  There is a pressing need for robust and straightforward methods to create
potentials for trapping Bose-Einstein condensates which are simultaneously
dynamic, fully arbitrary, and sufficiently stable to not heat the ultracold
gas. We show here how to accomplish these goals, using a rapidly-moving laser
beam that "paints" a time-averaged optical dipole potential in which we create
BECs in a variety of geometries, including toroids, ring lattices, and square
lattices. Matter wave interference patterns confirm that the trapped gas is a
condensate. As a simple illustration of dynamics, we show that the technique
can transform a toroidal condensate into a ring lattice and back into a toroid.
The technique is general and should work with any sufficiently polarizable
low-energy particles.
