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 parameters that the user must choose in order to have the best quality/performance ratio of the algorithm:

• Domain of x,y:
  C++

  // 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 influences 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 two 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 overridden 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

Use CGLContour as inherited function of CContour.

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

Retrieve Contours in Line Strip

Use CListContour as inherited function of CContour. Only the index of the points with respect to second grid are stored in the list. You can access their real value by using GetXi() and GetYi() functions.

CGLContour contour;
// Setting up contour : setting f,
// domain of x, isocurve values
[...]
// generating contour
contour.Generate();
// Retrieving 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 successive index of the points
    // See CContourGLDoc.OnDraw for further details
    [...]
}

Updates

• 31^st August, 2002: Added contribution from Chenggang Zhou: better strip compression, threshold merging, area of strip, boundary detection, also some minor changes I don't remember...
• 4^th March, 2002: All the code is now using STL. :)

References

• [1] "Implementation of an improved contour plotting algorithm.", M. Aramini. Submitted in partial fulfillment of the requirements for the degree of Master of Science in Computer Science in the Graduate College of the University of Illinois at Urbana-Champaign, 1981.

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