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Envelopes and tubular splines

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  • Paluszny, Marco
  • Tovar, Francisco

Abstract

Envelopes of monoparametric families of spheres determine canal surfaces. In the particular case of a quadratic family of spheres the envelope is an algebraic surface of degree four that is composed of circles. We are interested in the construction of smooth tubular splines with pieces of envelopes of quadratic families of spheres. We present a scheme for the construction of a tubular spline that interpolates a sequence of circles in 3D. We control the shape near each circle by prescribing a sphere that contains it and is tangent to the spline. We offer further shape handles for local control through weights that are assigned to the controlling spheres.

Suggested Citation

  • Paluszny, Marco & Tovar, Francisco, 2009. "Envelopes and tubular splines," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(6), pages 1971-1976.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:6:p:1971-1976
    DOI: 10.1016/j.matcom.2007.04.014
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    References listed on IDEAS

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    1. Franquiz, J. & Paluszny, M. & Tovar, F., 2006. "Cyclides and the guiding circle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(1), pages 168-174.
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