Picking a random orientation depends on trigonometric functions. In order for this to calculate, it would be a lot cooler if it didn't depend on transcendental functions.
You can pick a uniform random orientation without trig functions by first generating a random point in the unit disk via rejection sampling, then projecting it onto the boundary [0].
Of course, using rejection sampling for disk points will give you an estimate for π more directly.
context: https://en.wikipedia.org/wiki/Buffon's_needle_problem
Picking a random orientation depends on trigonometric functions. In order for this to calculate, it would be a lot cooler if it didn't depend on transcendental functions.
You can pick a uniform random orientation without trig functions by first generating a random point in the unit disk via rejection sampling, then projecting it onto the boundary [0].
Of course, using rejection sampling for disk points will give you an estimate for π more directly.
[0] https://mathworld.wolfram.com/CirclePointPicking.html
It's not numerically converging for me, no matter how long I run it.