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2.1 Basic usage

MathGL library can be used by several manners. Each has positive and negative sides:

MathGL drawing can be created not only by object oriented languages (like, C++ or Python), but also by pure C or Fortran-like languages. The usage of last one is mostly identical to usage of classes (except the different function names). But there are some differences. C functions must have argument HMGL (for graphics) and/or HMDT (for data arrays) which specifies the object for drawing or manipulating (changing). Fortran users may regard these variables as integer. So, firstly the user has to create this object by function mgl_create_*() and has to delete it after the using by function mgl_delete_*().

Let me consider the aforesaid in more detail.


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2.1.1 Using MathGL window

The “interactive” way of drawing in MathGL consists in window creation with help of class mglWindow or mglGLUT (see Widget classes) and the following drawing in this window. There is a corresponding code:

#include <mgl2/window.h>
int sample(mglGraph *gr)
{
  gr->Rotate(60,40);
  gr->Box();
  return 0;
}
//-----------------------------------------------------
int main(int argc,char **argv)
{
  mglWindow gr(sample,"MathGL examples");
  return gr.Run();
}

Here callback function sample is defined. This function does all drawing. Other function main is entry point function for console program. For compilation, just execute the command

gcc test.cpp -lmgl-wnd -lmgl

Alternatively you can create yours own class inherited from class mglDraw and re-implement the function Draw() in it:

#include <mgl2/window.h>
class Foo : public mglDraw
{
public:
  int Draw(mglGraph *gr);
};
//-----------------------------------------------------
int Foo::Draw(mglGraph *gr)
{
  gr->Rotate(60,40);
  gr->Box();
  return 0;
}
//-----------------------------------------------------
int main(int argc,char **argv)
{
  Foo foo;
  mglWindow gr(&foo,"MathGL examples");
  return gr.Run();
}

Or use pure C-functions:

#include <mgl2/mgl_cf.h>
int sample(HMGL gr, void *)
{
  mgl_rotate(gr,60,40,0);
  mgl_box(gr);
}
int main(int argc,char **argv)
{
  HMGL gr;
  gr = mgl_create_graph_qt(sample,"MathGL examples",0,0);
  return mgl_qt_run();
/* generally I should call mgl_delete_graph() here,
 * but I omit it in main() function. */
}

The similar code can be written for mglGLUT window (function sample() is the same):

#include <mgl2/glut.h>
int main(int argc,char **argv)
{
  mglGLUT gr(sample,"MathGL examples");
  return 0;
}

The rotation, shift, zooming, switching on/off transparency and lighting can be done with help of tool-buttons (for mglWindow) or by hot-keys: ‘a’, ‘d’, ‘w’, ‘s’ for plot rotation, ‘r’ and ‘f’ switching on/off transparency and lighting. Press ‘x’ for exit (or closing the window).

In this example function sample rotates axes (Rotate(), see section Subplots and rotation) and draws the bounding box (Box()). Drawing is placed in separate function since it will be used on demand when window canvas needs to be redrawn.


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2.1.2 Drawing to file

Another way of using MathGL library is the direct writing of the picture to the file. It is most usable for plot creation during long calculation or for using of small programs (like Matlab or Scilab scripts) for visualizing repetitive sets of data. But the speed of drawing is much higher in comparison with a script language.

The following code produces a bitmap PNG picture:

#include <mgl2/mgl.h>
int main(int ,char **)
{
  mglGraph gr;
  gr.Alpha(true);   gr.Light(true);
  sample(&gr);              // The same drawing function.
  gr.WritePNG("test.png");  // Don't forget to save the result!
  return 0;
}

For compilation, you need only libmgl library not the one with widgets

gcc test.cpp -lmgl

This can be important if you create a console program in computer/cluster where X-server (and widgets) is inaccessible.

The only difference from the previous variant (using windows) is manual switching on the transparency Alpha and lightning Light, if you need it. The usage of frames (see Animation) is not advisable since the whole image is prepared each time. If function sample contains frames then only last one will be saved to the file. In principle, one does not need to separate drawing functions in case of direct file writing in consequence of the single calling of this function for each picture. However, one may use the same drawing procedure to create a plot with changeable parameters, to export in different file types, to emphasize the drawing code and so on. So, in future I will put the drawing in the separate function.

The code for export into other formats (for example, into vector EPS file) looks the same:

#include <mgl2/mgl.h>
int main(int ,char **)
{
  mglGraph gr;
  gr.Light(true);
  sample(&gr);              // The same drawing function.
  gr.WriteEPS("test.eps");  // Don't forget to save the result!
  return 0;
}

The difference from the previous one is using other function WriteEPS() for EPS format instead of function WritePNG(). Also, there is no switching on of the plot transparency Alpha since EPS format does not support it.


