EllipseFitData doEllipseFit()
{
//Data preparation: normalize data
List <double> xData = symmetricNormalize(m_xData);
List <double> yData = symmetricNormalize(m_yData);
//Bulid n*6 design matrix, n is size of xData or yData
List <List <double> > dMtrx = getDesignMatrix(xData, yData);
//Bulid 6*6 scatter matrix
List <List <double> > sMtrx = getScatterMatrix(dMtrx);
//Build 6*6 constraint matrix
List <List <double> > cMtrx = getConstraintMatrix();
//Solve eigensystem
List <List <double> > eigVV = new List <List <double> >();
bool flag = solveGeneralEigens(sMtrx, cMtrx, eigVV);
if (!flag)
{
throw (new ApplicationException("Eigenvalue calculatin failed"));
}
EllipseFitData ellip = calcEllipsePara(eigVV);
return(ellip);
}
/**
* @brief calcEllipsePara: calculate ellipse parameter form eigen information
* @param eigVV: eigenvalues and eigenvectors
* @return ellipse parameter
*/
EllipseFitData calcEllipsePara(List <List <double> > eigVV)
{
//Extract eigenvector corresponding to negative eigenvalue
int eigIdx = -1;
for (int i = 0; i < eigVV.Count; ++i)
{
double tmpV = eigVV[i][0];
if (tmpV < 1e-6 & !double.IsInfinity(tmpV))
{
eigIdx = i;
break;
}
}
if (eigIdx < 0)
{
return(new EllipseFitData());
}
//Unnormalize and get coefficients of conic section
double tA = eigVV[eigIdx][1];
double tB = eigVV[eigIdx][2];
double tC = eigVV[eigIdx][3];
double tD = eigVV[eigIdx][4];
double tE = eigVV[eigIdx][5];
double tF = eigVV[eigIdx][6];
double mx = getMeanValue(m_xData);
double my = getMeanValue(m_yData);
double sx = getScaleValue(m_xData);
double sy = getScaleValue(m_yData);
EllipseFitData ellip = new EllipseFitData();
ellip.a = tA * sy * sy;
ellip.b = tB * sx * sy;
ellip.c = tC * sx * sx;
ellip.d = -2 * tA * sy * sy * mx - tB * sx * sy * my + tD * sx * sy * sy;
ellip.e = -tB * sx * sy * mx - 2 * tC * sx * sx * my + tE * sx * sx * sy;
ellip.f = tA * sy * sy * mx * mx + tB * sx * sy * mx * my + tC * sx * sx * my * my
- tD * sx * sy * sy * mx - tE * sx * sx * sy * my + tF * sx * sx * sy * sy;
ellip.algeFlag = true;
ellip.alge2geom();
return(ellip);
}
