The kinematics of cutting solid objects

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Abstract

This paper studies how the cutting of one solid object by another can be described in a formal theory. We present two alternative first-order representations for this domain. The first views an object as gradually changing its shape until it is split, at which time the original object ceases to exist and two (or more) new objects come into existence. The second focuses instead on chunks of material which are part of the overall object. A chunk persists with constant shape until some pieces of it is cut away, when the chunk ceases to exist. We prove that the two theories are equivalent under ordinary circumstances, and we show that they are sufficient to support some simple commonsense inferences and algorithms.

Original languageEnglish (US)
Pages (from-to)253-305
Number of pages53
JournalAnnals of Mathematics and Artificial Intelligence
Volume9
Issue number3-4
DOIs
StatePublished - Sep 1 1993

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ASJC Scopus subject areas

  • Artificial Intelligence
  • Applied Mathematics

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