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 // This file is part of the ACTS project.
 //
 // Copyright (C) 2016 CERN for the benefit of the ACTS project
 //
 // This Source Code Form is subject to the terms of the Mozilla Public
 // License, v. 2.0. If a copy of the MPL was not distributed with this
 // file, You can obtain one at https://mozilla.org/MPL/2.0/.
 
 #pragma once
 
 #include "Acts/Definitions/Algebra.hpp"
 #include "Acts/Material/IVolumeMaterial.hpp"
 #include "Acts/Material/Material.hpp"
 #include "Acts/Utilities/BinUtility.hpp"
 #include "Acts/Utilities/Interpolation.hpp"
 
 #include <functional>
 #include <optional>
 
 namespace Acts {
 
 /// @addtogroup material
 /// @{
 
 /// @brief Struct for mapping global 3D positions to material values
 ///
 /// Global 3D positions are transformed into a @c DIM_POS Dimensional vector
 /// which is used to look up the material classification value in the
 /// underlying material map.
 template <typename G>
 struct MaterialMapLookup {
  public:
   /// Type alias for material grid
   using Grid_t = G;
   /// Dimensionality of the position space for material interpolation
   static constexpr std::size_t DIM_POS = Grid_t::DIM;
 
   /// @brief Struct representing smallest grid unit in material grid
   ///
   /// This type encapsulate all required information to perform linear
   /// interpolation of material classification values within a 3D volume.
   struct MaterialCell {
     /// Number of corner points defining the confining hyper-box
     static constexpr unsigned int N = 1 << DIM_POS;
 
     /// @brief Default constructor
     ///
     /// @param [in] transformPos   Mapping of global 3D coordinates onto grid
     /// space
     /// @param [in] lowerLeft   Generalized lower-left corner of hyper box
     ///                         (containing the minima of the hyper box along
     ///                         each Dimension)
     /// @param [in] upperRight  Generalized upper-right corner of hyper box
     ///                         (containing the maxima of the hyper box along
     ///                         each Dimension)
     /// @param [in] materialValues Material classification values at the hyper
     /// box corners sorted in the canonical order defined in Acts::interpolate
     MaterialCell(
         std::function<ActsVector<DIM_POS>(const Vector3&)> transformPos,
         std::array<double, DIM_POS> lowerLeft,
         std::array<double, DIM_POS> upperRight,
         std::array<Material::ParametersVector, N> materialValues)
         : m_transformPos(std::move(transformPos)),
           m_lowerLeft(std::move(lowerLeft)),
           m_upperRight(std::move(upperRight)),
           m_materialValues(std::move(materialValues)) {}
 
     /// @brief Retrieve material at given position
     ///
     /// @param [in] position Global 3D position
     /// @return Material at the given position
     ///
     /// @pre The given @c position must lie within the current cell.
     Material getMaterial(const Vector3& position) const {
       // defined in Interpolation.hpp
       return Material(interpolate(m_transformPos(position), m_lowerLeft,
                                   m_upperRight, m_materialValues));
     }
 
     /// @brief Check whether given 3D position is inside this cell
     ///
     /// @param [in] position Global 3D position
     /// @return @c true if position is inside the current cell,
     ///         otherwise @c false
     bool isInside(const Vector3& position) const {
       const auto& gridCoordinates = m_transformPos(position);
       for (unsigned int i = 0; i < DIM_POS; ++i) {
         if (gridCoordinates[i] < m_lowerLeft.at(i) ||
             gridCoordinates[i] >= m_upperRight.at(i)) {
           return false;
         }
       }
       return true;
     }
 
    private:
     /// Geometric transformation applied to global 3D positions
     std::function<ActsVector<DIM_POS>(const Vector3&)> m_transformPos;
 
     /// Generalized lower-left corner of the confining hyper-box
     std::array<double, DIM_POS> m_lowerLeft;
 
     /// Generalized upper-right corner of the confining hyper-box
     std::array<double, DIM_POS> m_upperRight;
 
     /// @brief Material component vectors at the hyper-box corners
     ///
     /// @note These values must be order according to the prescription detailed
     ///       in Acts::interpolate.
     std::array<Material::ParametersVector, N> m_materialValues;
   };
 
   /// @brief Default constructor
   ///
   /// @param [in] transformPos Mapping of global 3D coordinates (cartesian)
   /// onto grid space
   /// @param [in] grid Grid storing material classification values
   MaterialMapLookup(
       std::function<ActsVector<DIM_POS>(const Vector3&)> transformPos,
       Grid_t grid)
       : m_transformPos(std::move(transformPos)), m_grid(std::move(grid)) {}
 
