Ding dong - singular algebraic surface

thingiverse

Ding dong, a unique geometric surface of degree four emerges. This is the set of real points where \x^2 + y^2 + z^3 - z^2 = 0.\ Has a single singularity, a bounded cluster, and an unbounded border! I have provided these files: * `dingdong_thickened_smooth_fixed.stl` -- has normal vectors fixed, and is thickened for printing. * `blocky_fixed_2.stl` -- the blocky version, good for printing. 2, because it's number two. * `dingdong_raw_smooth.stl` -- raw triangulation coming from Bertini_real. Since the program works in arbitrary dimensions, I make no effort to control normals from it -- they don't exist for four- and higher-dimensional surfaces, but instead a tangent space which is not immediately useful for 3d printing. Hence, the surface was thickened in Blender, before being passed through Microsoft's 3D Builder to fix internal geometry. The raw versions are not directly suitable for 3d printing. Infinitely thin, ran through `sampler` with fairly tight tolerances. * `input` -- the Bertini_real input file used to compute it. 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](https://bertinireal.com) and printed as part of my long-term project to reproduce [Herwig Hauser's gallery of algebraic surface ray-traces](http://homepage.univie.ac.at/herwig.hauser/gallery.html) in [my own gallery of 3d prints](https://danibrake.org/gallery). The ACM ToMS algorithm number is 976; the major published paper is [DOI 10.1145/3056528](https://doi.org/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](https://www.thingiverse.com/ofloveandhate/collections/algebraic-surfaces).