regularData3D.h

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// -*- Mode: C++; tab-width: 2; -*-
// vi: set ts=2:
//
 
#ifndef BALL_DATATYPE_REGULARDATA3D_H
#define BALL_DATATYPE_REGULARDATA3D_H
 
#ifndef BALL_MATHS_VECTOR3_H
# include <BALL/MATHS/vector3.h>
#endif
 
#ifndef BALL_SYSTEM_FILE_H
# include <BALL/SYSTEM/file.h>
#endif
 
#ifndef BALL_SYSTEM_BINARYFILEADAPTOR_H
# include <BALL/SYSTEM/binaryFileAdaptor.h>
#endif
 
#ifndef BALL_MATHS_COMMON_H
# include <BALL/MATHS/common.h>
#endif
 
#include <iostream>
#include <fstream>
#include <iterator>
#include <algorithm>
 
namespace BALL 
{
  template <typename ValueType>
  class TRegularData3D 
  {
    public:
 
    BALL_CREATE(TRegularData3D<ValueType>)
 
    

    class IndexType
    {
      public:
      inline IndexType() : x(0), y(0), z(0) {}
      inline IndexType(Position p) : x(p), y(p), z(p) {}
      inline IndexType(Position p, Position q, Position r) : x(p), y(q), z(r) {}

      Position x;
      Position y;
      Position z;
    };

    typedef std::vector<ValueType> VectorType;
    typedef TVector3<float> CoordinateType;
    typedef typename std::vector<ValueType>::iterator Iterator;
    typedef typename std::vector<ValueType>::const_iterator ConstIterator;
 
    //  STL compatibility types
    //
    typedef ValueType value_type;
    typedef typename std::vector<ValueType>::iterator iterator;
    typedef typename std::vector<ValueType>::const_iterator const_iterator;
    typedef typename std::vector<ValueType>::reference reference;
    typedef typename std::vector<ValueType>::const_reference const_reference;
    typedef typename std::vector<ValueType>::pointer pointer;
    typedef typename std::vector<ValueType>::difference_type difference_type;
    typedef typename std::vector<ValueType>::size_type size_type;


    TRegularData3D(); 
  
    TRegularData3D(const TRegularData3D<ValueType>& grid);

    TRegularData3D(const CoordinateType& origin, const CoordinateType& dimension, const CoordinateType& spacing);

    TRegularData3D(const CoordinateType& origin, const CoordinateType& x_axis, 
                   const CoordinateType& y_axis, const CoordinateType& z_axis, const IndexType& size);

    TRegularData3D
      (const IndexType& size, 
       const CoordinateType& origin = CoordinateType(0.0),
       const CoordinateType& dimension = CoordinateType(1.0));

    virtual ~TRegularData3D();

    virtual void clear();


    TRegularData3D& operator = (const TRegularData3D<ValueType>& data);
 


    bool operator == (const TRegularData3D<ValueType>& grid) const;

    BALL_INLINE bool operator != (const TRegularData3D<ValueType>& grid) const {  return !this->operator == (grid); }

    BALL_INLINE bool empty() const { return data_.empty(); }

    bool isInside(const CoordinateType& r) const;

    BALL_INLINE bool isOrthogonal() const { return is_orthogonal_;}


    BALL_INLINE ConstIterator begin() const { return data_.begin(); }
    BALL_INLINE ConstIterator end() const { return data_.end(); }
    BALL_INLINE Iterator begin() { return data_.begin(); }
    BALL_INLINE Iterator end() { return data_.end(); }

 
    // STL compatibility
    BALL_INLINE size_type size() const { return data_.size(); }
    BALL_INLINE size_type max_size() const { return data_.max_size(); }
    BALL_INLINE void swap(TRegularData3D<ValueType>& grid) { std::swap(*this, grid); }
 

    const vector<ValueType>& getData() const;

    const ValueType& getData(const IndexType& index) const;

    ValueType& getData(const IndexType& index);

    const ValueType& getData(Position index) const;

    ValueType& getData(Position index);

    const ValueType& operator [] (const IndexType& index) const 
    {   
      return data_[index.x + size_.x * index.y + index.z * size_.x * size_.y]; 
    }

    ValueType& operator [] (const IndexType& index)
    {   
      return data_[index.x + size_.x * index.y + index.z * size_.x * size_.y]; 
    }

    const ValueType& operator [] (Position index) const { return data_[index]; }

    ValueType& operator [] (Position index) { return data_[index]; }

    ValueType operator () (const CoordinateType& x) const;
    
    ValueType getInterpolatedValue(const CoordinateType& x) const;

    const ValueType& getClosestValue(const CoordinateType& x) const;

    ValueType& getClosestValue(const CoordinateType& x);

    IndexType getClosestIndex(const CoordinateType& v) const;

