English

Deformation Spaces and Static Animations

History and Overview 2022-11-16 v1 Computational Geometry Complex Variables

Abstract

We study applications of 3D printing to the broad goal of understanding how mathematical objects vary continuously in families. To do so, we model the varying parameter as the vertical axis of a 3D print, introducing the notion of a static animation: a 3D printed object each of whose layers is a member of the continuously deforming family. We survey examples and draw connections to algebraic geometry, complex dynamics, chaos theory, and more. We also include a detailed tutorial (with accompanying code and files) so that the reader can create static animations of their own.

Keywords

Cite

@article{arxiv.2211.08333,
  title  = {Deformation Spaces and Static Animations},
  author = {Gabriel Dorfsman-Hopkins},
  journal= {arXiv preprint arXiv:2211.08333},
  year   = {2022}
}

Comments

50 Pages, 52 figures. From the JMM Mini-Course "3D Printing in Mathematics: Challenges and Applications." Submitted to the conference proceedings in PSAPM. Comments are welcome

R2 v1 2026-06-28T05:58:13.655Z