1. A method for producing a three-dimensional structure from a digital model, comprising: determining a plurality of two-dimensional layers in response to the digital model; rendering an image corresponding to each of the layers on each of a corresponding plurality of sheets of at least partially transparent material; and assembling the plurality of sheets of material together to produce a three-dimensional structure corresponding to the digital model, wherein the step of determining a plurality of two-dimensional layers comprises, for each layer: determining a vector corresponding to each pixel of the layer; determining a ray having an origin at the pixel and a direction parallel to the vector; determining an intersection of the ray with a surface of the digital model; and determining a color of the surface of the digital model at the intersection.