I have a dataset of 3-dimensional points for which I'd like to construct a mesh, using python. All the software I've seen requires that you provide the edges. Is there a program in python which takes as the input a set of points in 3D and output a mesh? If possible, I'd like the meshing to be uniform.
If an unrestricted triangulation is OK, you can do it with scipy.spatial.Delaunay which uses Qhull.
CGAL (http://www.cgal.org) has a number of modules for triangulating points in 3D (surface meshes from points, triangulations of points in 3D, etc). Python wrappers for a subset of CGAL modules are available (https://code.google.com/p/cgal-bindings), including for 3D triangulations. I've used the CGAL C++ interface for triangulating points in 3D, but I have no experience with the Python interface.
You could try VTK which has a Python API. I would first try ParaView and bring your points into that and then try some of the filters (e.g. Delaunay). If the filters work in ParaView with your data (which is VTK based) then you can use VTK to do the job. How successful you will be will depend on what the points look like and how nicely they suit the filters.
If VTK looks like it will work, have a look at the Kitware tutorials on VTK as I know there is one that walks through using Python/VTK.