Function trackHyperbolaCore

plugin/seq/plotPDF.cpp:2381–2451

	Cx.push_back( Cx_local );
	Cy.push_back( Cy_local );
    }

    return;
}

void trackHyperbolaCore( std::vector< std::vector<double> > &Cx, std::vector< std::vector<double> > &Cy,
			 const double sign, const double a, const double b, std::vector<double> &x,
			 const double *const Vx, const double *const Vy )
{
    const int INTERVALS = PLOTPDFVAR::DEFAULT_P2_INERVALS;

    // y = sign * sqrt( a * x^2 + b )

    std::sort( x.begin(),  x.end() );

    std::vector<double> Y;
    for(size_t i = 0; i < x.size(); i++)
	Y.push_back( sign * sqrt( a*x[i]*x[i] + b ) );
	    
    // algorithm in "Mathematical Illustrations" by Bill Casselman,
    // Chapter 7, (2005) Cambridge University Press.
    // https://www.cambridge.org/jp/academic/subjects/mathematics/geometry-and-topology/mathematical-illustrations-manual-geometry-and-postscript?format=PB&isbn=9780521547888
    // See also http://www.math.ubc.ca/~cass/graphics/text/www/

    for(size_t i = 0; i+1 < x.size(); i++){

	std::vector<double> Cx_local, Cy_local;

	const double &X0 = x[i];
	const double &X1 = x[i+1];
	const double h   = (X1 - X0) / INTERVALS;

	const double EPS = 1e-10;
	if( h < EPS )
	    continue;

	// examine the arc X[i]--X[i+1] is inside triangle or not
	const double mX0 = X0 + h/100;
	const double mY0 = sign * sqrt( a*mX0*mX0 + b );

	const double mX1 = X1 - h/100;
	const double mY1 = sign * sqrt( a*mX1*mX1 + b );
	if( !(isInsideTriangle( mX0, mY0, Vx, Vy ) && isInsideTriangle( mX1, mY1, Vx, Vy )) )
	    continue;

	Cx_local.push_back( X0 );
	Cy_local.push_back( Y[i] );
		
	for(int k = 0; k < INTERVALS; k++){

	    const double P0x = X0 + k*h;
	    const double P3x = X0 + (k+1)*h;
	    const double P1x = P0x + h/3;
	    const double P2x = P3x - h/3;

	    const double P0y = sign * sqrt( a*P0x*P0x + b );
	    const double P3y = sign * sqrt( a*P3x*P3x + b );
	    // y = f(x) = sqrt(a*x*x + b)