &properties,
                                const double gravity_norm,
                                const std::vector<size_t> &entry_in_output,
                                std::vector<double> &output) const
    {
      // The depth variable is the distance from the surface to the position, the depth
      // coordinate is the distance from the bottom of the model to the position and
      // the starting radius is the distance from the bottom of the model to the surface.
      const double starting_radius = position_in_natural_coordinates.get_depth_coordinate() + depth - starting_depth;

      WBAssert(std::abs(starting_radius) > std::numeric_limits<double>::epsilon(), "World Builder error: starting_radius can not be zero. "
               << "Position = " << position_in_cartesian_coordinates[0] << ':' << position_in_cartesian_coordinates[1] << ':' << position_in_cartesian_coordinates[2]
               << ", position_in_natural_coordinates.get_depth_coordinate() = " << position_in_natural_coordinates.get_depth_coordinate()
               << ", depth = " << depth
               << ", starting_depth " << starting_depth
              );

      // todo: explain and check -starting_depth
      if (depth <= maximum_depth && depth >= starting_depth && depth <= maximum_total_slab_length + maximum_slab_thickness &&
          get_surface_bounding_box().point_inside(Point<2>(position_in_natural_coordinates.get_surface_coordinates(),
                                                           world->parameters.coordinate_system->natural_coordinate_system())))
        {
          /*WBAssert(coordinates.size() == slab_segment_lengths.size(),
                   "Internal error: The size of coordinates (" << coordinates.size()
                   << ") and slab_segment_lengths (" << slab_segment_lengths.size() << ") are different.");
          WBAssert(coordinates.size() == slab_segment_angles.size(),
                   "Internal error: The size of coordinates (" << coordinates.size()
                   << ") and slab_segment_angles (" << slab_segment_angles.size() << ") are different.");
          WBAssert(coordinates.size() == slab_segment_angles.size(),
                   "Internal error: The size of coordinates (" << coordinates.size()
                   << ") and one_dimensional_coordinates (" << one_dimensional_coordinates.size() << ") are different.");*/
          // todo: explain
          const WorldBuilder::Utilities::PointDistanceFromCurvedPlanes distance_from_planes =
            WorldBuilder::Utilities::distance_point_from_curved_planes(position_in_cartesian_coordinates,
                                                                       position_in_natural_coordinates,
                                                                       reference_point,
                                                                       coordinates,
                                                                       slab_segment_lengths,
                                                                       slab_segment_angles,
                                                                       starting_radius,
                                                                       this->world->parameters.coordinate_system,
                                                                       false,
                                                                       this->bezier_curve);

          const double distance_from_plane = distance_from_planes.distance_from_plane;
          const double distance_along_plane = distance_from_planes.distance_along_plane;
          const double section_fraction = distance_from_planes.fraction_of_section;
          const size_t current_section = distance_from_planes.section;
          const size_t next_section = current_section + 1;
          const size_t current_segment = distance_from_planes.segment; // the original value was a unsigned in, converting it back.
          //const size_t next_segment = current_segment + 1;
          const double segment_fraction = distance_from_planes.fraction_of_segment;

          if (abs(distance_from_plane) < std::numeric_limits<double>::infinity() || (distance_along_plane) < std::numeric_limits<double>::infinity())
            {
              // We want to do both section (horizontal) and segment (vertical) interpolation.
              // first for thickness
              const double thickness_up = slab_segment_thickness[current_section][current_segment][0]
                                          + section_fraction
                                          * (slab_segment_thickness[next_section][current_segment][0]
                                             - slab_segment_thickness[current_section][current_segment][0]);
              const double thickness_down = slab_segment_thickness[current_section][current_segment][1]
                                            + section_fraction
                                            * (slab_segment_thickness[next_section][current_segment][1]
                                               - slab_segment_thickness[current_section][current_segment][1]);
              const double thickness_local = thickness_up + segment_fraction * (thickness_down - thickness_up);

              // if the thickness is zero, we don't need to compute anything, so return.
              if (std::fabs(thickness_local) < 2.0 * std::numeric_limits<double>::epsilon())
                return;

