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RESEARCH PRODUCT

Salkowski curves revisited: A family of curves with constant curvature and non-constant torsion

Juan Monterde

subject

Mathematical analysisAerospace EngineeringDifferential geometry of curvesCurvatureComputer Graphics and Computer-Aided DesignConstant curvatureParametric surfaceModeling and SimulationFundamental theorem of curvesTorsion of a curveAutomotive EngineeringFamily of curvesConstant (mathematics)Mathematics

description

In the paper [Salkowski, E., 1909. Zur Transformation von Raumkurven, Mathematische Annalen 66 (4), 517-557] published one century ago, a family of curves with constant curvature but non-constant torsion was defined. We characterize them as space curves with constant curvature and whose normal vector makes a constant angle with a fixed line. The relation between these curves and rational curves with double Pythagorean hodograph is studied. A method to construct closed curves, including knotted curves, of constant curvature and continuous torsion using pieces of Salkowski curves is outlined.

yearjournalcountryeditionlanguage
2009-03-01Computer Aided Geometric Design
https://doi.org/10.1016/j.cagd.2008.10.002