Dini surface is also known as the one-soliton surface.

Dini Surface Parametric Equations x = (u - t) y = (r * cos(v)) z = (r * sin(v)) Where: psi := aa; if (psi < 0.001) then psi := 0.001; if (psi > 0.999) then psi := 0.999; psi := psi * pi; sinpsi := sin(psi); cospsi := cos(psi); g := (u - cospsi * v) / sinpsi; s := exp(g); r := (2 * sinpsi) / (s + 1 / s); t := r * (s - 1 / s) * 0.5;