              // secondly for top truncation
              const double top_truncation_up = slab_segment_top_truncation[current_section][current_segment][0]
                                               + section_fraction
                                               * (slab_segment_top_truncation[next_section][current_segment][0]
                                                  - slab_segment_top_truncation[current_section][current_segment][0]);
              const double top_truncation_down = slab_segment_top_truncation[current_section][current_segment][1]
                                                 + section_fraction
                                                 * (slab_segment_top_truncation[next_section][current_segment][1]
                                                    - slab_segment_top_truncation[current_section][current_segment][1]);
              const double top_truncation_local = top_truncation_up + segment_fraction * (top_truncation_down - top_truncation_up);

              // if the thickness is smaller than what is truncated off at the top, we don't need to compute anything, so return.
              if (thickness_local < top_truncation_local)
                return;

              const double max_slab_length = total_slab_length[current_section] +
                                             section_fraction *
                                             (total_slab_length[next_section] - total_slab_length[current_section]);

              if (distance_from_plane >= top_truncation_local &&
                  distance_from_plane <= thickness_local &&
                  distance_along_plane >= 0 &&
                  distance_along_plane <= max_slab_length)
                {
                  // Inside the slab!
                  const Features::AdditionalParameters additional_parameters = {max_slab_length,thickness_local};
                  for (unsigned int i_property = 0; i_property < properties.size(); ++i_property)
                    {
                      switch (properties[i_property][0])
                        {
                          case 1: // temperature
                          {
                            double temperature_current_section = output[entry_in_output[i_property]];
                            double temperature_next_section = output[entry_in_output[i_property]];

                            for (const auto &temperature_model: segment_vector[current_section][current_segment].temperature_systems)
                              {
                                temperature_current_section = temperature_model->get_temperature(position_in_cartesian_coordinates,
                                                                                                 depth,
                                                                                                 gravity_norm,
                                                                                                 temperature_current_section,
                                                                                                 starting_depth,
                                                                                                 maximum_depth,
                                                                                                 distance_from_planes,
                                                                                                 additional_parameters);

                                WBAssert(!std::isnan(temperature_current_section), "Temperature is not a number: " << temperature_current_section
                                         << ", based on a temperature model with the name " << temperature_model->get_name() << ", in feature " << this->name);
                                WBAssert(std::isfinite(temperature_current_section), "Temperature is not a finite: " << temperature_current_section
                                         << ", based on a temperature model with the name " << temperature_model->get_name() << ", in feature " << this->name);

                              }

                            for (const auto &temperature_model: segment_vector[next_section][current_segment].temperature_systems)
                              {
                                temperature_next_section = temperature_model->get_temperature(position_in_cartesian_coordinates,
                                                                                              depth,
                                                                                              gravity_norm,
                                                                                              temperature_next_section,
                                                                                              starting_depth,
                                                                                              maximum_depth,
                                                                                              distance_from_planes,
                                                                                              additional_parameters);

                                WBAssert(!std::isnan(temperature_next_section), "Temperature is not a number: " << temperature_next_section
                                         << ", based on a temperature model with the name " << temperature_model->get_name() << ", in feature " << this->name);
                                WBAssert(std::isfinite(temperature_next_section), "Temperature is not a finite: " << temperature_next_section
                                         << ", based on a temperature model with the name " << temperature_model->get_name() << ", in feature " << this->name);

                              }

                            // linear interpolation between current and next section temperatures
                            output[entry_in_output[i_property]] = temperature_current_section + section_fraction * (temperature_next_section - temperature_current_section);
                            break;
                          }
                          case 2: // composition
                          {
                            double composition_current_section = output[entry_in_output[i_property]];
                            double composition_next_section = output[entry_in_output[i_property]];

                            for (const auto &composition_model: segment_vector[current_section][current_segment].composition_systems)
                              {
                                composition_current_section = composition_model->get_composition(position_in_cartesian_coordinates,
                                                                                                 depth,
                                                                                                 properties[i_property][1],
                                                                                                 composition_current_section,
                                                                                                 starting_depth,
                                                                                                 maximum_depth,
                                                                                                 distance_from_planes,
                                                                                                 additional_parameters);

