Adjusted Enneper Surface

thingiverse

This is a minimal surface, which means that the mean curvature is zero. It's creation was inspired from the Weierstrass–Enneper parameterization f(z) = 1 and g(z) = z. The differential equation is completed with the implied f(z) = g(z)/h(z) where g is meromorphic (meaning a holomorphic function except on poles), f is analytic, and h is the harmonic function. The parameterization means it is differentiable everywhere on the complex plane (so, smooth). The changes to this function preserve affinity since the functions share the same associate family. Citation (recommended by source): Snyder, Evan, "Minimal Surfaces and The Weierstrass-Enneper Representation" (2020). Electronic Theses, Projects, and Dissertations. 1112. https://scholarworks.lib.csusb.edu/etd/1112