Subversion Repositories public iLand

/********************************************************************************************

**    iLand - an individual based forest landscape and disturbance model

**    http://iland.boku.ac.at

**    Copyright (C) 2009-  Werner Rammer, Rupert Seidl

**

**    This program is free software: you can redistribute it and/or modify

**    it under the terms of the GNU General Public License as published by

**    the Free Software Foundation, either version 3 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 General Public License for more details.

**

**    You should have received a copy of the GNU General Public License

**    along with this program.  If not, see <http://www.gnu.org/licenses/>.

********************************************************************************************/

#ifndef GRID_H

#define GRID_H

#include <QtCore>

#include <stdexcept>

#include <limits>

#include <cstring>

#include "global.h"

/** Grid class (template).

@ingroup tools

Orientation

The grid is oriented as typically coordinates on the northern hemisphere: higher y-values -> north, higher x-values-> east.

The projection is reversed for drawing on screen (Viewport).

          N

  (0/2) (1/2) (2/2)

W (0/1) (1/1) (2/1)  E

  (0/0) (1/0) (2/0)

          S

*/

template <class T>

class Grid {

public:

    Grid();

    Grid(int cellsize, int sizex, int sizey) { mData=0; setup(cellsize, sizex, sizey); }

    /// create from a metric rect

    Grid(const QRectF rect_metric, const float cellsize) { mData=0; setup(rect_metric,cellsize); }

    // copy ctor

    Grid(const Grid<T>& toCopy);

    ~Grid() { clear(); }

    void clear() { if (mData) delete[] mData; mData=0; }

    bool setup(const float cellsize, const int sizex, const int sizey);

    bool setup(const QRectF& rect, const double cellsize);

    bool setup(const Grid<T>& source) { clear();  mRect = source.mRect; return setup(source.mRect, source.mCellsize); }

    void initialize(const T& value) {for( T *p = begin();p!=end(); ++p) *p=value; }

    void wipe(); ///< write 0-bytes with memcpy to the whole area

    void wipe(const T value); ///< overwrite the whole area with "value" size of T must be the size of "int" ERRORNOUS!!!

    /// copies the content of the source grid to this grid.

    /// no operation, if the grids are not of the same size.

    void copy(const Grid<T> source) { if (source.count()==count()) memcpy(mData, source.mData, count()*sizeof(T)); }

    /// create a double grid (same size as this grid) and convert this grid to double values.

    /// NOTE: caller is responsible for freeing memory!

    Grid<double> *toDouble() const;

    // get the number of cells in x and y direction

    int sizeX() const { return mSizeX; }

    int sizeY() const { return mSizeY; }

    // get the size of the grid in metric coordinates (x and y direction)

    float metricSizeX() const { return mSizeX*mCellsize; }

    float metricSizeY() const { return mSizeY*mCellsize; }

    /// get the metric rectangle of the grid

    QRectF metricRect() const { return mRect; }

    /// get the rectangle of the grid in terms of indices

    QRect rectangle() const { return QRect(QPoint(0,0), QPoint(sizeX(), sizeY())); }

    /// get the length of one pixel of the grid

    float cellsize() const { return mCellsize; }

    int count() const { return mCount; } ///< returns the number of elements of the grid

    bool isEmpty() const { return mData==NULL; } ///< returns false if the grid was not setup

    // operations

    // query

    /// access (const) with index variables. use int.

    inline const T& operator()(const int ix, const int iy) const { return constValueAtIndex(ix, iy); }

    /// access (const) using metric variables. use float.

    inline const T& operator()(const float x, const float y) const { return constValueAt(x, y); }

    /// access value of grid with a QPoint

    inline const T& operator[](const QPoint &p) const { return constValueAtIndex(p); }

    /// use the square brackets to access by index

    inline T& operator[](const int idx) const { return mData[idx]; }

    /// use the square bracket to access by QPointF

    inline T& operator[] (const QPointF &p) { return valueAt(p); }

    inline T& valueAtIndex(const QPoint& pos) {return valueAtIndex(pos.x(), pos.y());}  ///< value at position defined by a QPoint defining the two indices (x,y)

    T& valueAtIndex(const int ix, const int iy) { return mData[iy*mSizeX + ix];  } ///< const value at position defined by indices (x,y)

    T& valueAtIndex(const int index) {return mData[index]; } ///< get a ref ot value at (one-dimensional) index 'index'.

