Assembling Algebraic Surfaces

Abstract

Algebraic surfaces are beautiful objects that describe sets of space where a system of polynomials vanishes. Their surface is smooth, but can have corners, cusps, self-intersections, and sharp points. When 3D printing such surfaces, the smooth places are simple. Singularities, where the surface meets at a single point of no dimension, occur at all corners and crossings. This lack of dimensions at singularities presents inherent problems for accurately representing a 3D model. Past methods for creating a 3D printed model rely on global solidification, applying a thickness to the entire model, forcing the singularity to appear as a smooth surface.