Skip to main content
SpringerLink
Log in

The kinematics of cutting solid objects

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. Davis, A logical framework for commonsense predictions of solid object behavior, AI in Eng. 3(1988)125–140.

    Google Scholar 

  2. E. Davis,Representations of Commonsense Knowledge (Kaufmann, San Mateo, CA, 1990).

    Google Scholar 

  3. E. Davis, Infinite loops in finite time: Some observations, in:Proc. 3rd Int. Symp. on Principle of Knowledge Representation and Reasoning, ed. B. Rich, C. Nebel and W. Swartout (Kaufmann, 1992).

  4. B. Faltings, Qualitative kinematics in mechanisms,Proc. 10th IJCAI (1987) pp. 436–442.

  5. C. Hoffmann,Geometric and Solid Modelling (Kaufmann, San Mateo, CA, 1990).

    Google Scholar 

  6. L. Joskowicz, Shape and function in mechanical devices,Proc. 6th AAAI (1987) pp. 611–618.

  7. D. McDermott, A temporal logical for reasoning about processes and plans, Cognitive Sci. 2(1982)277–282.

    Google Scholar 

  8. A.A.G. Requicha, Representations for rigid solids: Theory, methods and systems, ACM Computing Surveys 12(1980)437–464.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Courant Institute, 10012, New York, NY, USA

    Ernest Davis

Authors
  1. Ernest Davis
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research has been supported by NSF Grant No. IRI-9001447.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Davis, E. The kinematics of cutting solid objects. Ann Math Artif Intell 9, 253–305 (1993). https://doi.org/10.1007/BF01530935

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01530935

Keywords

Search

Navigation