    IndexType getLowerIndex(const CoordinateType& v) const;

    inline const IndexType& getSize() const { return size_; }
    
    inline const CoordinateType& getOrigin() const { return origin_; }

    const CoordinateType& getSpacing() const {  return spacing_; }
    void setOrigin(const CoordinateType& origin) { origin_ = origin; }

    const CoordinateType& getDimension() const { return dimension_; }

    void setDimension(const CoordinateType& dimension)  
    {
      dimension_ = dimension;
      if (is_orthogonal_)
      {
        spacing_.x = dimension_.x / (double)(size_.x - 1);
        spacing_.y = dimension_.y / (double)(size_.y - 1);
        spacing_.z = dimension_.z / (double)(size_.z - 1);
      }
    }

    void resize(const IndexType& size);

    void rescale(const IndexType& new_size);

    CoordinateType getCoordinates(const IndexType& index) const;

    CoordinateType getCoordinates(Position index) const;

    void getEnclosingIndices
      (const CoordinateType& r,
      Position& llf, Position& rlf, Position& luf, Position& ruf,
      Position& llb, Position& rlb, Position& lub, Position& rub) const;

    void getEnclosingValues
      (const CoordinateType& r,
       ValueType& llf, ValueType& rlf, ValueType& luf, ValueType& ruf,
       ValueType& llb, ValueType& rlb, ValueType& lub, ValueType& rub) const;
    
    ValueType calculateMean() const;
    
    ValueType calculateSD() const;
    
    void binaryWrite(const String& filename) const;   
 
    void binaryWriteRaw(const String& filename) const;

    void binaryRead(const String& filename);
    
    protected:
      
    const CoordinateType mapToCartesian_(CoordinateType r) const
    {
      Vector3 result;
      r.x /= (size_.x - 1.);
      r.y /= (size_.y - 1.);
      r.z /= (size_.z - 1.);
 
      result.x = mapping_[0] * r.x + mapping_[1] * r.y + mapping_[2] * r.z + origin_.x;
      result.y = mapping_[3] * r.x + mapping_[4] * r.y + mapping_[5] * r.z + origin_.y;
      result.z = mapping_[6] * r.x + mapping_[7] * r.y + mapping_[8] * r.z + origin_.z;
 
      return result;
    }
    
    const CoordinateType mapInverse_(CoordinateType r) const
    {
      r -= origin_;
 
      Vector3 result;
      result.x = inverse_mapping_[0] * r.x + inverse_mapping_[1] * r.y + inverse_mapping_[2] * r.z;
      result.y = inverse_mapping_[3] * r.x + inverse_mapping_[4] * r.y + inverse_mapping_[5] * r.z;
      result.z = inverse_mapping_[6] * r.x + inverse_mapping_[7] * r.y + inverse_mapping_[8] * r.z;
 
      result.x *= (size_.x - 1);
      result.y *= (size_.y - 1);
      result.z *= (size_.z - 1);
 
      return result;
    }
    
    VectorType data_;

    CoordinateType  origin_;

    CoordinateType  dimension_;

    CoordinateType  spacing_;

    IndexType size_;

    typedef struct { ValueType bt[1024]; } BlockValueType;

    bool is_orthogonal_;

    std::vector<double> mapping_;
    std::vector<double> inverse_mapping_;
  };

  typedef TRegularData3D<float> RegularData3D;
 
  // default constructor.
  template <class ValueType>
  TRegularData3D<ValueType>::TRegularData3D()
    : data_(0),
      origin_(0.0),
      dimension_(0.0),
      spacing_(1.0),
      size_(0, 0, 0),
      is_orthogonal_(true)
  {
  }
 
  // copy constructor
  template <class ValueType>
  TRegularData3D<ValueType>::TRegularData3D
    (const TRegularData3D<ValueType>& data)
    : data_(),
      origin_(data.origin_),
      dimension_(data.dimension_),
      spacing_(data.spacing_),
      size_(data.size_),
      is_orthogonal_(data.is_orthogonal_),
      mapping_(data.mapping_),
      inverse_mapping_(data.inverse_mapping_)
  {
    try
    {
      data_ = data.data_;
    }
    catch (std::bad_alloc&)
    {
      data_.resize(0);
      throw Exception::OutOfMemory(__FILE__, __LINE__, data.data_.size() * sizeof(ValueType));
    }
  }
 
  template <class ValueType>
  TRegularData3D<ValueType>::TRegularData3D
    (const typename TRegularData3D<ValueType>::IndexType& size,
     const typename TRegularData3D<ValueType>::CoordinateType& origin,
     const typename TRegularData3D<ValueType>::CoordinateType& dimension)
    : data_(),
      origin_(origin),
      dimension_(dimension),
      spacing_(0.0),
      size_(size),
      is_orthogonal_(true)
  {
    // Compute the grid spacing
    spacing_.x = dimension_.x / (double)(size_.x - 1);
    spacing_.y = dimension_.y / (double)(size_.y - 1);
    spacing_.z = dimension_.z / (double)(size_.z - 1);
 
