Woody from Kingsville, Ontario has a great tip for giving your Plexiglas project a smooth flowing rounded edge.
First sand out any saw cuts or other imperfections, but rather than trying to sand over the sharp edge, hold a propane torch about 4 inches from the edge and slightly melt the plastic. It will polish off the edge and round off the sharp corners and edges.
Be careful to not create unsightly bubbles. Go very gently. It appears to do nothing, then all of a sudden, it softens and polishes the edge. You will see the change that means you need to move further down the plastic.
Practice on the scrap.