This is called the alpha complex of the points. The alpha shape is the geometric object defined as the union of the elements in the complex. Important applications of alpha shapes include the construction of 3D models of proteins in which holes and tunnels can be identified so that biologists can determine the possible location and volume of water molecules. Chemists and physicists can use it to define the volume of atom clusters. Astronomers can explore the global cosmological structure of the universe.
Biologists are currently the largest users of the alpha shapes software.
For instance, at Illinois they are using it to investigate the shapes of proteins and to look at fluid flow in the brain. Shankar Subramaniam and Eric Jakobsson and, both professors of biophysics, have found alpha shapes to be a good tool for defining molecular shapes. Jakobsson and postdoc Sudhakar Pamidingantham have been working with alpha shapes to understand protein docking with toxins. Specifically, they are examining a protein, called a potassium channel, and its interaction with scorpion toxin. Finally, it locks into place, fitting into the channel like a glove.