$\begingroup$

What is the difference between a convex hull and alpha shape? What I get to understand from wiki, is that, alpha shape generates a set of boundary points such that together they form a smaller surface area when considering the selected points than a normal convex hull. I am unable to understand the difference mathematically. Can someone please explain it in a simple way if possible?

$\endgroup$ 2

1 Answer

$\begingroup$

With an alpha shape you fix the radius of a circle and define a starting point (SP). Then you rotate the circle with its circumference on the SP until it hits another point. Then transfer the circle to this point and repeat.

With a convex hull, the 'finding object' (FO) is a line.

A good picture to demonstrate this, from here, is:

Another way of visualizing an alpha hull is to use a line of fixed length as the FO. A problem is that the FO might not hit anything - this defines the minimum resolution of a set of points.

An advantage of a circular FO is the final object can be rendered 'curvy'.

$\endgroup$ 2

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy