A C++ implementation of an improved contour plotting algorithm

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Introduction

This article presents  a contour plot class. It is designed to draw iso-contour of a user-defined function f(x,y). I wrote it to integrate it in a graphic library : Plot Graphic Library

The class is based on the algorithm presented in [1] (Check References section). It is basically an improved version of the Level Curve Tracing Algorithm.

Understanding the algorithm

The algorithm uses several tuning parameter that the user must choose in order to have the best quality/performance ratio of the algorithm :

• Domain of x,y:

       // Setting domain x=[0,1], y=[2,3]
      double pLimits[4]={0,1,2,3,4};
      CContour contour;
      contour.SetLimits(pLimits);
  

• Size of the primary grid : The grid on which evaluate the function f(x,y). See SetFirGrid, GetColFir, GetRowFir. The parameter influence greatly the quality of the contour.
• Size of the secondary grid : The grid where the function is going to be evaluated. This grid can be much finer that the first grid. See SetSecGrid, GetColSec, GetRowSec.

Classes

CContour

Main contour class. This class cannot be directly but has to be inherited. The inherited class must implement the ExportLine function. To generate contours, use

void Generate()

Make to have set the field function (f(x,y)) before calling this function. The function will call ExportLine for each new segment.

CGLContour

Use this class to draw contours to an OpenGL device context.

CListContour

Use this class to generate contour and store them as line strip. The user can retrieve each contour and use it as he wills. This function uses to sub-classes :

• CLineStrip, a list < int > containing the index of the points.
• CLineStripList, a list <CLineStrip*>.

The line strip can be accessed by

CLineStripList* GetList(iPane);

where iPane is the index of the contour.

How to...

Set up a contour object

Suppose that we have inherited a class from CContour and overriden ExportLine function.

    class CMyContour : CContour
    { 
        void ExportLine(...);
    }

Now, first set the function f(x,y):

    double  myF(double x, double y)
    { [...] return ... };
	
    CMyContour contour;
    // Setting f(x,y)=myF
    contour.SetFieldFcn(myF);

Then set the iso-contour values, i.e.

    int n;
    CMyContour contour;
    vector<double> vIso(n); 
    for (int i=0;i<n;i++)
    { ... }
    // setting iso-lines
    contour.SetPlanes(vIso);

The contour is ready to be used.

Draw contours using OpenGL

    CGLContour contour;
    // Setting up contour : setting f, domain of x, 
    // isocurve values
    [...]
    // generating contour
    contour.Generate();

    CGLContour contour;
    // Setting up contour : setting f, 
    // domain of x, isocurve values
    [...]
    // generating contour
    contour.Generate();
    // Retreiving info
    CLineStripList* pStripList;
    // getting 0-th iso-curve
    pStripList=contour.GetLines(0); 
    ASSERT(pStripList);
    // iterating liststrip vertices
    CLineStrip::iterator pos;
    for (pos=pStripList->begin(); 
        pos != pStripList->end() ; pos++)
    {
        pStrip=(*pos);
        ASSERT(pStrip);
        if (pStrip->empty())
            continue;
        // using info of strip list
        // pStrip contains the succesive index of the points
        // See CContourGLDoc.OnDraw for further details
        [...]       
    }