Publications Group A finite set of points in 3D space and a real parameter alpha uniquely define a simplicial complex, also called the alpha complex of the points. An alpha shape is the geometric object defined as the union of the elements in the complex. The first notion of alpha shapes is the 2D analog of the spatial notion described below.
Alpha shapes formalize the intuitive notion of shape.
For varying parameter alpha, it ranges from crude to fine in complexity. The most crude shape is a convex hull, which is obtained for very large values of alpha. As alpha decreases, the shape shrinks and develops cavities that may join to form tunnels and voids. A related notion is the space filling diagram, which is used in biology and chemistry to represent molecular structures. The space filling diagram is the union of balls centered at the points, and it has a geometrically dual alpha complex.