Computation of Offset Curves by the Huygens Principle

Михеев, А. А.; Nozik, M.; Rubinstein, Jacob

doi:10.1111/1467-8659.1340249

Cited by 4 publications

(2 citation statements)

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“…(In Figure 11, the rungs [45, 46], [27,28], and [13,14] form these gates.) Every channel is paired with a neighboring "dead end" (ladder): in the figure, channel I is paired with the dead end extending between [43, 44] and [1,2], channel II is paired with the dead end between [29,30] and [3,4], and III is paired with the dead end between [11,12] and [5,6]. For shorthand, we define A to be channel I and its paired dead end, B to be II and its dead end, and C to be III and its dead end.…”

Section: Hardness For Multiply Connected Pocketsmentioning

confidence: 99%

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Optimization Problems Related to Zigzag Pocket Machining

Arkin¹,

Held²,

Smith³

2000

Algorithmica

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A fundamental problem of manufacturing is to produce mechanical parts from billets by clearing areas within specified boundaries from the material. Based on a graph-theoretical formulation, the algorithmic handling of one particular machining problem-"zigzag pocket machining"-is investigated. We present a linear-time algorithm that ensures that every region of the pocket is machined exactly once, while attempting to minimize the number of tool retractions required. This problem is shown to be N P-hard for pockets with holes. Our algorithm is provably good in the sense that the machining path generated for a pocket with h holes requires at most 5 · OPT + 6 · h retractions, where OPT is the (unknown) minimum number of retractions required by any algorithm. The algorithm has been implemented, and practical tests for pockets without holes suggest that one can expect an approximation factor of about 1.5 for practical examples, rather than the factor 5 as proved by our analysis.

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Section: Hardness For Multiply Connected Pocketsmentioning

confidence: 99%

“…For shorthand, we define A to be channel I and its paired dead end, B to be II and its dead end, and C to be III and its dead end. The six top rungs of A, B, C,-i.e., [43,44], [45,46], [27,28], [29,30], [11,12], and [13,14]-are called entries to a clause gadget.…”

Section: Hardness For Multiply Connected Pocketsmentioning

confidence: 99%