Reliable Computing

, Volume 6, Issue 1, pp 81–92 | Cite as

Interval Constraint Plotting for Interactive Visual Exploration of Implicitly Defined Relations

  • Timothy J. Hickey
  • Zhe Qju
  • Maarten H. Van Emden


Conventional plotting programs adopt techniques such as adaptive sampling to approximate, but not to guarantee, correctness and completeness in graphing functions. Moreover, implicitly defined mathematical relations can impose an even greater challenge as they either cannot be plotted directly, or otherwise are likely to be misrepresented. In this paper, we address these problems by investigating interval constraint plotting as an alternative approach that plots a hull of the specified curve. We present some empirical evidence that this hull property can be achieved by a \(\mathcal{O}(n)\) algorithm. Practical experience shows that the hull obtained is the narrowest possible whenever the precision of the underlying floating-point arithmetic is adequate. We describe IASolver, a Java applet ( that serves as testbed for this idea.


Mathematical Modeling Empirical Evidence Computational Mathematic Industrial Mathematic Practical Experience 


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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Timothy J. Hickey
    • 1
  • Zhe Qju
  • Maarten H. Van Emden
    • 2
  1. 1.Michtom School of Computer ScienceBrandeis UniversityWalthamUSA
  2. 2.Department of Computer ScienceUniversity of VictoriaVictoriaCanada

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