Consider a sequence of values x_{1} .. x_{n} sampled from a distribution. Construct a piecewise linear function through all the points (i, x_{i}). Or a spline of higher order. The distribution could be something like uniform between plus/minus a maximum (the minimum turning radius).

Let this function be the curvature of a point traveling at constant speed on a plane. Construct the path of this "drunk driver" from the path curvature function, probably something involving integration and arc length.

Instead of a plane, consider the point moving on a sphere. Will it sample the space of all possible orientations? How do we handle the additional degree of freedom of twist along the view axis? Is it aesthetically pleasing? From what distribution should the curvature knots be sampled?

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