Search results for "Pythagorean hodograph"

showing 2 items of 2 documents

A Characterization of Quintic Helices

2005

A polynomial curve of degree 5, @a, is a helix if and only if both @[email protected]^'@? and @[email protected]^'@[email protected]^''@? are polynomial functions.

PolynomialTheorem of LancreteducationComputingMilieux_LEGALASPECTSOFCOMPUTINGCharacterization (mathematics)behavioral disciplines and activitiesMathematics::Algebraic TopologyCombinatoricsMathematics - Geometric TopologyTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYhealth services administrationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONFOS: Mathematicshealth care economics and organizationsMathematicsPhysics::Biological PhysicsQuantitative Biology::BiomoleculesDegree (graph theory)InformationSystems_INFORMATIONSYSTEMSAPPLICATIONSApplied MathematicsMathematical analysisGeometric Topology (math.GT)Pythagorean hodograph curveshumanitiesQuintic functionComputational MathematicsGeneralized polynomial helices
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An isoperimetric type problem for primitive Pythagorean hodograph curves

2012

An isoperimetric type problem for primitive Pythagorean hodograph curves is studied. We show how to compute, for each possible degree, the Pythagorean hodograph curve of a given perimeter enclosing the greatest area. We also discuss the existence and construction of smooth solutions, obtaining a relationship with an interesting sequence of Appell polynomials.

Pure mathematicsSequenceDegree (graph theory)Mathematics::General MathematicsMathematical analysisAerospace EngineeringPythagorean fieldType (model theory)Computer Graphics and Computer-Aided DesignPythagorean hodographNonlinear Sciences::Exactly Solvable and Integrable SystemsModeling and SimulationPythagorean tripleAutomotive EngineeringIsoperimetric inequalityMathematicsComputer Aided Geometric Design
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