Parabolic cyclide

 From: bemfarmer 5 Sep 2017  (1 of 6)
 Parabolic cyclide: _FxGraph3D (a/2)*(2*v*v + b*(1-u*u-v*v))/(1+u*u+v*v);(a*u)*(v*v+b)/(1+u*u+v*v);(a*v)*(1+u*u-b)/(1+u*u+v*v);-10;10;-10;10;50;50;1;0.5;1;UV Network works at this density. Open circles show up in v mode, or u mode. The u and v in the parametric equation range over +/- infinity, so the circles are not closed. The open circles could be replaced with 3 point circles, and lofted... Parabola1: _FxGraph3D u*u;0;sqrt(2)*u;-3.536;3.536;0;1;20;0;1;0;1;UV Parabola2: _FxGraph3D 0.5 - 0.5*u*u;-u;0;-5;5;0;1;20;0;1;0;1;UV The parametric formulas for the two parabolas were mathematically manipulated to match the two standard formula formats. - Brian Formulas from Wikipedia and: http://www.math-only-math.com/parametric-equations-of-a-parabola.html

 From: mkdm 5 Sep 2017  (2 of 6)
 8576.2 In reply to 8576.1 Thanks a lot bemfarmer! Wow! Awesome formula!! Bye. - Marco (mkdm)

 From: Mike (MGG942) 5 Sep 2017  (3 of 6)
 8576.3 In reply to 8576.1 Brian, loft seems to work OK on u, or v, curves without any changes to the formula you provided. Further, an extrusion of either lofted surface will produce a solid. I like the shape - reminds me of a 4 leaved clover. Mike.