27 results about "Circular surface" patented technology

In mathematics and, in particular, differential geometry a circular surface is the image of a map ƒ : I × S¹ → R³, where I ⊂ R is an open interval and S¹ is the unit circle, defined by f(t,θ):=γ(t)+r(t)𝐮(t)cosθ+r(t)𝐯(t)sinθ, where γ, u, v : I → R³ and r : I → R>0, when R>0 := { x ∈ R : x > 0 }. Moreover, it is usually assumed that u · u = v · v = 1 and u · v = 0, where dot denotes the canonical scalar product on R³, i.e. u and v are unit length and mutually perpendicular.