I'd like to know if there is an algorithm that given a set o points and an angle computes the convex-hull if the angle is $\alpha = 0$ and given an $\alpha > 0$ computes an envelope that follows more closely the "perimeter".
And if there is a definition of a non intersecting perimeter of a set of points, in this case the resulting polygon when $\alpha$ is big.
Another view of the problem can be to find an algorithm that can be parametrized to find for $\alpha = 0$ the minimum perimeter solution (convex-hull) and for $\alpha = 1$ (normalized) the minimum area polyline enclosing all the points.