Towards a Geometric-Object-Oriented Language

  • Tielin Liang
  • Dongming Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3763)


This paper proposes a geometric-object-oriented language for symbolic geometric computation, reasoning, and visualization. In this language, geometric objects are constructed with indefinite parametric data. Modifications and basic operations on these objects are enabled. Degeneracy and uncertainty are handled effectively by means of imposing conditions and assumptions and geometric statements are formulated by declaring relations among different objects. A system implemented on the basis of this language will allow the user to perform geometric computation and reasoning rigorously and to prove geometric theorems and generate geometric diagrams and interactive documents automatically. We present the overall design of the language, explain the capabilities, features, main components of the proposed system, provide specifications for some of its functors, report our experiments with a preliminary implementation of the system, and discuss some encountered difficulties and research problems.


Geometric Meaning Geometric Constraint Geometric Object Algebraic Expression Geometric Relation 
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 2006

Authors and Affiliations

  • Tielin Liang
    • 1
  • Dongming Wang
    • 2
    • 3
  1. 1.Department of MathematicsUniversity of Science and Technology of ChinaHefeiChina
  2. 2.LMIB – School of ScienceBeihang UniversityBeijingChina
  3. 3.Laboratoire d’Informatique de Paris 6Université Pierre et Marie Curie – CNRSParisFrance

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