Search results for "Fundamental theorem of curves"

showing 2 items of 2 documents

On the number of singularities, zero curvature points and vertices of a simple convex space curve

1995

We prove a generalization of the 4 vertex theorem forC3 closed simple convex space curves including singular and zero curvature points.

Convex analysisCombinatoricsFundamental theorem of curvesConvex polytopeConvex curveMathematical analysisConvex setTotal curvatureFour-vertex theoremGeometry and TopologyCurvatureMathematicsJournal of Geometry
researchProduct

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

2009

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.

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)MathematicsComputer Aided Geometric Design
researchProduct