    // Compute the number of grid points
    size_type number_of_points = size_.x * size_.y * size_.z;
    try
    {
      data_.resize(number_of_points);
    }
    catch (std::bad_alloc&)
    {
      data_.resize(0);
      throw Exception::OutOfMemory(__FILE__, __LINE__, number_of_points * sizeof(ValueType));
    }
  }
 
 
  template <class ValueType>
  TRegularData3D<ValueType>::TRegularData3D
    (const typename TRegularData3D<ValueType>::CoordinateType& origin,
     const typename TRegularData3D<ValueType>::CoordinateType& dimension,
     const typename TRegularData3D<ValueType>::CoordinateType& spacing)
    : data_(),
      origin_(origin),
      dimension_(dimension),
      spacing_(spacing),
      size_(0),
      is_orthogonal_(true)
  {
    // Compute the grid size
    size_.x = (Size)(dimension_.x / spacing_.x + 0.5) + 1;
    size_.y = (Size)(dimension_.y / spacing_.y + 0.5) + 1;
    size_.z = (Size)(dimension_.z / spacing_.z + 0.5) + 1;
 
    // Compute the number of grid points
    size_type size = size_.x * size_.y * size_.z;
    try
    {
      data_ .resize(size);
    }
    catch (std::bad_alloc&)
    {
      data_.resize(0);
      throw Exception::OutOfMemory(__FILE__, __LINE__, size * sizeof(ValueType));
    }
 
    // Adjust the spacing -- dimension has precedence.
    spacing_.x = dimension_.x / (double)(size_.x - 1);
    spacing_.y = dimension_.y / (double)(size_.y - 1);
    spacing_.z = dimension_.z / (double)(size_.z - 1);
  }
 
  template <class ValueType>
  TRegularData3D<ValueType>::TRegularData3D
    (const typename TRegularData3D<ValueType>::CoordinateType& origin, 
     const typename TRegularData3D<ValueType>::CoordinateType& x_axis,
     const typename TRegularData3D<ValueType>::CoordinateType& y_axis, 
     const typename TRegularData3D<ValueType>::CoordinateType& z_axis, 
     const typename TRegularData3D<ValueType>::IndexType& new_size)
    : data_(),
      origin_(origin),
      dimension_(x_axis+y_axis+z_axis),
      spacing_(0.0),
      size_(new_size),
      is_orthogonal_(false)
  {
    // compute the spacing
    spacing_.x = x_axis.getLength() / (new_size.x - 1.);
    spacing_.y = y_axis.getLength() / (new_size.y - 1.);
    spacing_.z = z_axis.getLength() / (new_size.z - 1.);  
 
    size_type size = size_.x * size_.y * size_.z;
    try
    {
      data_.resize(size);
    }
    catch (std::bad_alloc&)
    {
      data_.resize(0);
      throw Exception::OutOfMemory(__FILE__, __LINE__, size * sizeof(ValueType));
    }
 
    // prepare the mapping matrix and its inverse
    mapping_.resize(9);
    inverse_mapping_.resize(9);
 
    mapping_[0] = x_axis.x; mapping_[1] = y_axis.x; mapping_[2] = z_axis.x;
    mapping_[3] = x_axis.y; mapping_[4] = y_axis.y; mapping_[5] = z_axis.y;
    mapping_[6] = x_axis.z; mapping_[7] = y_axis.z; mapping_[8] = z_axis.z;
 
    // this is numerically instable and only works well for the "simple"
    // cases. should be replaced by QR or an SVD
 
    // just for readability
    double a = mapping_[0]; double b = mapping_[1]; double c = mapping_[2];
    double d = mapping_[3]; double e = mapping_[4]; double f = mapping_[5];
    double g = mapping_[6]; double h = mapping_[7]; double i = mapping_[8];
 
    double determinant = 1. / (a*(e*i - f*h) - b*(d*i - f*g) + c*(d*h - e*g));
 
    inverse_mapping_[0] = determinant * (e*i - f*h);
    inverse_mapping_[1] = determinant * (b*i - c*h);
    inverse_mapping_[2] = determinant * (b*f - c*e);
 
    inverse_mapping_[3] = determinant * (f*g - d*i);
    inverse_mapping_[4] = determinant * (a*i - c*g);
    inverse_mapping_[5] = determinant * (c*d - a*f);
 
    inverse_mapping_[6] = determinant * (d*h - e*g);
    inverse_mapping_[7] = determinant * (b*g - a*h);
    inverse_mapping_[8] = determinant * (a*e - b*d);
  }   
 
  template <class ValueType>
  TRegularData3D<ValueType>::~TRegularData3D()
  {
  }
 
  template <typename ValueType>
  BALL_INLINE
  TRegularData3D<ValueType>& TRegularData3D<ValueType>::operator =
    (const TRegularData3D<ValueType>& rhs)
  {
    // Avoid self-assignment.
    if (&rhs != this)
    {
      // Copy the coordinate-related attributes and
      // the size.
      origin_ = rhs.origin_;
      dimension_ = rhs.dimension_;
      spacing_ = rhs.spacing_;
      size_ = rhs.size_;
      
