Calyx - singular algebraic surface

thingiverse

Calyx, a singular algebraic surface of degree five. This is the set of real points for which ``` x^2+y^2*z^3 - z^4 = 0. ``` Has a point singularity on a cusp-line singularity. I have provided these files: * `Calyx_blocky_xy.stl` -- has the normal vectors fixed, and is thickened for printing. * `calyx_medium_smooth_xy.stl` -- the blocky version, ran through the `sampler` module for `bertini_real`. * `calyx_raw_blocky.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 4- 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. * `calyx_raw_medium_smooth.stl` -- infinitely thin, but ran through `sampler` with medium tolerances. * `calyx_raw_refined.stl` -- 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. See also, [my Thingiverse collection of algebraic surfaces](https://www.thingiverse.com/ofloveandhate/collections/algebraic-surfaces).