    /// value at position defined by a (integer) QPoint

    inline const T& constValueAtIndex(const QPoint& pos) const {return constValueAtIndex(pos.x(), pos.y()); }

    /// value at position defined by a pair of integer coordinates

    inline const T& constValueAtIndex(const int ix, const int iy) const { return mData[iy*mSizeX + ix];  }

    /// value at position defined by the index within the grid

    const T& constValueAtIndex(const int index) const {return mData[index]; } ///< get a ref ot value at (one-dimensional) index 'index'.

    T& valueAt(const QPointF& posf); ///< value at position defined by metric coordinates (QPointF)

    const T& constValueAt(const QPointF& posf) const; ///< value at position defined by metric coordinates (QPointF)

    T& valueAt(const float x, const float y); ///< value at position defined by metric coordinates (x,y)

    const T& constValueAt(const float x, const float y) const; ///< value at position defined by metric coordinates (x,y)

    bool coordValid(const float x, const float y) const { return x>=mRect.left() && x<mRect.right()  && y>=mRect.top() && y<mRect.bottom(); }

    bool coordValid(const QPointF &pos) const { return coordValid(pos.x(), pos.y()); }

    QPoint indexAt(const QPointF& pos) const { return QPoint(int((pos.x()-mRect.left()) / mCellsize),  int((pos.y()-mRect.top())/mCellsize)); } ///< get index of value at position pos (metric)

    /// get index (x/y) of the (linear) index 'index' (0..count-1)

    QPoint indexOf(const int index) const {return QPoint(index % mSizeX,  index / mSizeX); }

    bool isIndexValid(const QPoint& pos) const { return (pos.x()>=0 && pos.x()<mSizeX && pos.y()>=0 && pos.y()<mSizeY); } ///< return true, if position is within the grid

    bool isIndexValid(const int x, const int y) const {return (x>=0 && x<mSizeX && y>=0 && y<mSizeY); } ///< return true, if index is within the grid

    /// returns the index of an aligned grid (with the same size and matching origin) with the double cell size (e.g. to scale from a 10m grid to a 20m grid)

    int index2(int idx) const {return ((idx/mSizeX)/2)*mSizeX/2 + (idx%mSizeX)/2; }

    /// returns the index of an aligned grid (the same size) with the 5 times bigger cells (e.g. to scale from a 2m grid to a 10m grid)

    int index5(int idx) const {return ((idx/mSizeX)/5)*mSizeX/5 + (idx%mSizeX)/5; }

    /// force @param pos to contain valid indices with respect to this grid.

    void validate(QPoint &pos) const{ pos.setX( qMax(qMin(pos.x(), mSizeX-1), 0) );  pos.setY( qMax(qMin(pos.y(), mSizeY-1), 0) );} ///< ensure that "pos" is a valid key. if out of range, pos is set to minimum/maximum values.

    /// get the (metric) centerpoint of cell with index @p pos

    QPointF cellCenterPoint(const QPoint &pos) const { return QPointF( (pos.x()+0.5)*mCellsize+mRect.left(), (pos.y()+0.5)*mCellsize + mRect.top());} ///< get metric coordinates of the cells center

    /// get the metric cell center point of the cell given by index 'index'

    QPointF cellCenterPoint(const int &index) const { QPoint pos=indexOf(index); return QPointF( (pos.x()+0.5)*mCellsize+mRect.left(), (pos.y()+0.5)*mCellsize + mRect.top());}

    /// get the metric rectangle of the cell with index @pos

    QRectF cellRect(const QPoint &pos) const { QRectF r( QPointF(mRect.left() + mCellsize*pos.x(), mRect.top() + pos.y()*mCellsize),

                                                   QSizeF(mCellsize, mCellsize)); return r; } ///< return coordinates of rect given by @param pos.

    inline  T* begin() const { return mData; } ///< get "iterator" pointer

    inline  T* end() const { return mEnd; } ///< get iterator end-pointer

    inline QPoint indexOf(const T* element) const; ///< retrieve index (x/y) of the pointer element. returns -1/-1 if element is not valid.

    // special queries

    T max() const; ///< retrieve the maximum value of a grid

    T sum() const; ///< retrieve the sum of the grid

    T avg() const; ///< retrieve the average value of a grid

    // modifying operations

    void add(const T& summand);

    void multiply(const T& factor);

    /// limit each cell value to (including) min_value and (including) max_value

    void limit(const T min_value, const T max_value);

    /// creates a grid with lower resolution and averaged cell values.