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2.1.3 Animation

Widget classes (mglWindow, mglGLUT) support a delayed drawing, when all plotting functions are called once at the beginning of writing to memory lists. Further program displays the saved lists faster. Resulting redrawing will be faster but it requires sufficient memory. Several lists (frames) can be displayed one after another (by pressing ‘,’, ‘.’) or run as cinema. To switch these feature on one needs to modify function sample:

int sample(mglGraph *gr)
{
  gr->NewFrame();             // the first frame
  gr->Rotate(60,40);
  gr->Box();
  gr->EndFrame();             // end of the first frame
  gr->NewFrame();             // the second frame
  gr->Box();
  gr->Axis("xy");
  gr->EndFrame();             // end of the second frame
  return gr->GetNumFrame();   // returns the frame number
}

First, the function creates a frame by calling NewFrame() for rotated axes and draws the bounding box. The function EndFrame() must be called after the frame drawing! The second frame contains the bounding box and axes Axis("xy") in the initial (unrotated) coordinates. Function sample returns the number of created frames GetNumFrame().

Note, that such kind of animation is rather slow and not well suitable for visualization of running calculations. For the last case one can use Update() function. The most simple case for doing this is to use mglDraw class and reimplement its Calc() method.

#include <mgl2/window.h>
class Foo : public mglDraw
{
  mglPoint pnt;  // some result of calculation
public:
  mglWindow *Gr;  // graphics to be updated
  int Draw(mglGraph *gr);
  void Calc();
} foo;
//-----------------------------------------------------
void Foo::Calc()
{
  for(int i=0;i<30;i++)   // do calculation
  {
    sleep(2);             // which can be very long
    pnt = mglPoint(2*mgl_rnd()-1,2*mgl_rnd()-1);
    Gr->Update();         // update window
  }
}
//-----------------------------------------------------
int Foo::Draw(mglGraph *gr)
{
  gr->Line(mglPoint(),pnt,"Ar2");
  gr->Box();
  return 0;
}
//-----------------------------------------------------
int main(int argc,char **argv)
{
  mglWindow gr(&foo,"MathGL examples");
  foo.Gr = &gr;   foo.Run();
  return gr.Run();
}

Previous sample can be run in C++ only since it use C++ class mglDraw. However similar idea can be used even in Fortran or SWIG-based (Python/Octave/...) if one use FLTK window. Such limitation come from the Qt requirement to be run in the primary thread only. The sample code will be:

int main(int argc,char **argv)
{
  mglWindow gr("test");   // create window
  gr.RunThr();            // run event loop in separate thread
  for(int i=0;i<10;i++)   // do calculation
  {
    sleep(1);             // which can be very long
    pnt = mglPoint(2*mgl_rnd()-1,2*mgl_rnd()-1);
    gr.Clf();             // make new drawing
    gr.Line(mglPoint(),pnt,"Ar2");
    char str[10] = "i=0"; str[2] = '0'+i;
    gr.Puts(mglPoint(),"");
    gr.Update();          // update window when you need it
  }
  return 0;   // finish calculations and close the window
}

Pictures with animation can be saved in file(s) as well. You can: export in animated GIF, or save each frame in separate file (usually JPEG) and convert these files into the movie (for example, by help of ImageMagic). Let me show both methods.

The simplest methods is making animated GIF. There are 3 steps: (1) open GIF file by StartGIF() function; (2) create the frames by calling NewFrame() before and EndFrame() after plotting; (3) close GIF by CloseGIF() function. So the simplest code for “running” sinusoid will look like this:

#include <mgl2/mgl.h>
int main(int ,char **)
{
  mglGraph gr;
  mglData dat(100);
  char str[32];
  gr.StartGIF("sample.gif");
  for(int i=0;i<40;i++)
  {
    gr.NewFrame();     // start frame
    gr.Box();          // some plotting
    for(int j=0;j<dat.nx;j++)
      dat.a[j]=sin(M_PI*j/dat.nx+M_PI*0.05*i);
    gr.Plot(dat,"b");
    gr.EndFrame();     // end frame
  }
  gr.CloseGIF();
  return 0;
}

The second way is saving each frame in separate file (usually JPEG) and later make the movie from them. MathGL have special function for saving frames – it is WriteFrame(). This function save each frame with automatic name ‘frame0001.jpg, frame0002.jpg’ and so on. Here prefix ‘frame’ is defined by PlotId variable of mglGraph class. So the similar code will look like this:

#include <mgl2/mgl.h>
int main(int ,char **)
{
  mglGraph gr;
  mglData dat(100);
  char str[32];
  for(int i=0;i<40;i++)
  {
    gr.NewFrame();     // start frame
    gr.Box();          // some plotting
    for(int j=0;j<dat.nx;j++)
      dat.a[j]=sin(M_PI*j/dat.nx+M_PI*0.05*i);
    gr.Plot(dat,"b");
    gr.EndFrame();     // end frame
    gr.WriteFrame();   // save frame
  }
  return 0;
}

Created files can be converted to movie by help of a lot of programs. For example, you can use ImageMagic (command ‘convert frame*.jpg movie.mpg’), MPEG library, GIMP and so on.