      is_orthogonal_ = rhs.is_orthogonal_;
      mapping_ = rhs.mapping_;
      inverse_mapping_ = rhs.inverse_mapping_;
      // Copy the data itself and rethrow allocation exceptions.
      try
      {
        data_ = rhs.data_;
      }
      catch (std::bad_alloc&)
      {
        data_.resize(0);
        throw Exception::OutOfMemory(__FILE__, __LINE__, rhs.data_.size() * sizeof(ValueType));
      }
    }
 
    return *this;
  }
 
  template <typename ValueType>
  void TRegularData3D<ValueType>::resize(const typename TRegularData3D<ValueType>::IndexType& size)
  {
    if (is_orthogonal_)
    {
      // If the old size equals the new size, we're done.
      if ((size.x == size_.x) && (size_.y == size.y) && (size_.z == size.z))
      {
        return;
      }
 
      // If the new grid is empty, this whole thing is quite easy.
      if ((size.x == 0) || (size.y == 0) || (size.z == 0))
      {
        data_.resize(0);
        dimension_.set(0.0, 0.0, 0.0);
        return;
      }
      // Compute the new array size.
      size_type new_size = (size_type)(size.x * size.y * size.z);
 
      // Catch any bad_allocs thrown by vector::resize
      try
      {
        // Create a new temporary array.
        std::vector<ValueType> old_data(data_);
 
        // Resize the data to its new size.
        data_.resize(new_size);
 
        // walk over the new grid and copy the old stuff back.
        static ValueType default_value = (ValueType)0;
        for (size_type i = 0; i < new_size; i++)
        {
          size_type x = i % size.x;
          size_type y = (i % (size.x * size.y)) / size.x;
          size_type z = i / (size.x * size.y);
          if ((x >= size_.x) || (y >= size_.y) || (z >= size_.z))
          {
            data_[i] = default_value;
          }
          else
          {
            data_[i] = old_data[x + y * size_.x + z * size_.x * size_.y];
          }
        }
 
        // Correct the grid dimension. Origin and spacing remain constant.
        if ((size_.x != 0) && (size_.y != 0) && (size_.z != 0))
        {
          dimension_.x *= (double)size.x / (double)size_.x;
          dimension_.y *= (double)size.y / (double)size_.y;
          dimension_.z *= (double)size.z / (double)size_.z;
        }
        size_ = size;
      }
      catch (std::bad_alloc&)
      {
        throw Exception::OutOfMemory(__FILE__, __LINE__, new_size * (Size)sizeof(ValueType));
      }
    }
  }
 
  template <typename ValueType>
  void TRegularData3D<ValueType>::rescale(const typename TRegularData3D<ValueType>::IndexType& size)
  {
    if (is_orthogonal_)
    {
      // If the old size equals the new size, we're done.
      if ((size.x == size_.x) && (size_.y == size.y) && (size_.z == size.z))
      {
        return;
      }
 
      // If the new grid is empty, this whole thing is quite easy.
      if ((size.x == 0) || (size.y == 0) || (size.z == 0))
      {
        data_.resize(0);
        dimension_.set(0.0);
        return;
      }
 
      // Compute the new array size.
      size_type new_size = (size_type)(size.x * size.y * size.z);
 
      // Catch any bad_allocs thrown by vector::resize
      try
      {
        // Create a new temporary array.
        TRegularData3D<ValueType> old_data(*this);
 
        // Resize the data array to its new size.
        data_.resize(new_size);
        spacing_.x = dimension_.x / (double)(size.x - 1);
        spacing_.y = dimension_.y / (double)(size.y - 1);
        spacing_.z = dimension_.z / (double)(size.z - 1);
 
        // Correct the grid size. Origin and dimension remain constant.
        size_ = size;
 
        // Walk over the new grid and copy the (interpolated) old stuff back.
        for (size_type i = 0; i < data_.size(); i++)
        {
          try
          {
            data_[i] = old_data.getInterpolatedValue(getCoordinates(i));
          }
          catch (Exception::OutOfGrid&)
          {
            data_[i] = old_data.getClosestValue(getCoordinates(i));
          }
        }
      }
      catch (std::bad_alloc&)
      {
        throw Exception::OutOfMemory(__FILE__, __LINE__, new_size * (Size)sizeof(ValueType));
      }
    }
  }
 
  template <class ValueType> 
  BALL_INLINE
  bool TRegularData3D<ValueType>::isInside(const typename TRegularData3D<ValueType>::CoordinateType& r) const   
  {
    if (is_orthogonal_)
    {
      return !((r.x > (origin_.x + dimension_.x )) 
          || (r.y > (origin_.y + dimension_.y))  
          || (r.z > (origin_.z + dimension_.z))
          || (r.x < origin_.x) || (r.y < origin_.y) || (r.z < origin_.z));
    } 
    else 
    {
      // compute A^-1 * pos and see whether the indices are part of the grid
      CoordinateType ri = mapInverse_(r);
      ri.x = Maths::round(ri.x);
      ri.y = Maths::round(ri.y);
      ri.z = Maths::round(ri.z);
      
