An optimal algorithm for 3D triangle mesh slicing

We describe an algorithm for slicing an unstructured triangular mesh model by a series of parallel planes. We prove that the algorithm is asymptotically optimal: its time complexity is O(nlogk+k+m) for irregularly spaced slicing planes, where n is the number of triangles, k is the number of slicing planes, and m is the number of triangle-plane intersections segments. The time complexity reduces to O(n+k+m) if the planes are uniformly spaced or the triangles of the mesh are given in the proper order. We also describe an asymptotically optimal linear time algorithm for constructing a set of polygons from the unsorted lists of line segments produced by the slicing step. The proposed algorithms are compared both theoretically and experimentally against known methods in the literature.