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Automatic determination of envelopes and other derived curves within a graphic environment

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  • Botana, Francisco
  • Valcarce, José L.

Abstract

Dynamic geometry programs provide environments where accurate construction of geometric configurations can be done. Nevertheless, intrinsic limitations in their standard development technology mostly produce objects that are equationally unknown and so can not be further used in constructions. In this paper, we pursue the development of a geometric system that uses in the background the symbolic capabilities of two computer algebra systems, CoCoA and Mathematica. The cooperation between the geometric and symbolic modules of the software is illustrated by the computation of plane envelopes and other derived curves. These curves are described both graphically and analytically. Since the equations of these curves are known, the system allows the construction of new elements depending on them.

Suggested Citation

  • Botana, Francisco & Valcarce, José L., 2004. "Automatic determination of envelopes and other derived curves within a graphic environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 67(1), pages 3-13.
    • Handle: RePEc:eee:matcom:v:67:y:2004:i:1:p:3-13
    DOI: 10.1016/j.matcom.2004.05.004
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    References listed on IDEAS

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    1. Botana, F. & Valcarce, J.L., 2003. "A software tool for the investigation of plane loci," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(2), pages 139-152.
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    Cited by:

    1. Marco, Ana & Martínez, José-Javier, 2007. "Structured matrices in the application of bivariate interpolation to curve implicitization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(6), pages 378-385.
    2. Botana, Francisco & Recio, Tomas, 2016. "Some issues on the automatic computation of plane envelopes in interactive environments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 125(C), pages 115-125.
    3. Roanes-Lozano, Eugenio & van Labeke, Nicolas & Roanes-Macías, Eugenio, 2010. "Connecting the 3D DGS Calques3D with the CAS Maple," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(6), pages 1153-1176.
    4. Botana, Francisco, 2014. "A parametric approach to 3D dynamic geometry," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 104(C), pages 3-20.

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    4. Escribano, Jesús & Botana, Francisco & Abánades, Miguel A., 2010. "Adding remote computational capabilities to Dynamic Geometry Systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(6), pages 1177-1184.

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