    /// @param factor factor by which grid size is reduced (e.g. 3 -> 3x3=9 pixels are averaged to 1 result pixel)

    /// @param offsetx, offsety: start averaging with an offset from 0/0 (e.g.: x=1, y=2, factor=3: -> 1/2-3/4 -> 0/0)

    /// @return Grid with size sizeX()/factor x sizeY()/factor

    Grid<T> averaged(const int factor, const int offsetx=0, const int offsety=0) const;

    /// normalized returns a normalized grid, in a way that the sum()  = @param targetvalue.

    /// if the grid is empty or the sum is 0, no modifications are performed.

    Grid<T> normalized(const T targetvalue) const;

    T* ptr(int x, int y) { return &(mData[y*mSizeX + x]); } ///< get a pointer to the element indexed by "x" and "y"

    inline double distance(const QPoint &p1, const QPoint &p2); ///< distance (metric) between p1 and p2

    const QPoint randomPosition() const; ///< returns a (valid) random position within the grid

private:

    T* mData;

    T* mEnd; ///< pointer to 1 element behind the last

    QRectF mRect;

    float mCellsize; ///< size of a cell in meter

    int mSizeX; ///< count of cells in x-direction

    int mSizeY; ///< count of cells in y-direction

    int mCount; ///< total number of cells in the grid

};

typedef Grid<float> FloatGrid;

enum GridViewType { GridViewRainbow=0, GridViewRainbowReverse=1, GridViewGray=2, GridViewGrayReverse=3, GridViewHeat=4,

                    GridViewGreens=5, GridViewReds=6, GridViewBlues=7,

                    GridViewBrewerDiv=10, GridViewBrewerQual=11, GridViewTerrain=12, GridViewCustom=14  };

/** @class GridRunner is a helper class to iterate over a rectangular fraction of a grid

*/

template <class T>

class GridRunner {

public:

    // constructors with a QRectF (metric coordinates)

    GridRunner(Grid<T> &target_grid, const QRectF &rectangle) {setup(&target_grid, rectangle);}

    GridRunner(const Grid<T> &target_grid, const QRectF &rectangle) {setup(&target_grid, rectangle);}

    GridRunner(Grid<T> *target_grid, const QRectF &rectangle) {setup(target_grid, rectangle);}

    // constructors with a QRect (indices within the grid)

    GridRunner(Grid<T> &target_grid, const QRect &rectangle) {setup(&target_grid, rectangle);}

    GridRunner(const Grid<T> &target_grid, const QRect &rectangle) {setup(&target_grid, rectangle);}

    GridRunner(Grid<T> *target_grid, const QRect &rectangle) {setup(target_grid, rectangle);}

    GridRunner(Grid<T> *target_grid) {setup(target_grid, target_grid->rectangle()); }

    T* next(); ///< to to next element, return NULL if finished

    T* current() const { return mCurrent; }

    bool isValid() const {return mCurrent>=mFirst && mCurrent<=mLast; }

    /// return the (index) - coordinates of the current position in the grid

    QPoint currentIndex() const { return mGrid->indexOf(mCurrent); }

    /// return the coordinates of the cell center point of the current position in the grid.

    QPointF currentCoord() const {return mGrid->cellCenterPoint(mGrid->indexOf(mCurrent));}

    void reset() { mCurrent = mFirst-1; mCurrentCol = -1; }

    /// set the internal pointer to the pixel at index 'new_index'. The index is relative to the base grid!

    void setPosition(QPoint new_index) { if (mGrid->isIndexValid(new_index)) mCurrent = const_cast<Grid<T> *>(mGrid)->ptr(new_index.x(), new_index.y()); else mCurrent=0; }

    // helpers

    /// fill array with pointers to neighbors (north, east, west, south)

    /// or Null-pointers if out of range.

    /// the target array (rArray) is not checked and must be valid!

    void neighbors4(T** rArray);

    void neighbors8(T** rArray);

private:

    void setup(const Grid<T> *target_grid, const QRectF &rectangle);

    void setup(const Grid<T> *target_grid, const QRect &rectangle);

    const Grid<T> *mGrid;

    T* mFirst; // points to the first element of the grid

    T* mLast; // points to the last element of the grid

    T* mCurrent;

    size_t mLineLength;

    size_t mCols;

    int mCurrentCol;

};

/** @class Vector3D is a simple 3d vector.

  QVector3D (from Qt) is in QtGui so we needed a replacement.

