This is just one of my several run-ins with computational geometry. Geomview is an interactive 3D geometry viewing program originally written at The Geometry Center. It is now supported by volunteers, and commercially support is available from Geometry Technologies. Geomview runs well under Linux and other platforms but does not yet have a Windows port. Geomview makes it easy to add interactive visualization to your own programs. It takes advantage of the Mesa 3D graphics library, which taps the capabilities of 3D graphics cards.
The web has been very good to computational geometry. Netlib continues to provide access to triangle, hull, and sweep. When you really need a mesh for finite element analysis, you should check out Finite element mesh generation . If you need a really fancy mesh, look in the Meshing Research Corner. Some of those guys mesh like their lives depend on it.
When you need the Voronoi object, and you have more dimensions than you should, then you can find relief at the Home page for Qhull.
I shouldn't be amazed, but I am anyway, by the claims made about The Ipe extendible drawing editor . How about editing arbitrary postscript, extensibility, computing Voronoi diagrams, and clipping to polygons? After all, we're talking free software that runs on Linux!
It seems like we all live within a world of constraints, and it is difficult to see what all our possibilities are. Some nice work has been done on Geometric Constraint Solving, but they aren't giving away the code.
Now, what if you wanted to glue a mesh generator to Matlab and solve an isotropic nonconstant-coefficient Laplace equation?
Polygon soups are models which contain no adjacency information and obey no topological constraints. RAPID is a rapid and accurate polygon interference detection library for large polygon soups.
Since this is supposed to be both fun and educational, maybe you should just go straight to David Eppstein's pages, which include The Geometry Junkyard, one of the most interesting places on the net.