      return !(   (ri.x < 0) || (ri.y < 0) || (ri.z < 0)
               || (ri.x >= size_.x) || (ri.y >= size_.y) || (ri.z >= size_.z) );
    }
  }
 
  template <class ValueType>
  BALL_INLINE
  const ValueType& TRegularData3D<ValueType>::getData
    (const typename TRegularData3D<ValueType>::IndexType& index) const
  {
    size_type pos = index.x + index.y * size_.x + index.z * size_.x * size_.y;
    if (pos >= data_.size())
    {
      throw Exception::OutOfGrid(__FILE__, __LINE__);
    }
    return data_[pos];
  }
 
  template <class ValueType>
  BALL_INLINE
  const vector<ValueType>& TRegularData3D<ValueType>::getData() const
  {
    return data_;
  }
 
  template <typename ValueType>
  BALL_INLINE
  ValueType& TRegularData3D<ValueType>::getData
    (const typename TRegularData3D<ValueType>::IndexType& index)
  {
    size_type pos = index.x + index.y * size_.x + index.z * size_.x * size_.y;
    if (pos >= data_.size())
    {
      throw Exception::OutOfGrid(__FILE__, __LINE__);
    }
    return data_[pos];
  }
 
  template <class ValueType>
  BALL_INLINE
  const ValueType& TRegularData3D<ValueType>::getData(Position index) const
  {
    if (index >= data_.size())
    {
      throw Exception::OutOfGrid(__FILE__, __LINE__);
    }
    return data_[index];
  }
 
  template <class ValueType>
  BALL_INLINE
  ValueType& TRegularData3D<ValueType>::getData(Position index)
  {
    if (index >= data_.size())
    {
      throw Exception::OutOfGrid(__FILE__, __LINE__);
    }
    return data_[index];
  }
 
  template <class ValueType>
  BALL_INLINE
  typename TRegularData3D<ValueType>::CoordinateType TRegularData3D<ValueType>::getCoordinates
    (const typename TRegularData3D<ValueType>::IndexType& index) const
  {
    if ((index.x >= size_.x) || (index.y >= size_.y) || (index.z >= size_.z))
    {
      throw Exception::OutOfGrid(__FILE__, __LINE__);
    }
 
    if (is_orthogonal_)
    {
      CoordinateType r(origin_.x + index.x * spacing_.x,
          origin_.y + index.y * spacing_.y,
          origin_.z + index.z * spacing_.z);
      return r;
    }
    else
    {
      CoordinateType r(index.x, index.y, index.z);
      r = mapToCartesian_(r);
 
      return r;
    }
  }
 
  template <class ValueType>
  BALL_INLINE
  typename TRegularData3D<ValueType>::CoordinateType
  TRegularData3D<ValueType>::getCoordinates(Position position) const
  {
    if (position >= data_.size())
    {
      throw Exception::OutOfGrid(__FILE__, __LINE__);
    }
 
    Position x = (Position)(position %  size_.x);
    Position y = (Position)((position % (size_.x * size_.y))/ size_.x);
    Position z = (Position)(position / (size_.x * size_.y));
 
    if (is_orthogonal_)
    {
      return CoordinateType(origin_.x + (double)x * spacing_.x,
                            origin_.y + (double)y * spacing_.y,
                            origin_.z + (double)z * spacing_.z);
    }
    else
    {
      CoordinateType r(x,y,z);
      r = mapToCartesian_(r);
 
      return r;
    }
  }
 
  template <typename ValueType>
  BALL_INLINE
  void TRegularData3D<ValueType>::getEnclosingIndices
    (const typename TRegularData3D<ValueType>::CoordinateType& r,
    Position& llf, Position& rlf, Position& luf, Position& ruf,
    Position& llb, Position& rlb, Position& lub, Position& rub) const
  {
    if (!isInside(r))
    {
      throw Exception::OutOfGrid(__FILE__, __LINE__);
    }   
 
    // calculate the grid indices of the lower left front corner
    // of the enclosing box
    IndexType position;
    if (is_orthogonal_)
    {
      position.x = (Position)((r.x - origin_.x) / spacing_.x);
      position.y = (Position)((r.y - origin_.y) / spacing_.y);
      position.z = (Position)((r.z - origin_.z) / spacing_.z);
    }
    else
    {
      CoordinateType pos = mapInverse_(r);
      position.x = (Position) pos.x;  
      position.y = (Position) pos.y;  
      position.z = (Position) pos.z;  
    } 
    