                                WBAssert(!std::isnan(composition_current_section), "Composition_current_section is not a number: " << composition_current_section
                                         << ", based on a composition model with the name " << composition_model->get_name() << ", in feature " << this->name);
                                WBAssert(std::isfinite(composition_current_section), "Composition_current_section is not a finite: " << composition_current_section
                                         << ", based on a composition model with the name " << composition_model->get_name() << ", in feature " << this->name);

                              }

                            for (const auto &composition_model: segment_vector[next_section][current_segment].composition_systems)
                              {
                                composition_next_section = composition_model->get_composition(position_in_cartesian_coordinates,
                                                                                              depth,
                                                                                              properties[i_property][1],
                                                                                              composition_next_section,
                                                                                              starting_depth,
                                                                                              maximum_depth,
                                                                                              distance_from_planes,
                                                                                              additional_parameters);

                                WBAssert(!std::isnan(composition_next_section), "Composition_next_section is not a number: " << composition_next_section
                                         << ", based on a composition model with the name " << composition_model->get_name() << ", in feature " << this->name);
                                WBAssert(std::isfinite(composition_next_section), "Composition_next_section is not a finite: " << composition_next_section
                                         << ", based on a composition model with the name " << composition_model->get_name() << ", in feature " << this->name);

                              }

                            // linear interpolation between current and next section temperatures
                            output[entry_in_output[i_property]] = composition_current_section + section_fraction * (composition_next_section - composition_current_section);
                            break;
                          }
                          case 3: // grains
                          {
                            WorldBuilder::grains grains(output,properties[i_property][2],entry_in_output[i_property]);
                            WorldBuilder::grains  grains_current_section = grains;
                            WorldBuilder::grains  grains_next_section = grains;

                            for (const auto &grains_model: segment_vector[current_section][current_segment].grains_systems)
                              {
                                grains_current_section = grains_model->get_grains(position_in_cartesian_coordinates,
                                                                                  depth,
                                                                                  properties[i_property][1],
                                                                                  grains_current_section,
                                                                                  starting_depth,
                                                                                  maximum_depth,
                                                                                  distance_from_planes,
                                                                                  additional_parameters);

                              }

                            for (const auto &grains_model: segment_vector[next_section][current_segment].grains_systems)
                              {
                                grains_next_section = grains_model->get_grains(position_in_cartesian_coordinates,
                                                                               depth,
                                                                               properties[i_property][1],
                                                                               grains_next_section,
                                                                               starting_depth,
                                                                               maximum_depth,
                                                                               distance_from_planes,
                                                                               additional_parameters);

                              }

                            // linear interpolation between current and next section temperatures
                            for (size_t i = 0; i < grains.sizes.size(); i++)
                              {
                                grains.sizes[i] = grains_current_section.sizes[i] + section_fraction * (grains_next_section.sizes[i] - grains_current_section.sizes[i]);
                              }

                            // average two rotations matrices through quaternions.
                            for (size_t i = 0; i < grains_current_section.rotation_matrices.size(); i++)
                              {
                                const glm::quaternion::quat quat_current = glm::quaternion::quat_cast(grains_current_section.rotation_matrices[i]);
                                const glm::quaternion::quat quat_next = glm::quaternion::quat_cast(grains_next_section.rotation_matrices[i]);

                                const glm::quaternion::quat quat_average = glm::quaternion::slerp(quat_current,quat_next,section_fraction);

                                grains.rotation_matrices[i] = glm::quaternion::mat3_cast(quat_average);
                              }

                            grains.unroll_into(output,entry_in_output[i_property]);
                            break;
                          }
                          case 4:
                          {
                            output[entry_in_output[i_property]] = static_cast<double>(tag_index);
                            break;
                          }
                          case 5: // velocity
                          {
                            std::array<double,3> velocity_current_section;// = Point<3>(cartesian);
                            velocity_current_section[0] = output[entry_in_output[i_property]];
                            velocity_current_section[1] = output[entry_in_output[i_property]+1];
                            velocity_current_section[2] = output[entry_in_output[i_property]]+2;
                            std::array<double,3> velocity_next_section = velocity_current_section;// output[entry_in_output[i_property]];

                            for (const auto &velocity_model: segment_vector[current_section][current_segment].velocity_systems)
                              {
                                velocity_current_section = velocity_model->get_velocity(position_in_cartesian_coordinates,
                                                                                        depth,
                                                                                        gravity_norm,
                                                                                        velocity_current_section,
                                                                                        starting_depth,
                                                                                        maximum_depth,
                                                                                        distance_from_planes,
                                                                                        additional_parameters);

