English

3-D Shadows of 4-D Algebraic Hypersurfaces in a 4-D Perspective

General Mathematics 2026-04-03 v2

Abstract

The paper is focused on the four-dimensional visualization of hypersurfaces represented by implicit equations without their parametrization. We describe a general method to find shadow boundaries in an arbitrary dimension and apply it in a three- and four-dimensional space. Furthermore, we design a system of polynomial equations to construct occluding contours of algebraic surfaces in a 4-D perspective. The method is presented on a composed 3-D scene and three 4-D cases with gradual complexity. In general, our goal is to improve the understanding of spatial properties in a four-dimensional space.

Keywords

Cite

@article{arxiv.2307.12986,
  title  = {3-D Shadows of 4-D Algebraic Hypersurfaces in a 4-D Perspective},
  author = {Jakub Řada and Michal Zamboj},
  journal= {arXiv preprint arXiv:2307.12986},
  year   = {2026}
}