Envelopes and tubular splines

Marco Paluszny and Francisco Tovar

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 79, issue 6, 1971-1976

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.

Keywords: Envelopes; Bézier conics; General cyclide; Tubular splines; Path splines (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2009:i:6:p:1971-1976

DOI: 10.1016/j.matcom.2007.04.014

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