Hyperbolic Helicoid

Hyperbolic Helicoid. I like how it looks with two spheres. x = sinh(v)*cos(a*u)/( 1 + cosh(u)*cosh(v) ) y = cosh(v)*sinh(u)/( 1 + cosh(u)*cosh(v) ) z = sinh(v)*sin(a*u)/( 1 + cosh(u)*cosh(v) ) a = 6 -4 <= u <= 4 -4 <= v <= 4

Proyección estereográfica de una pieza de papel picado. ¡Feliz día de muertos!

Topology + Astronomy, all objects here are parametric surfaces :D

Lawson minimal surface (u,v)->(x,y,z)

Playing with supershapes and toroidal projections #python #C4D #coding #supershapes #generative #toroidal #generativeart #superformulas #generativedesign

I don't know how to name this :D #loop #C4D #Cinema4D #3Dart #3D #SuperMario #Torus

And using the normal vector, you can get something like this, taking the depth, but as this is a non-orientable surface, the U,V,W object needs to be mirrored 😬

Testing with a growing region algorithm I forgot to change the Kernel and the growing effect is beautiful 😬

Proyección estereografica de una pieza de papel picado. ¡Feliz día de muertos! Soc. Matemática Mex.

And you can plot it! using: r = 4*(1-cos(u)/2) x =(a*cos(u)*(1+sin(u))+r(u)*cos(u)*cos(v))*(u<=pi)+ (a*cos(u)*(1+sin (u)) + r(u)*cos(v+pi))*(u>pi) y = (b * sin(u)+r(u)*sin(u)*cos(v))*(u <= pi)+ (b*sin(u))*(u>pi) z = (r(u)*sin(v))*(u<=pi)+ (r(u)*sin(v))*(u > pi) a=2.7 b= 12.8

Happy to share that my plugin ParaSurface for Cinema4D is now available for free at jmmorph.gumroad.com/l/ParaSurface I used this plugin to create all these animations. This is an Open source repository, any feedback and donation is welcome :D