Computing Optimal Hatching Directions in Layered Manufacturing

Abstract

Abstract. 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.

Geometric algorithms for layered manufacturing

“…This heuristic is described in [9], and in the Master's thesis [11] of Man Chung Hon, who graduated in 2000 at the University of Minnesota. A summary of our work on the hatching problem appears in [10].…”

Casting with Skewed Ejection Direction

“…The manufacturing industry has at its disposal a number of processes for constructing objects, including gravity casting, injection molding [7], [21], stereolithography [3], NC-machining [10], [11], and layered manufacturing [15], [12], [19]. In all of these manufacturing contexts, computer-aided design systems of growing sophistication are presently being introduced, and more and more real-world objects are modeled as geometric objects within a computer.…”