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A Note on Interpolation with Hypo- and Epicycloidal Arcs

Citace: [] BASTL, B. A Note on Interpolation with Hypo- and Epicycloidal Arcs. 2010.
Druh: PŘEDNÁŠKA, POSTER
Jazyk publikace: eng
Anglický název: A Note on Interpolation with Hypo- and Epicycloidal Arcs
Rok vydání: 2010
Autoři: Ing. Bohumír Bastl Ph.D.
Abstrakt EN: Hypo- and epicycloids are well-known curves, in detail studied in classical geometry and widely used in many technical applications. Despite this fact, their Bezier representation, which allows to use these curves easily in CAD/CAM software packages, has been studied quite recently. In this talk we present the proof that all rational hypocycloids and epicycloids are curves with Pythagorean normals (PN curves), i.e., these curves have rational o ffsets, and we provide a method for fi nding their PN parametrization. Further, we use (implicit) support function representation of these curves for designing algorithms for G^1 and also G^2 Hermite interpolation with arcs of hypo- and epicycloids { we obtain so-called HE-splines as a one of the rare cases of interpolation techniques with rational PN curves. The algorithms will be demonstrated on several examples.
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