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?
2026-03-25 19:00:34.1774465234
Difference between a convex hull and alpha shape
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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'.