    // calculate the (linear) indices of the eight
    // box corners
    llf = position.x + size_.x * position.y 
        + size_.x * size_.y * position.z;
    rlf = llf + 1;
    luf = llf + size_.x;
    ruf = luf + 1;
    llb = llf + size_.x * size_.y;
    rlb = llb + 1;
    lub = llb + size_.x;
    rub = lub + 1;
  }
 
  template <typename ValueType>
  BALL_INLINE
  void TRegularData3D<ValueType>::getEnclosingValues
    (const typename TRegularData3D<ValueType>::CoordinateType& r,
    ValueType& llf, ValueType& rlf, ValueType& luf, ValueType& ruf,
    ValueType& llb, ValueType& rlb, ValueType& lub, ValueType& rub) const
  {
    if (!isInside(r))
    {
      throw Exception::OutOfGrid(__FILE__, __LINE__);
    }   
    
    // compute the eight grid indices forming the enclosing box
    Position llf_idx, rlf_idx, luf_idx, ruf_idx, llb_idx, rlb_idx, lub_idx, rub_idx;
    getEnclosingIndices(r, llf_idx, rlf_idx, luf_idx, ruf_idx, llb_idx, rlb_idx, lub_idx, rub_idx);
        
    // retrieve the grid values
    llf = data_[llf_idx];
    rlf = data_[rlf_idx];
    luf = data_[luf_idx];
    ruf = data_[ruf_idx];
    llb = data_[llb_idx];
    rlb = data_[rlb_idx];
    lub = data_[lub_idx];
    rub = data_[rub_idx];
  }
 
  template <typename ValueType>
  BALL_INLINE
  ValueType TRegularData3D<ValueType>::getInterpolatedValue
    (const typename TRegularData3D<ValueType>::CoordinateType& r) const
  {
    if (!isInside(r))
    {
      throw Exception::OutOfGrid(__FILE__, __LINE__);
    }   
    return operator () (r);
  }
 
  template <typename ValueType>
  BALL_INLINE
  ValueType TRegularData3D<ValueType>::operator ()
    (const typename TRegularData3D<ValueType>::CoordinateType& r) const
  {
    Position x;
    Position y;   
    Position z;   
    TVector3<double> r_0;
    
    if (is_orthogonal_)
    { 
      Vector3 h(r - origin_);
 
      x = (Position)(h.x / spacing_.x);
      y = (Position)(h.y / spacing_.y);
      z = (Position)(h.z / spacing_.z);
 
      while (x >= (size_.x - 1)) x--;
      while (y >= (size_.y - 1)) y--;
      while (z >= (size_.z - 1)) z--;
 
      r_0.x = origin_.x + x*spacing_.x;
      r_0.y = origin_.y + y*spacing_.y;
      r_0.z = origin_.z + z*spacing_.z;
    }
    else
    {
      Vector3 pos = mapInverse_(r);
      x = (Position) pos.x;
      y = (Position) pos.y;
      z = (Position) pos.z;
 
      while (x >= (size_.x - 1)) x--;
      while (y >= (size_.y - 1)) y--;
      while (z >= (size_.z - 1)) z--;
 
      // This can probably be done much faster...
      Vector3 lower_pos(x,y,z);
      lower_pos = mapToCartesian_(lower_pos);
      r_0.x = lower_pos.x;
      r_0.y = lower_pos.y;
      r_0.z = lower_pos.z;
    }
    
    Position Nx = size_.x;
    Position Nxy = size_.y * Nx;
    Position l = x + Nx * y + Nxy * z;
 
    double dx = 1. - ((double)(r.x - r_0.x) / spacing_.x);
    double dy = 1. - ((double)(r.y - r_0.y) / spacing_.y);
    double dz = 1. - ((double)(r.z - r_0.z) / spacing_.z);
 
    return  data_[l] * dx * dy * dz
          + data_[l + 1] * (1. - dx) * dy * dz
          + data_[l + Nx] * dx * (1. - dy) * dz
          + data_[l + Nx + 1] * (1. - dx) * (1. - dy) * dz
          + data_[l + Nxy] * dx * dy * (1. - dz)
          + data_[l + Nxy + 1] * (1. - dx) * dy * (1. - dz)
          + data_[l + Nxy + Nx] * dx * (1. - dy) * (1. - dz)
          + data_[l + Nxy + Nx + 1] * (1. - dx) * (1. - dy) * (1. - dz);
  }
 
  template <typename ValueType>
  BALL_INLINE
  typename TRegularData3D<ValueType>::IndexType TRegularData3D<ValueType>::getClosestIndex
    (const typename TRegularData3D<ValueType>::CoordinateType& r) const
  {
    if (!isInside(r))
    {
      throw Exception::OutOfGrid(__FILE__, __LINE__);
    }
 
    static IndexType position;
 
    if (is_orthogonal_)
    {
      position.x = (Position)((r.x - origin_.x) / spacing_.x + 0.5);
      position.y = (Position)((r.y - origin_.y) / spacing_.y + 0.5);
      position.z = (Position)((r.z - origin_.z) / spacing_.z + 0.5);
    }
    else
    {
      Vector3 pos = mapInverse_(r);
      position.x = (Position) Maths::round(pos.x);
      position.y = (Position) Maths::round(pos.y);
      position.z = (Position) Maths::round(pos.z);
    }
      