*/

class Vector3D

{

 public:

    Vector3D(): mX(0.), mY(0.), mZ(0.) {}

    Vector3D(const double x, const double y, const double z): mX(x), mY(y), mZ(z) {}

    double x() const { return mX; } ///< get x-coordinate

    double y() const { return mY; } ///< get y-coordinate

    double z() const { return mZ; } ///< get z-coordinate

    // set variables

    void setX(const double x) { mX=x; } ///< set value of the x-coordinate

    void setY(const double y) { mY=y; } ///< set value of the y-coordinate

    void setZ(const double z) { mZ=z; } ///< set value of the z-coordinate

private:

    double mX;

    double mY;

    double mZ;

};

// copy constructor

template <class T>

Grid<T>::Grid(const Grid<T>& toCopy)

{

    mData = 0;

    mRect = toCopy.mRect;

    setup(toCopy.metricRect(), toCopy.cellsize());

    //setup(toCopy.cellsize(), toCopy.sizeX(), toCopy.sizeY());

    const T* end = toCopy.end();

    T* ptr = begin();

    for (T* i= toCopy.begin(); i!=end; ++i, ++ptr)

       *ptr = *i;

}

// normalize function

template <class T>

Grid<T> Grid<T>::normalized(const T targetvalue) const

{

    Grid<T> target(*this);

    T total = sum();

    T multiplier;

    if (total)

        multiplier = targetvalue / total;

    else

        return target;

    for (T* p=target.begin();p!=target.end();++p)

        *p *= multiplier;

    return target;

}

template <class T>

Grid<T> Grid<T>::averaged(const int factor, const int offsetx, const int offsety) const

{

    Grid<T> target;

    target.setup(cellsize()*factor, sizeX()/factor, sizeY()/factor);

    int x,y;

    T sum=0;

    target.initialize(sum);

    // sum over array of 2x2, 3x3, 4x4, ...

    for (x=offsetx;x<mSizeX;x++)

        for (y=offsety;y<mSizeY;y++) {

            target.valueAtIndex((x-offsetx)/factor, (y-offsety)/factor) += constValueAtIndex(x,y);

        }

    // divide

    double fsquare = factor*factor;

    for (T* p=target.begin();p!=target.end();++p)

        *p /= fsquare;

    return target;

}

template <class T>

T&  Grid<T>::valueAt(const float x, const float y)

{

    return valueAtIndex( indexAt(QPointF(x,y)) );

}

template <class T>

const T&  Grid<T>::constValueAt(const float x, const float y) const

{

    return constValueAtIndex( indexAt(QPointF(x,y)) );

}

template <class T>

T&  Grid<T>::valueAt(const QPointF& posf)

{

    return valueAtIndex( indexAt(posf) );

}

template <class T>

const T&  Grid<T>::constValueAt(const QPointF& posf) const

{

    return constValueAtIndex( indexAt(posf) );

}

template <class T>

Grid<T>::Grid()

{

    mData = 0; mCellsize=0.f;

    mEnd = 0;

    mSizeX=0; mSizeY=0; mCount=0;

}

template <class T>

bool Grid<T>::setup(const float cellsize, const int sizex, const int sizey)

{

    mSizeX=sizex; mSizeY=sizey;

    if (mRect.isNull()) // only set rect if not set before (e.g. by call to setup(QRectF, double))

        mRect.setCoords(0., 0., cellsize*sizex, cellsize*sizey);

    if (mData) {

        // test if we can re-use the allocated memory.

        if (mSizeX*mSizeY > mCount || mCellsize != cellsize) {

            // we cannot re-use the memory - create new data

            delete[] mData; mData=NULL;

        }

    }

    mCellsize=cellsize;

    mCount = mSizeX*mSizeY;

    if (mCount==0)

        return false;

    if (mData==NULL)

        mData = new T[mCount];

    mEnd = &(mData[mCount]);

    return true;

}

template <class T>

bool Grid<T>::setup(const QRectF& rect, const double cellsize)

{

    mRect = rect;

    int dx = int(rect.width()/cellsize);

    if (mRect.left()+cellsize*dx<rect.right())

        dx++;

    int dy = int(rect.height()/cellsize);

    if (mRect.top()+cellsize*dy<rect.bottom())

        dy++;

    return setup(cellsize, dx, dy);

}

/** retrieve from the index from an element reversely from a pointer to that element.

