See finished product under "TABLES"-- IMPOSSIBLE CURVES SIDEBOARD.
When fabricating acrylic parts, there are a few consistently used steps. First, create the exact shapes you want out of wood, called “templates.” Then, trace those onto your acrylic (leaving the protective paper on), and rough cut the pieces out using a jigsaw. For extra protection, first apply felt pads to your jigsaw base. Clamp the template firmly to your acrylic, and use a router with a ball-bearing straight bit to cut the exact shape. Finally, if the edges will be showing, wet sand them up to 2,000 grit, then polish.