Computing Optimal Hatching Directions in Layered Manufacturing

In Layered Manufacturing, a three-dimensional polyhedral solid is built as a stack of two-dimensional slices. Each slice (a polygon) is built by filling its interior with a sequence of parallel line segments, of small non-zero width, in a process called hatching. A critical step in hatching is choosing a direction which minimizes the number of segments. Exact and approximation algorithms are given here for this problem, and their performance is analyzed both experimentally and analytically. Extensions to several related problems are discussed briefly.