Geometric Constraint Propagation with Quantum Labels

  • Remco C. Veltkamp
  • Farhad Arbab
Conference paper
Part of the Focus on Computer Graphics book series (FOCUS COMPUTER)

Abstract

This paper presents an incremental approach to geometric constraint satisfaction that categorizes solutions into so-called quanta. A quantum is a range of solutions with uniform geometric characteristics. This approach is suitable for interactive design because it can handle (perhaps temporarily) incomplete specifications and alternative solutions, and performs satisfaction locally and incrementally. The intermediate solutions are kept in the geometric domain, so that new geometric constraints can be interpreted on the same high level of abstraction, allowing powerful reasoning. Both alternative discrete solutions and continuous ranges of solutions are determined. Propagation of information is performed by ‘propagation of known state’, and the information itself results from ‘solution set inference’, where a solution set is represented in geometrical form by unions and intersections of quantum labels. This representation allows the use of simple logical expressions of constraints, it uniformly handles delayed satisfaction, and it supports ‘constraint inference’, the derivation of implied constraints by geometric reasoning.

Keywords

Geometric Constraint Line Cylinder Geometric Reasoning Geometric Primitive Alternative Constraint 
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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References

  1. [1]
    F. Arbab and B. Wang. A Geometric Constraint Management System in Oar. In P.J.W. ten Hagen and P. Veerkamp, editors, Intelligent CAD Systems III–Practical Experience and Evaluation (Proceedings 3rd Eurographics Workshop on Intelligent CAD Systems, 1989), pages 231–252. EurographicSeminar Series, Springer-Verlag, 1991.Google Scholar
  2. [2]
    A. Horning. The Programming Language Aspects of ThingLab, a Constraint-Oriented Simulation Laboratory. ACM Transactions on Programming Languages and Systems, 3 (4): 353–387, October 1981.CrossRefGoogle Scholar
  3. [3]
    S.-C. Chou and X.-S. Gao. A Collection of 120 Computer Solved Geometry Problems in Mechanical Formula Derivation. Technical Report TR-89–22, University of Texas, Department of Computer Science, August 1989.Google Scholar
  4. [4]
    E. Davis. Constraint Propagation with Interval Labels. Artificial Intelligence, 32: 281–331, 1987.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    M.J.G.M. van Emmerik. A System for Interactive Graphical Modeling with 3D Constraints. In Proceedings CGI ‘80, 1990.Google Scholar
  6. [6]
    H.-W. Güsgen and J. Hertzberg. Some Fundamental Properties of Local Constraint Propagation. Artificial Intelligence, 36: 237–247, 1988.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    N.C. Heintze, S. Michaylov and P.J. Stuckey. CLP(IR) and Some Problems in Electrical Engineering. In J.-L. Lassez, editor, Proceedings of the 4th International Conference on Logic Programming, MIT Press, 1987.Google Scholar
  8. [8]
    W. Leler. Constraint Programming Languages, Their Specification and Generation. Addison-Wesley, 1988.Google Scholar
  9. [9]
    V.C. Lin, D.C. Gossard and R.A. Light. Variational Geometry in Computer-Aided Design. Proceedings SIGGRAPH ‘81, Computer Graphics, 15 (3): 171–177, August 1981.CrossRefGoogle Scholar
  10. [10]
    A.K. Mackworth. Consistency in Networks of Relations. Artificial Intelligence, pages 99–118, 1977.Google Scholar
  11. [11]
    G. Nelson. Juno, a Constraint-based Graphics System. Proceedings SIGGRAPH ‘85, Computer Graphics, 19 (3): 235–243, 1985.CrossRefGoogle Scholar
  12. [12]
    J.C. Owen. Algebraic Solution for Geometry from Dimensional Constraints. In Proceedings of the ACM Conference on Solid Modeling, pages 397–407. ACM Press, 1991.Google Scholar
  13. [13]
    J.R. Rossignac. Constraints in Constructive Solid Geometry. In F. Crow and S.M. Pizer, editors, Proceedings of the 1986 ACM Workshop on Interactive 3D Graphics, pages 93–110. ACM Press, 1986.Google Scholar
  14. [14]
    Zs. Ruttkay. A Co-operative Graphical Editor Based on Dynamically Constrained Objects. In C. Laffra and E. Blake, editors, Advances in Object-Oriented Graphics II (Proceedings of the second Eurographics Workshop on Object-Oriented Graphics, 1991), EurographicSeminars Series, Springer-Verlag, to appear in 1992.Google Scholar
  15. [15]
    G.L. Steele Jr. and G.J. Sussman. CONSTRAINTS. APL Quote Quad, 9(4—Part 1):208 — 225, June 1979.Google Scholar
  16. [16]
    I. Sutherland. Sketchpad: A Man-Machine Graphical Communication System. In Proceedings of the Spring Joint Computer Conference (IFIPS), pages 329 — 345, 1963.Google Scholar
  17. [17]
    R.C. Veltkamp. Geometric Constraint Management with Quanta. In D.C. Brown, M. Waldron and H. Yoshikawa, editors, Proceedings of the IFIP TC5/WG5.2 Working Conference on Intelligent Computer Aided Design, 1991, North-Holland, to appear in 1992.Google Scholar
  18. [18]
    R.C. Veltkamp. A Quantum Approach to Geometric Constraint Satisfaction. In C. Laffra and E. Blake, editors, Advances in Object Oriented Graphics II (Proceedings of the 2nd Eurographics Workshop on Object Oriented Graphics, 1991), EurographicSeminar Series, Springer-Verlag, to appear in 1992.Google Scholar
  19. [19]
    D.L. Waltz. Generating Semantic Descriptions from Drawings of Scenes with Shadows. PhD thesis, MIT, 1972.Google Scholar

Copyright information

© EUROGRAPHICS The European Association for Computer Graphics 1992

Authors and Affiliations

  • Remco C. Veltkamp
  • Farhad Arbab

There are no affiliations available

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