be to instead make the number of discretization points on the loop sufficiently large to ensure that simple inside/outside checks applied to each point give a reasonably close approximation. Still, generic ray/surface intersection checks can become useful, especially if the complicated multiple integral in Equation \[eq:loopenergy.final\] (over loop shapes, loop sizes, and loop centers of gravity) can partially be evaluated by analytic, or rather semi-analytic means that involve numerical approximation of integral boundaries. This is relevant for the discussion in Section \[sec:scaling\], and may make major computational improvements of the method possible. In this context, we want to point out the existence of advanced algorithms useful for ray/surface intersection problems, such as Comba and Stolfi’s Affine Arithmetic [@CombaStolfiSiggraph93; @Knoll09]. In order to generate a properly distributed random sample of loops, we first generalize the problem to finding a process that produces piecewise straight paths with gaussian length distribution (of given standard deviation) for a given starting and end point (not necessarily coincident). This problem can be re-phrased as finding pairs of such paths, each with its own starting point but at first without any constraint on their endpoints, and imposing the condition that they meet at their endpoints. Concatenating the 