Formal specification and theorem proving breakthroughs in geometric modeling

  • FranÇois Puitg
  • Jean -FranÇois Dufourd
Refereed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1479)


An innovative attempt to develop formal techniques in geometric modeling is reported through the axiomatization of the combinatorial maps in the Calculus of Inductive Constructions. A hierarchical specification of ordered sorts is presented and validated by inductive proofs of consistency and completeness in the Coq prover. Classical difficulties in theorem proving like cohabitation of objects with their generalization, smooth handling of subtyping, completion of partial relations or objects, observationality v. constructivism, and symmetry of relations, are addressed. Geometrical modeling issues are thus solved in a new and unquestionable fashion, giving a great insight on the domain and a deep understanding of the model, and so validating the methodology.


Geometric Modeling Boundary Representation Planarity Criterion Inductive Construction Inductive Definition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • FranÇois Puitg
    • 1
  • Jean -FranÇois Dufourd
    • 1
  1. 1.Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection LSIITUPRES-A 7005Illkirch CedexFrance

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