A Sham Schwarz Surface Based on a Squircle

Year: 2022 Authors: Chamberlain Fong; Douglas Dunham

Core claim

The sham Schwarz surface, defined by cos(x) + cos(y) + cos(z) = 0, can replace the mucube for hyperbolic pattern visualization and is the 3D counterpart of an oblique squircle.

Topics

hyperbolic tilings, triply periodic surfaces, implicit surfaces, squircle geometry, 3D visualization

Domains

hyperbolic geometry, minimal surfaces, crystallographic symmetry, implicit equations, Bézier approximation, mathematical visualization, generative patterning, computer graphics

Methods

Marching Cubes, bicubic Bézier patches, implicit surface modeling, texture mapping

Media

GeoGebra, Desmos, CalcPlot3D, Escher art, video overview

Source status

This page publishes metadata and extracted analytical signals only. Raw PDF and full OCR text are kept local for now.