Finally, you can use mglconv tool for doing the same with MGL scripts (see section Utilities for parsing MGL).


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2.1.4 Drawing in memory

The last way of MathGL using is the drawing in memory. Class mglGraph allows one to create a bitmap picture in memory. Further this picture can be displayed in window by some window libraries (like wxWidgets, FLTK, Windows GDI and so on). For example, the code for drawing in wxWidget library looks like:

void MyForm::OnPaint(wxPaintEvent& event)
{
  int w,h,x,y;
  GetClientSize(&w,&h);   // size of the picture
  mglGraph gr(w,h);

  gr.Alpha(true);         // draws something using MathGL
  gr.Light(true);
  sample(&gr,NULL);

  wxImage img(w,h,gr.GetRGB(),true);
  ToolBar->GetSize(&x,&y);    // gets a height of the toolbar if any
  wxPaintDC dc(this);         // and draws it
  dc.DrawBitmap(wxBitmap(img),0,y);
}

The drawing in other libraries is most the same.

For example, FLTK code will look like

void Fl_MyWidget::draw()
{
  mglGraph gr(w(),h());
  gr.Alpha(true);         // draws something using MathGL
  gr.Light(true);
  sample(&gr,NULL);
  fl_draw_image(gr.GetRGB(), x(), y(), gr.GetWidth(), gr.GetHeight(), 3);
}

Qt code will look like

void MyWidget::paintEvent(QPaintEvent *)
{
  mglGraph gr(w(),h());

  gr.Alpha(true);         // draws something using MathGL
  gr.Light(true);         gr.Light(0,mglPoint(1,0,-1));
  sample(&gr,NULL);

  // Qt don't support RGB format as is. So, let convert it to BGRN.
  long w=gr.GetWidth(), h=gr.GetHeight();
  unsigned char *buf = new uchar[4*w*h];
  gr.GetBGRN(buf, 4*w*h)
  QPixmap pic = QPixmap::fromImage(QImage(*buf, w, h, QImage::Format_RGB32));

  QPainter paint;
  paint.begin(this);  paint.drawPixmap(0,0,pic);  paint.end();
  delete []buf;
}

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2.1.5 Using QMathGL

MathGL have several interface widgets for different widget libraries. There are QMathGL for Qt, Fl_MathGL for FLTK. These classes provide control which display MathGL graphics. Unfortunately there is no uniform interface for widget classes because all libraries have slightly different set of functions, features and so on. However the usage of MathGL widgets is rather simple. Let me show it on the example of QMathGL.

First of all you have to define the drawing function or inherit a class from mglDraw class. After it just create a window and setup QMathGL instance as any other Qt widget:

#include <QApplication>
#include <QMainWindow>
#include <QScrollArea>
#include <mgl2/qmathgl.h>
int main(int argc,char **argv)
{
  QApplication a(argc,argv);
  QMainWindow *Wnd = new QMainWindow;
  Wnd->resize(810,610);  // for fill up the QMGL, menu and toolbars
  Wnd->setWindowTitle("QMathGL sample");
  // here I allow to scroll QMathGL -- the case
  // then user want to prepare huge picture
  QScrollArea *scroll = new QScrollArea(Wnd);

  // Create and setup QMathGL
  QMathGL *QMGL = new QMathGL(Wnd);
//QMGL->setPopup(popup); // if you want to setup popup menu for QMGL
  QMGL->setDraw(sample);
  // or use QMGL->setDraw(foo); for instance of class Foo:public mglDraw
  QMGL->update();

  // continue other setup (menu, toolbar and so on)
  scroll->setWidget(QMGL);
  Wnd->setCentralWidget(scroll);
  Wnd->show();
  return a.exec();
}