                                //WBAssert(!std::isnan(velocity_current_section), "Velocity is not a number: " << velocity_current_section
                                //         << ", based on a velocity model with the name " << velocity_model->get_name() << ", in feature " << this->name);
                                //WBAssert(std::isfinite(velocity_current_section), "Velocity is not a finite: " << velocity_current_section
                                //         << ", based on a velocity model with the name " << velocity_model->get_name() << ", in feature " << this->name);

                              }

                            for (const auto &velocity_model: segment_vector[next_section][current_segment].velocity_systems)
                              {
                                velocity_next_section = velocity_model->get_velocity(position_in_cartesian_coordinates,
                                                                                     depth,
                                                                                     gravity_norm,
                                                                                     velocity_next_section,
                                                                                     starting_depth,
                                                                                     maximum_depth,
                                                                                     distance_from_planes,
                                                                                     additional_parameters);

                                //WBAssert(!std::isnan(velocity_next_section), "Velocity is not a number: " << velocity_next_section
                                //         << ", based on a velocity model with the name " << velocity_model->get_name() << ", in feature " << this->name);
                                //WBAssert(std::isfinite(velocity_next_section), "Velocity is not a finite: " << velocity_next_section
                                //         << ", based on a velocity model with the name " << velocity_model->get_name() << ", in feature " << this->name);

                              }

                            // linear interpolation between current and next section velocitys
                            output[entry_in_output[i_property]] = velocity_current_section[0] + section_fraction * (velocity_next_section[0] - velocity_current_section[0]);
                            output[entry_in_output[i_property]+1] = velocity_current_section[1] + section_fraction * (velocity_next_section[1] - velocity_current_section[1]);
                            output[entry_in_output[i_property]+2] = velocity_current_section[2] + section_fraction * (velocity_next_section[2] - velocity_current_section[2]);
                            break;
                          }
                          default:
                          {
                            WBAssertThrow(false,
                                          "Internal error: Unimplemented property provided. " <<
                                          "Only temperature (1), composition (2), grains (3), tag (4) or velocity (5) are allowed. "
                                          "Provided property number was: " << properties[i_property][0]);
                          }
                        }
                    }

                }
            }
        }

    }

    Objects::PlaneDistances
    SubductingPlate::distance_to_feature_plane(const Point<3> &position_in_cartesian_coordinates,
                                               const Objects::NaturalCoordinate &position_in_natural_coordinates,
                                               const double depth) const
    {
      // The depth variable is the distance from the surface to the position, the depth
      // coordinate is the distance from the bottom of the model to the position and
      // the starting radius is the distance from the bottom of the model to the surface.
      const double starting_radius = position_in_natural_coordinates.get_depth_coordinate() + depth - starting_depth;

      WBAssert(std::abs(starting_radius) > std::numeric_limits<double>::epsilon(), "World Builder error: starting_radius can not be zero. "
               << "Position = " << position_in_cartesian_coordinates[0] << ':' << position_in_cartesian_coordinates[1] << ':' << position_in_cartesian_coordinates[2]
               << ", natural_coordinate.get_depth_coordinate() = " << position_in_natural_coordinates.get_depth_coordinate()
               << ", depth = " << depth
               << ", starting_depth " << starting_depth
              );

      const WorldBuilder::Utilities::PointDistanceFromCurvedPlanes distance_from_planes =
        WorldBuilder::Utilities::distance_point_from_curved_planes(position_in_cartesian_coordinates,
                                                                   position_in_natural_coordinates,
                                                                   reference_point,
                                                                   coordinates,
                                                                   slab_segment_lengths,
                                                                   slab_segment_angles,
                                                                   starting_radius,
                                                                   this->world->parameters.coordinate_system,
                                                                   false,
                                                                   this->bezier_curve);

      Objects::PlaneDistances plane_distances(distance_from_planes.distance_from_plane, distance_from_planes.distance_along_plane);
      return plane_distances;
    }

    WB_REGISTER_FEATURE(SubductingPlate, subducting plate)
  } // namespace Features
} // namespace WorldBuilder