Almost any 3D shape can by constructed by stacking a large number of carefully cutout layers. This method of construction is popular with architects when creating models of terrain and artists creating sculptures with an ‘edgy’ effect. Layering can also be used as a rapid prototyping method (known as
Laminated Object Manufacturing).
The problem with making 3D shapes with layers is the number of layers necessary to form a smooth finish. Using thicker layers is quick and easy, but at the cost of a stepping effect (resembling rice terraces). Using thin layers overcomes the terraced look, but requires a large number of layers which is time consuming and restricts the type of materials that can be used.
If the angle of the edges could be varied when cutting out each layer, a much smoother 3D shape could be constructed with relatively thick layers.
This would be achieved with a computer controlled scroll saw (a scroll saw is a hybrid of a bandsaw and jigsaw). The sheet would be pushed into the blade by three actuators (one for movement in the x-axis of the plane, one for the y-axis of the plane and one for rotating the sheets in the plane (i.e. the yaw)).
The surface on which the sheet lies when being cut would be moved in the roll direction. Thus the angle of the edge could be varied.
The layers could be made of any material and adhesive applied between sheets when stacking. Two or more alignment holes could be cut into each layer (with alignment rods threaded through holes when stacking the layers).
For a robust object, metal sheets could be used and adhered with thermite welding.