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2.1.6 MathGL and PyQt

Generally SWIG based classes (including the Python one) are the same as C++ classes. However, there are few tips for using MathGL with PyQt. Below I place a very simple python code which demonstrate how MathGL can be used with PyQt. This code is mostly written by Prof. Dr. Heino Falcke. You can just copy it to a file mgl-pyqt-test.py and execute it from python shell by command execfile("mgl-pyqt-test.py")

from PyQt4 import QtGui,QtCore
from mathgl import *
import sys
app = QtGui.QApplication(sys.argv)
qpointf=QtCore.QPointF()

class hfQtPlot(QtGui.QWidget):
    def __init__(self, parent=None):
        QtGui.QWidget.__init__(self, parent)
        self.img=(QtGui.QImage())
    def setgraph(self,gr):
        self.buffer='\t'
        self.buffer=self.buffer.expandtabs(4*gr.GetWidth()*gr.GetHeight())
        gr.GetBGRN(self.buffer,len(self.buffer))
        self.img=QtGui.QImage(self.buffer, gr.GetWidth(),gr.GetHeight(),QtGui.QImage.Format_ARGB32)
        self.update()
    def paintEvent(self, event):
        paint = QtGui.QPainter()
        paint.begin(self)
        paint.drawImage(qpointf,self.img)
        paint.end()

BackgroundColor=[1.0,1.0,1.0]
size=100
gr=mglGraph()
y=mglData(size)
#y.Modify("((0.7*cos(2*pi*(x+.2)*500)+0.3)*(rnd*0.5+0.5)+362.135+10000.)")
y.Modify("(cos(2*pi*x*10)+1.1)*1000.*rnd-501")
x=mglData(size)
x.Modify("x^2");

def plotpanel(gr,x,y,n):
    gr.SubPlot(2,2,n)
    gr.SetXRange(x)
    gr.SetYRange(y)
    gr.AdjustTicks()
    gr.Axis()
    gr.Box()
    gr.Label("x","x-Axis",1)
    gr.Label("y","y-Axis",1)
    gr.ClearLegend()
    gr.AddLegend("Legend: "+str(n),"k")
    gr.Legend()
    gr.Plot(x,y)


gr.Clf(BackgroundColor[0],BackgroundColor[1],BackgroundColor[2])
gr.SetPlotFactor(1.5)
plotpanel(gr,x,y,0)
y.Modify("(cos(2*pi*x*10)+1.1)*1000.*rnd-501")
plotpanel(gr,x,y,1)
y.Modify("(cos(2*pi*x*10)+1.1)*1000.*rnd-501")
plotpanel(gr,x,y,2)
y.Modify("(cos(2*pi*x*10)+1.1)*1000.*rnd-501")
plotpanel(gr,x,y,3)

gr.WritePNG("test.png","Test Plot")

qw = hfQtPlot()
qw.show()
qw.setgraph(gr)
qw.raise_()

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2.1.7 MathGL and MPI

For using MathGL in MPI program you just need to: (1) plot its own part of data for each running node; (2) collect resulting graphical information in a single program (for example, at node with rank=0); (3) save it. The sample code below demonstrate this for very simple sample of surface drawing.

First you need to initialize MPI

#include <stdio.h>
#include <mgl2/mgl.h>
#include <mpi.h>

int main(int argc, char *argv[])
{
  // initialize MPI
  int rank=0, numproc=1;
  MPI_Init(&argc, &argv);
  MPI_Comm_size(MPI_COMM_WORLD,&numproc);
  MPI_Comm_rank(MPI_COMM_WORLD,&rank);
  if(rank==0) printf("Use %d processes.\n", numproc);

Next step is data creation. For simplicity, I create data arrays with the same sizes for all nodes. At this, you have to create mglGraph object too.

  // initialize data similarly for all nodes
  mglData a(128,256);
  mglGraph gr;

Now, data should be filled by numbers. In real case, it should be some kind of calculations. But I just fill it by formula.

  // do the same plot for its own range
  char buf[64];
  sprintf(buf,"xrange %g %g",2.*rank/numproc-1,2.*(rank+1)/numproc-1);
  gr.Fill(a,"sin(2*pi*x)",buf);

It is time to plot the data. Don’t forget to set proper axis range(s) by using parametric form or by using options (as in the sample).

  // plot data in each node
  gr.Clf();   // clear image before making the image
  gr.Rotate(40,60);
  gr.Surf(a,"",buf);

Finally, let send graphical information to node with rank=0.

  // collect information
  if(rank!=0) gr.MPI_Send(0);
  else for(int i=1;i<numproc;i++)  gr.MPI_Recv(i);

Now, node with rank=0 have whole image. It is time to save the image to a file. Also, you can add a kind of annotations here – I draw axis and bounding box in the sample.

  if(rank==0)
  {
    gr.Box();   gr.Axis();   // some post processing
    gr.WritePNG("test.png"); // save result
  }

In my case the program is done, and I finalize MPI. In real program, you can repeat the loop of data calculation and data plotting as many times as you need.

  MPI_Finalize();
  return 0;
}

You can type ‘mpic++ test.cpp -lmgl && mpirun -np 8 ./a.out’ for compilation and running the sample program on 8 nodes. Note, that you have to set enable-mpi=ON at MathGL configure to use this feature.


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