    The internal memory layout is (for dimx=6, dimy=3):

6  7  8  9  10 11

12 13 14 15 16 17

Note: north and south are reversed, thus the item with index 0 is located in the south-western edge of the grid! */

template <class T> inline

QPoint Grid<T>::indexOf(const T* element) const

{

//    QPoint result(-1,-1);

    if (element==NULL || element<mData || element>=end())

        return QPoint(-1, -1);

    int idx = element - mData;

    return QPoint(idx % mSizeX,  idx / mSizeX);

//    result.setX( idx % mSizeX);

//    result.setY( idx / mSizeX);

//    return result;

}

template <class T>

T  Grid<T>::max() const

{

    T maxv = -std::numeric_limits<T>::max();

    T* p;

    T* pend = end();

    for (p=begin(); p!=pend;++p)

       maxv = std::max(maxv, *p);

    return maxv;

}

template <class T>

T  Grid<T>::sum() const

{

    T* pend = end();

    T total = 0;

    for (T *p=begin(); p!=pend;++p)

       total += *p;

    return total;

}

template <class T>

T  Grid<T>::avg() const

{

    if (count())

        return sum() / T(count());

    else return 0;

}

template <class T>

void Grid<T>::add(const T& summand)

{

    T* pend = end();

    for (T *p=begin(); p!=pend;*p+=summand,++p)

       ;

}

template <class T>

void Grid<T>::multiply(const T& factor)

{

    T* pend = end();

    for (T *p=begin(); p!=pend;*p*=factor,++p)

        ;

}

template <class T>

void Grid<T>::limit(const T min_value, const T max_value)

{

    T* pend = end();

    for (T *p=begin(); p!=pend;++p)

        *p = *p < min_value ? min_value : (*p>max_value? max_value : *p);

}

template <class T>

void  Grid<T>::wipe()

{

    memset(mData, 0, mCount*sizeof(T));

}

template <class T>

void  Grid<T>::wipe(const T value)

{

    /* this does not work properly !!! */

    if (sizeof(T)==sizeof(int)) {

        float temp = value;

        float *pf = &temp;

        memset(mData, *((int*)pf), mCount*sizeof(T));

    } else

        initialize(value);

}

template <class T>

Grid<double> *Grid<T>::toDouble() const

{

    Grid<double> *g = new Grid<double>();

    g->setup(metricRect(), cellsize());

    if (g->isEmpty())

        return g;

    double *dp = g->begin();

    for (T *p=begin(); p!=end(); ++p, ++dp)

        *dp = *p;

    return g;

}

template <class T>

double Grid<T>::distance(const QPoint &p1, const QPoint &p2)

{

    QPointF fp1=cellCenterPoint(p1);

    QPointF fp2=cellCenterPoint(p2);

    double distance = sqrt( (fp1.x()-fp2.x())*(fp1.x()-fp2.x()) + (fp1.y()-fp2.y())*(fp1.y()-fp2.y()));

    return distance;

}

template <class T>

const QPoint Grid<T>::randomPosition() const

{

    return QPoint(irandom(0,mSizeX-1), irandom(0, mSizeY-1));

}

////////////////////////////////////////////////////////////

// grid runner

////////////////////////////////////////////////////////////

template <class T>

void GridRunner<T>::setup(const Grid<T> *target_grid, const QRect &rectangle)

{

    QPoint upper_left = rectangle.topLeft();

    // due to the strange behavior of QRect::bottom() and right():

    QPoint lower_right = rectangle.bottomRight();

    mCurrent = const_cast<Grid<T> *>(target_grid)->ptr(upper_left.x(), upper_left.y());

    mFirst = mCurrent;

    mCurrent--; // point to first element -1

    mLast = const_cast<Grid<T> *>(target_grid)->ptr(lower_right.x()-1, lower_right.y()-1);

    mCols = lower_right.x() - upper_left.x(); //

    mLineLength =  target_grid->sizeX() - mCols;

    mCurrentCol = -1;

    mGrid = target_grid;

//    qDebug() << "GridRunner: rectangle:" << rectangle

//             << "upper_left:" << target_grid.cellCenterPoint(target_grid.indexOf(mCurrent))

//             << "lower_right:" << target_grid.cellCenterPoint(target_grid.indexOf(mLast));

}

template <class T>

void GridRunner<T>::setup(const Grid<T> *target_grid, const QRectF &rectangle_metric)

{

    QRect rect(target_grid->indexAt(rectangle_metric.topLeft()),

               target_grid->indexAt(rectangle_metric.bottomRight()) );

    setup (target_grid, rect);

}

template <class T>

T* GridRunner<T>::next()

{

    if (mCurrent>mLast)

        return NULL;

    mCurrent++;

    mCurrentCol++;

    if (mCurrentCol >= int(mCols)) {

        mCurrent += mLineLength; // skip to next line

        mCurrentCol = 0;

