Solitude - singular algebraic surface

thingiverse

Solitude is a singular algebraic surface of degree four, comprising the set of real points for which x^2*y*z +x*y^2+y^3+y^3*z-x^2*z^2 equals zero. It boasts two holes and two singular lines, one existing nakedly in the voids within the surface. Three files are provided: solitude_thickened.stl, which has normal vectors fixed and is thickened for printing; solitude_raw.stl, a raw triangulation coming from Bertini_real that needs further processing before being suitable for 3d printing; and input, the Bertini_real input file used to compute it. Computed with a Numerical Algebraic Geometry program called Bertini_real, this surface was printed as part of a 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. See also my Thingiverse collection of algebraic surfaces at https://www.thingiverse.com/ofloveandhate/collections/algebraic-surfaces.