Keskeiset käsitteet
This research paper presents a novel method for generating focal curves of 3D curves on a torus, derived from regular planar curves, by leveraging the relationship between their differential geometric invariants.
Tilastot
The torus has a major radius 'a' and a minor radius 'b', where a > b > 0.
Epicycloids are generated by rolling a circle of radius 'r' around a fixed circle of radius 'R', where R+2r ≤ a+b.
Hypocycloids are generated by rolling a circle of radius 'r' inside a fixed circle of radius 'R', where |2r-R| ≥ a-b.