   /// @brief Retrieve binned material at given position
   ///
   /// @param [in] position Global 3D position
   /// @return Material at the given position
   ///
   /// @pre The given @c position must lie within the range of the underlying
   /// map.
   Material material(const Vector3& position) const {
     return Material(m_grid.atLocalBins(
         m_grid.localBinsFromLowerLeftEdge(m_transformPos(position))));
   }
 
   /// @brief Retrieve interpolated material at given position
   ///
   /// @param [in] position Global 3D position
   /// @return Material at the given position
   ///
   /// @pre The given @c position must lie within the range of the underlying
   /// map.
   Material getMaterial(const Vector3& position) const {
     return Material(m_grid.interpolate(m_transformPos(position)));
   }
 
   /// @brief Retrieve material cell for given position
   ///
   /// @param [in] position Global 3D position
   /// @return material cell containing the given global position
   ///
   /// @pre The given @c position must lie within the range of the underlying
   /// map.
   MaterialCell getMaterialCell(const Vector3& position) const {
     const auto& gridPosition = m_transformPos(position);
     std::size_t bin = m_grid.globalBinFromPosition(gridPosition);
     const auto& indices = m_grid.localBinsFromPosition(bin);
     const auto& lowerLeft = m_grid.lowerLeftBinEdge(indices);
     const auto& upperRight = m_grid.upperRightBinEdge(indices);
 
     // Loop through all corner points
     constexpr std::size_t nCorners = 1 << DIM_POS;
     std::array<Material::ParametersVector, nCorners> neighbors{};
     const auto& cornerIndices = m_grid.closestPointsIndices(gridPosition);
 
     std::size_t i = 0;
     for (std::size_t index : cornerIndices) {
       neighbors.at(i++) = m_grid.at(index);
     }
 
     return MaterialCell(m_transformPos, lowerLeft, upperRight,
                         std::move(neighbors));
   }
 
   /// @brief Get the number of bins for all axes of the map
   ///
   /// @return Vector returning number of bins for all map axes
   std::vector<std::size_t> getNBins() const {
     auto nBinsArray = m_grid.numLocalBins();
     return std::vector<std::size_t>(nBinsArray.begin(), nBinsArray.end());
   }
 
   /// @brief Get the minimum value of all axes of the map
   ///
   /// @return Vector returning the minima of all map axes
   std::vector<double> getMin() const {
     auto minArray = m_grid.minPosition();
     return std::vector<double>(minArray.begin(), minArray.end());
   }
 
   /// @brief Get the maximum value of all axes of the map
   ///
   /// @return Vector returning the maxima of all map axes
   std::vector<double> getMax() const {
     auto maxArray = m_grid.maxPosition();
     return std::vector<double>(maxArray.begin(), maxArray.end());
   }
 
   /// @brief Check whether given 3D position is inside look-up domain
   ///
   /// @param [in] position Global 3D position
   /// @return @c true if position is inside the defined look-up grid,
   ///         otherwise @c false
   bool isInside(const Vector3& position) const {
     return m_grid.isInside(m_transformPos(position));
   }
 
   /// @brief Get a const reference on the underlying grid structure
   ///
   /// @return Grid reference
   const Grid_t& getGrid() const { return m_grid; }
 
  private:
   /// Geometric transformation applied to global 3D positions
   std::function<ActsVector<DIM_POS>(const Vector3&)> m_transformPos;
   /// Grid storing material values
   Grid_t m_grid;
 };
 
 /// @brief Interpolate material classification values from material values on a
 /// given grid
 ///
 /// This class implements a material service which is initialized by a
 /// material map defined by:
 /// - a list of material values on a regular grid in some n-Dimensional space,
 /// - a transformation of global 3D coordinates onto this n-Dimensional
 /// space.
 /// - a transformation of local n-Dimensional material coordinates into
 /// global (cartesian) 3D coordinates
 ///
 /// The material value for a given global position is then determined by:
 /// - mapping the position onto the grid,
 /// - looking up the material classification values on the closest grid points,
 /// - doing a linear interpolation of these values.
 /// @warning Each classification number of the material is interpolated
 /// independently and thus does not consider any correlations that exists
 /// between these values. This might work out since the used material is already
 /// a mean of the materials in a certain bin and can therewith be treated as a
 /// collection of numbers.
 /// @tparam G Type of the grid
 template <typename Mapper_t>
 class InterpolatedMaterialMap : public IVolumeMaterial {
  public:
   /// @brief Temporary storage of a certain cell to improve material access
   struct Cache {
     /// Stored material cell
     std::optional<typename Mapper_t::MaterialCell> matCell;
     /// Boolean statement if the cell is initialized
     bool initialized = false;
   };
 