    return position;
  }
 
  template <typename ValueType>
  BALL_INLINE
  typename TRegularData3D<ValueType>::IndexType  TRegularData3D<ValueType>::getLowerIndex
    (const typename TRegularData3D<ValueType>::CoordinateType& r) const
  {
    if (!isInside(r))
    {
      throw Exception::OutOfGrid(__FILE__, __LINE__);
    }
 
    static IndexType position;
    if (is_orthogonal_)
    {
      position.x = (Position)((r.x - origin_.x) / spacing_.x);
      position.y = (Position)((r.y - origin_.y) / spacing_.y);
      position.z = (Position)((r.z - origin_.z) / spacing_.z);
    }
    else
    {
      Vector3 pos = mapInverse_(r);
      position.x = (Position)pos.x;
      position.y = (Position)pos.y;
      position.z = (Position)pos.z;
    }
 
    return position;
  }
 
  template <typename ValueType>
  BALL_INLINE
  const ValueType& TRegularData3D<ValueType>::getClosestValue
    (const typename TRegularData3D<ValueType>::CoordinateType& r) const
  {
    if (!isInside(r))
    {
      throw Exception::OutOfGrid(__FILE__, __LINE__);
    }
 
    static IndexType position;
 
    if (is_orthogonal_)
    {
      position.x = (Position)((r.x - origin_.x) / spacing_.x + 0.5);
      position.y = (Position)((r.y - origin_.y) / spacing_.y + 0.5);
      position.z = (Position)((r.z - origin_.z) / spacing_.z + 0.5);
    }
    else
    {
      static Vector3 pos = mapInverse_(r);
      position.x = (Position) Maths::round(pos.x);
      position.y = (Position) Maths::round(pos.y);
      position.z = (Position) Maths::round(pos.z);
    }
 
    return operator [] (position);
  }
 
  template <typename ValueType>
  BALL_INLINE
  ValueType& TRegularData3D<ValueType>::getClosestValue
    (const typename TRegularData3D<ValueType>::CoordinateType& r)
  {
    if (!isInside(r))
    {
      throw Exception::OutOfGrid(__FILE__, __LINE__);
    }
 
    static IndexType position;
 
    if (is_orthogonal_)
    {
      position.x = (Position)((r.x - origin_.x) / spacing_.x + 0.5);
      position.y = (Position)((r.y - origin_.y) / spacing_.y + 0.5);
      position.z = (Position)((r.z - origin_.z) / spacing_.z + 0.5);
    }
    else
    {
      static Vector3 pos = mapInverse_(r);
      position.x = (Position) Maths::round(pos.x);
      position.y = (Position) Maths::round(pos.y);
      position.z = (Position) Maths::round(pos.z);
    }
 
 
    return operator [] (position);
  }
 
  template <typename ValueType>
  BALL_INLINE
  ValueType TRegularData3D<ValueType>::calculateMean() const
  {
    Position data_points  = (size_.x * size_.y * size_.z);
    ValueType mean = 0;
    for (Position i = 0; i < data_points; i++)
    {
      mean += data_[i];
    }
    mean /= data_points;
    return mean;
  }
 
  template <typename ValueType>
  BALL_INLINE
  ValueType TRegularData3D<ValueType>::calculateSD() const
  {
    Position data_points  = (size_.x * size_.y * size_.z);
    ValueType stddev = 0;
    ValueType mean = this->calculateMean();
    for (Position i = 0; i < data_points; i++)
    {
      stddev += (pow(data_[i]-mean,2));
    }
    stddev /= (data_points-1);
    stddev = sqrt(stddev);
    return stddev;
  }
  
  template <typename ValueType>
  void TRegularData3D<ValueType>::clear()
  {
    data_.resize(0);
 
    origin_.set(0.0);
    dimension_.set(0.0);
    size_.x = 0;
    size_.y = 0;
    size_.z = 0;
    spacing_.set(1.0);    
    is_orthogonal_ = true;
  }
 
  
  template <typename ValueType> 
  bool TRegularData3D<ValueType>::operator == (const TRegularData3D<ValueType>& grid) const 
  {
    return ((origin_ == grid.origin_)
            && (dimension_ == grid.dimension_)
            && (size_.x == grid.size_.x)
            && (size_.y == grid.size_.y)
            && (size_.z == grid.size_.z)
            && (data_ == grid.data_)
            && (is_orthogonal_ == grid.is_orthogonal_));
  } 
 
  template <typename ValueType>
  void TRegularData3D<ValueType>::binaryWrite(const String& filename) const
  {
    File outfile(filename, std::ios::out|std::ios::binary);
    if (!outfile.isValid()) throw Exception::FileNotFound(__FILE__, __LINE__, filename);
    
    BinaryFileAdaptor< BlockValueType > adapt_block;
    BinaryFileAdaptor< ValueType >       adapt_single;
    
