Okay- now that I have a way to define the convex hulls themselves, how do
I determine their volume?
Here’s site on
molecular shapes and surfaces that is a bit too detailed for me at the
moment, but that is interesting nonetheless. Wikipedia provides
the
information that in 3 dimensions, a convex hull is a type of convex
polyhedron.
Here
is a javascript implementation of a polyhedra volume calculator. However,
it needs to know not just the vertices, but also which vertices go along
with which sides of the polygon. Mathworld provides some
further
information about convex polyhedrons, including the somewhat
disheartening news that there is no general formula for the volume of a
convex polyhedron. However, it does say that there is an algorithm for
determining faces of a convex polyhedron and, as we have seen, there is a
way to figure out the volume once you have that figured out. Which then
seems to suggest that there is, in fact, a general formula for the volume
of a convex polyhedron but the, what can I say, I’m no mathematician.
posted at 12:19 on Fri, 21 Apr, 2006 |
path: /school
All material copyrighted by Jen Schellinck. All rights reserved.