In Layered Manufacturing (LM), a prototype of a virtual polyhedral object is built by slicing the object into polygonal layers, and then building the layers one after another. In StereoLithography, a specific LM-technology, a layer is built using a laser which follows paths along equally-spaced parallel lines and hatches all segments on these lines that are contained in the layer. We consider the problem of computing a direction of these lines for which the number of segments to be hatched is minimum, and present an algorithm that solves this problem exactly. The algorithm has been implemented and experimental results are reported for real-world polyhedral models obtained from industry.
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.
Shrinking process geometries and frequency scaling give rise to an increasing number of interconnects that require multiple clock cycles. This paper explores efficient techniques to insert flip-flops and latches to meet pre-determined latency and margin constraints at the receivers. Previous approaches push timing margins to either ends of interconnect. We present an O(n log n)-time algorithm to insert flipflops that evens out timing margins across the entire interconnect, resulting in more robust designs and faster design convergence. An O(n log n)-time extension to handle symmetric, two-phases latches is also presented. Experimental results verify the correctness and practicality of our approach.
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