I am trying to generate a set of points distributed in such a way as to give a "rough circle" sort of shape. The points should not deviate too far from neighboring points, with larger jumps being rarer, though the radius can gradually deviate from whatever the starting mean radius was. The angular seperation of the points are equally distributed, but the number of points can vary.

My first strategy was to do a random walk around the circle, with the next point having a radius that's different by a normally-distributed random number. The problem is once we get to the last point, it will more often than not have a big discontinuity with the first point, larger than what we would expect from the normal variation in neighboring points.

Now I don't need the last point to be exactly the same as the first, but I would like an approach that has the first and the last points to be as near as we would expect any other two adjacent points to be. Is there some way to pick random points in such a way, so that a random walk "returns to its starting position" so to speak?

For context, the use case is the creation of objects in an Asteroids (the arcade game) sort of style. Those asteroids simply used a uniformly distributed random radius for each point in the polygon, but that produces objects more jaggedy than what I would like, and lead to more visually spherical objects as you add more points. But my polygons still have few enough points where a full application of Perlin noise or some other fractal method would be overkill I would think.