Distel - smooth algebraic surface by ofloveandhate

Last crawled date: 3 years, 1 month ago

Distel, a smooth algebraic surface of degree six. This is the set of real points for which
x^2+y^2+z^2+1000 * (x^2+y^2)*(x^2+z^2)*(y^2+z^2)-1 = 0.
Has no holes! Has no singularities! Is actually smooth at its points! Not actually pointed! Topologically equivalent to a sphere!
I have provided these files:
Distel_Super_Smooth.stl -- sampled to decently tight tolerances.
Distel_Newsmooth.stl -- surprisingly, an older version of the sampler was used to refine it. Take the name with a grain of salt. Enjoy
input -- the Bertini_real input file used to compute it.
One of the first surfaces I computed with Bertini_real, in early 2014.
This surface was sampled before I implemented cyclenumber > 1 sampling, so the surface is undersampled near critical points and singularities.
Computed with a Numerical Algebraic Geometry program I wrote, called Bertini_real and printed as part of my long-term project to reproduce Herwig Hauser's gallery of algebraic surface ray-traces in my own gallery of 3d prints. The ACM ToMS algorithm number is 976; the major published paper is DOI 10.1145/3056528 with several others preceding. Bertini_real implements the implicit function theorem for algebraic surfaces and curves in any (reasonable) number of variables.
These surfaces are generally challenging to print. Rotate, and use careful support. I use Simplify3D for the manual support placement feature. These surfaces are also very tiny in scale (arbitrary units and math and all) so require significant upsizing.
See also, my Thingiverse collection of algebraic surfaces.