if (time_computed == false || parameter(always_compute_position) != 0)
	{
		// We haven't been informed about the position of the particle impact
		// position or we want to compute the particle position in any case. 
		// It will be determined by the following minimum search algorithm.
		double radius_sqr = parameter(radius)*parameter(radius);
		
		// Tiny random jitter around the beam axis is the starting point.
		x_particle = 0.2*parameter(radius)*(rand()%2000 - 1000)/1000.0;
		y_particle = 0.2*parameter(radius)*(rand()%2000 - 1000)/1000.0;
		
		// Select the start step size more or less arbitrary.
		// 1/7 of the disk radius seems to be a reasonable choice.
		double stepsize = parameter(radius)/7;
		int direction = 0;
		double last_variance = analyze(x_particle, y_particle, true);
		for (int n = 0;; ++n)
		{
			if (x_particle*x_particle + y_particle*y_particle > 4*radius_sqr) // we left the circular membrane
			{
				//std::cerr << n << " steps to break the circle at position "
				//		  << x_particle << " " << y_particle
				//		  << "   stepsize was " << stepsize << std::endl;
				return;
			}
			double variance;
			// From the current position go strictly downhill
			// in one of the four directions (+x,-x,+y,-y)
			// on the chi^2 plane.
			if (     (variance = analyze(x_particle + stepsize, y_particle,            true)) < last_variance)
				x_particle += stepsize;
			else if ((variance = analyze(x_particle - stepsize, y_particle,            true)) < last_variance)
				x_particle -= stepsize;
			else if ((variance = analyze(x_particle,            y_particle + stepsize, true)) < last_variance)
				y_particle += stepsize;
			else if ((variance = analyze(x_particle,            y_particle - stepsize, true)) < last_variance)
				y_particle -= stepsize;
			else
			{
				// If a minimum is found and the stepsize is not small
				// enough, reduce the stepsize and restart searching.
				if (stepsize > 2.0)
				{
					stepsize /= 2;
				}
				else
				{
					// If the stepsize was small enough (less than 2mm
					// seems to be reasonable, because the spacial
					// resolution of the device is approx. 6-7mm)
					// we are done.
					//std::cerr << n << " steps to find the position " << x_particle << " " << y_particle << std::endl;
					break;
				}
			}
			
			last_variance = variance;
		}