   /// @brief Create interpolated map
   ///
   /// @param [in] mapper Material map
   explicit InterpolatedMaterialMap(Mapper_t&& mapper)
       : m_mapper(std::move(mapper)) {}
 
   /// @brief Create interpolated map
   ///
   /// @param [in] mapper Material map
   /// @param [in] bu @c BinUtility for build from
   InterpolatedMaterialMap(Mapper_t&& mapper, BinUtility bu)
       : m_mapper(std::move(mapper)), m_binUtility(std::move(bu)) {}
 
   /// @brief Retrieve the binned material
   ///
   /// @param [in] position Global 3D position
   ///
   /// @return Material at given position
   const Material material(const Vector3& position) const override {
     return m_mapper.material(position);
   }
 
   /// @brief Retrieve the interpolated material
   ///
   /// @param [in] position Global 3D position
   ///
   /// @return material at given position
   Material getMaterial(const Vector3& position) const {
     return m_mapper.getMaterial(position);
   }
 
   /// @brief Retrieve material
   ///
   /// @param [in] position Global 3D position
   /// @param [in,out] cache Cache object. Contains material cell used for
   /// interpolation
   ///
   /// @return material at given position
   Material getMaterial(const Vector3& position, Cache& cache) const {
     if (!cache.initialized || !(*cache.matCell).isInside(position)) {
       cache.matCell = getMaterialCell(position);
       cache.initialized = true;
     }
     return (*cache.matCell).getMaterial(position);
   }
 
   /// @brief Retrieve material value & its "gradient"
   ///
   /// @param [in]  position   Global 3D position
   /// @return Material
   ///
   /// @note Currently the derivative is not calculated
   /// @todo return derivative
   Material getMaterialGradient(const Vector3& position,
                                ActsMatrix<5, 5>& /*derivative*/) const {
     return m_mapper.getMaterial(position);
   }
 
   /// @brief Retrieve material value & its "gradient"
   ///
   /// @param [in]  position   Global 3D position
   /// @return Material
   ///
   /// @note Currently the derivative is not calculated
   /// @note Cache is not used currently
   /// @todo return derivative
   Material getMaterialGradient(const Vector3& position,
                                ActsMatrix<5, 5>& /*derivative*/,
                                Cache& /*cache*/) const {
     return m_mapper.getMaterial(position);
   }
 
   /// @brief Convenience method to access underlying material mapper
   ///
   /// @return The material mapper
   const Mapper_t& getMapper() const { return m_mapper; }
 
   /// @brief Check whether given 3D position is inside look-up domain
   ///
   /// @param [in] position Global 3D position
   /// @return @c true if position is inside the defined map, otherwise @c false
   bool isInside(const Vector3& position) const {
     return m_mapper.isInside(position);
   }
 
   /// Return the BinUtility
   /// @return Const reference to the bin utility for the material map
   const BinUtility& binUtility() const { return m_binUtility; }
 
   /// Output Method for std::ostream
   ///
   /// @param sl The outoput stream
   /// @return Reference to the output stream for method chaining
   std::ostream& toStream(std::ostream& sl) const override {
     sl << "Acts::InterpolatedMaterialMap : " << std::endl;
     sl << "   - Number of Material bins [0,1] : " << m_binUtility.max(0) + 1
        << " / " << m_binUtility.max(1) + 1 << std::endl;
     sl << "   - Parse full update material    : " << std::endl;
     return sl;
   }
 
  private:
   /// @brief Retrieve cell for given position
   ///
   /// @param [in] position Global 3D position
   /// @return Material cell containing the given global position
   ///
   /// @pre The given @c position must lie within the range of the underlying
   /// map.
   typename Mapper_t::MaterialCell getMaterialCell(
       const Vector3& position) const {
     return m_mapper.getMaterialCell(position);
   }
 
   /// @brief object for global coordinate transformation and interpolation
   ///
   /// This object performs the mapping of the global 3D coordinates onto the
   /// material grid and the interpolation of the material component values on
   /// close-by grid points.
   Mapper_t m_mapper;
 
   BinUtility m_binUtility{};
 };
 
 /// @}
 }  // namespace Acts

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