Slicing Triangle Meshes: An Asymptotically Optimal Algorithm

Additive Manufacturing, popularly known as "3D printing", is a manufacturing process based on overlapping of flat layers in order to build a physical object. The data for building this object comes from a 3D model, usually represented by a triangle mesh. One of the first stages in this process is to slice the triangle mesh, resulting in 2.5-D contours, representing each one of the layers of the object. There are many strategies for slicing meshes, however most of the current literature is concerned with ad hoc issues such as the quality of the model, specific improvements in the slicing process and memory usage, whereas none of them addresses the problem from an algorithmic complexity perspective. While current algorithms for slicing run on O(n(2) + k(2)) or O(n(2) + n log n (k) over bar) for n triangles and k planes, the algorithm proposed in this paper runs on O(n (k) over bar), where (k) over bar is the average number of slices cutting each triangle, what is asymptotically the best that can be achieved under certain common assumptions.