Techniques for creating pop-up cards from 3D models

One embodiment of the invention is a pop-up engine that generates a pop-up card from a sliced 3D graphics model. In operation, the pop-up engine processes a sliced 3D model to identify locations where the sliced 3D model is to attach to a plane surface of a pop-up card. For a given set of slices associated with a sliced 3D model, the pop-up engine identifies at least two slices that intersect at a folding line of the plane surface. The pop-up engine then identifies locations on the slices that are the farthest from the folding line. The pop-up engine marks the identified locations as connection points, where the 3D model is to attach to the plane surface.