    // TODO: check for endiannes and swap bytes accordingly
 
    // write all information we need to recreate the grid
    BinaryFileAdaptor<CoordinateType> adapt_coordinate;
    BinaryFileAdaptor<Size>           adapt_size;
 
    adapt_size.setData(data_.size());
    outfile << adapt_size;
    
    adapt_coordinate.setData(origin_);
    outfile << adapt_coordinate;
 
    adapt_coordinate.setData(dimension_);
    outfile << adapt_coordinate;
 
    adapt_coordinate.setData(spacing_);
    outfile << adapt_coordinate;
 
    BinaryFileAdaptor<IndexType> adapt_index;
    adapt_index.setData(size_);
    outfile << adapt_index;
  
    // we slide a window of size 1024 over our data
    Index window_pos = 0;
    
    while ( ((int)data_.size() - (1024 + window_pos)) >= 0 )
    {
      adapt_block.setData(* (BlockValueType*)&(data_[window_pos]));
      outfile << adapt_block;
      window_pos+=1024;
    }
 
    // now we have to write the remaining data one by one
    for (Size i=window_pos; i<data_.size(); i++)
    {
      adapt_single.setData(data_[i]);
      outfile << adapt_single;
    }
 
    // that's it. I hope...
    outfile.close();
  }
 
  template <typename ValueType>
  void TRegularData3D<ValueType>::binaryRead(const String& filename)
  {
    File infile(filename, std::ios::in|std::ios::binary);
    if (!infile.isValid()) throw Exception::FileNotFound(__FILE__, __LINE__, filename);
    
    BinaryFileAdaptor< BlockValueType > adapt_block;
    BinaryFileAdaptor< ValueType >      adapt_single;
    
    // TODO: check for endiannes and swap bytes accordingly
 
    // read all information we need to recreate the grid
    BinaryFileAdaptor<CoordinateType> adapt_coordinate;
    BinaryFileAdaptor<Size>           adapt_size;
 
    infile >> adapt_size;
    Size new_size = adapt_size.getData();
  
    infile >> adapt_coordinate;
    origin_ = adapt_coordinate.getData();
 
    infile >> adapt_coordinate;
    dimension_ = adapt_coordinate.getData();
 
    infile >> adapt_coordinate;
    spacing_ = adapt_coordinate.getData();
 
    BinaryFileAdaptor<IndexType> adapt_index;
    infile >> adapt_index;
    size_ =  adapt_index.getData();
  
    data_.resize(new_size);
 
    // we slide a window of size 1024 over our data
    Index window_pos = 0;
    
    while ( ((int)data_.size() - (1024 + window_pos)) >= 0 )
    {
      infile >> adapt_block;
      *(BlockValueType*)(&(data_[window_pos])) = adapt_block.getData();
      /*
      for (Size i=0; i<1024; i++)
      {
        data_[i+window_pos] = adapt_block.getData().bt[i];
      }
      */
      window_pos+=1024;
    }
 
    // now we have to read the remaining data one by one
    for (Size i=window_pos; i<data_.size(); i++)
    {
      infile >> adapt_single;
      data_[i] = adapt_single.getData();
    }
 
    // that's it. I hope...
    infile.close();
  }


  template <typename ValueType>
  std::ostream& operator << (std::ostream& os, const TRegularData3D<ValueType>& grid)
  {
    // Write the grid origin, dimension, and number of grid points
    os << grid.getOrigin().x << " " << grid.getOrigin().y << " " << grid.getOrigin().z
       << std::endl
       << grid.getOrigin().x + grid.getDimension().x << " " 
       << grid.getOrigin().y + grid.getDimension().y << " " 
       << grid.getOrigin().z + grid.getDimension().z
       << std::endl
       << grid.getSize().x - 1 << " " << grid.getSize().y - 1 << " " << grid.getSize().z - 1 
       << std::endl;
 
    // Write the array contents.
    std::copy(grid.begin(), grid.end(), std::ostream_iterator<ValueType>(os, "\n"));
 
    return os;
  }

  template <typename ValueType>
  std::istream& operator >> (std::istream& is, TRegularData3D<ValueType>& grid)
  {
    typename TRegularData3D<ValueType>::CoordinateType origin;
    typename TRegularData3D<ValueType>::CoordinateType dimension;
    typename TRegularData3D<ValueType>::IndexType size;
 
    is >> origin.x >> origin.y >> origin.z;
    is >> dimension.x >> dimension.y >> dimension.z;
    is >> size.x >> size.y >> size.z;
 
    dimension -= origin;
    size.x++;
    size.y++;
    size.z++;
 
    grid.resize(size);
    grid.setOrigin(origin);
    grid.setDimension(dimension);
    std::copy(std::istream_iterator<ValueType>(is), std::istream_iterator<ValueType>(), grid.begin());
 
    return is;
  }

  
 } // namespace BALL
 
#endif // BALL_DATATYPE_REGULARDATA3D_H