    }

    if (mCurrent>mLast)

        return NULL;

    else

        return mCurrent;

}

template <class T>

/// get pointers the the 4-neighborhood

/// north, east, west, south

/// 0-pointers are returned for edge pixels.

void GridRunner<T>::neighbors4(T** rArray)

{

    // north:

    rArray[0] = mCurrent + mCols + mLineLength > mLast?0: mCurrent + mCols + mLineLength;

    // south:

    rArray[3] = mCurrent - (mCols + mLineLength) < mFirst?0: mCurrent -  (mCols + mLineLength);

    // east / west

    rArray[1] = mCurrentCol<int(mCols)? mCurrent + 1 : 0;

    rArray[2] = mCurrentCol>0? mCurrent-1 : 0;

}

/// get pointers to the 8-neighbor-hood

/// north/east/west/south/NE/NW/SE/SW

/// 0-pointers are returned for edge pixels.

template <class T>

void GridRunner<T>::neighbors8(T** rArray)

{

    neighbors4(rArray);

    // north-east

    rArray[4] = rArray[0] && rArray[1]? rArray[0]+1: 0;

    // north-west

    rArray[5] = rArray[0] && rArray[2]? rArray[0]-1: 0;

    // south-east

    rArray[6] = rArray[3] && rArray[1]? rArray[3]+1: 0;

    // south-west

    rArray[7] = rArray[3] && rArray[2]? rArray[3]-1: 0;

}

////////////////////////////////////////////////////////////

// global functions

////////////////////////////////////////////////////////////

/// dumps a FloatGrid to a String.

/// rows will be y-lines, columns x-values. (see grid.cpp)

QString gridToString(const FloatGrid &grid, const QChar sep=QChar(';'), const int newline_after=-1);

/// creates and return a QImage from Grid-Data.

/// @param black_white true: max_value = white, min_value = black, false: color-mode: uses a HSV-color model from blue (min_value) to red (max_value), default: color mode (false)

/// @param min_value, max_value min/max bounds for color calcuations. values outside bounds are limited to these values. defaults: min=0, max=1

/// @param reverse if true, color ramps are inversed (to: min_value = white (black and white mode) or red (color mode). default = false.

/// @return a QImage with the Grids size of pixels. Pixel coordinates relate to the index values of the grid.

QImage gridToImage(const FloatGrid &grid,

                   bool black_white=false,

                   double min_value=0., double max_value=1.,

                   bool reverse=false);

/** load into 'rGrid' the content of the image pointed at by 'fileName'.

    Pixels are converted to grey-scale and then transformend to a value ranging from 0..1 (black..white).

  */

bool loadGridFromImage(const QString &fileName, FloatGrid &rGrid);

/// template version for non-float grids (see also version for FloatGrid)

/// @param sep string separator

/// @param newline_after if <>-1 a newline is added after every 'newline_after' data values

template <class T>

        QString gridToString(const Grid<T> &grid, const QChar sep=QChar(';'), const int newline_after=-1)

{

    QString res;

    QTextStream ts(&res);

    int newl_counter = newline_after;

    for (int y=grid.sizeY()-1;y>=0;--y){

        for (int x=0;x<grid.sizeX();x++){

            ts << grid.constValueAtIndex(x,y) << sep;

            if (--newl_counter==0) {

                ts << "\r\n";

                newl_counter = newline_after;

            }

        }

        ts << "\r\n";

    }

    return res;

}

/// template version for non-float grids (see also version for FloatGrid)

/// @param valueFunction pointer to a function with the signature: QString func(const T&) : this should return a QString

/// @param sep string separator

/// @param newline_after if <>-1 a newline is added after every 'newline_after' data values

template <class T>

        QString gridToString(const Grid<T> &grid, QString (*valueFunction)(const T& value), const QChar sep=QChar(';'), const int newline_after=-1 )

        {

            QString res;

            QTextStream ts(&res);

            int newl_counter = newline_after;

            for (int y=grid.sizeY()-1;y>=0;--y){

                for (int x=0;x<grid.sizeX();x++){

                    ts << (*valueFunction)(grid.constValueAtIndex(x,y)) << sep;

                    if (--newl_counter==0) {

                        ts << "\r\n";

                        newl_counter = newline_after;

                    }

                }

                ts << "\r\n";

            }

            return res;

        }

void modelToWorld(const Vector3D &From, Vector3D &To);