Visual appearance of wireframe objects in special relativity

TL;DR

This paper derives how wireframe objects appear in special relativity, providing a method to visualize their appearance from any observer's perspective, useful for education and research.

Contribution

It offers a complete derivation and implementation for visualizing the apparent positions of wireframe objects in special relativity, facilitating educational and research applications.

Findings

Derived formulas for apparent positions of points and complex objects

Implemented visualization tools in Python and Asymptote

Scripts suitable for undergraduate teaching and student projects

Abstract

The visual appearance of a moving object in special relativity can be constructed in a straightforward manner when representing the surface of the object, or at least a wire frame model of it, as a point cloud. The apparent position of each individual point is then found by intersecting its worldline with the observer's backward light cone. In this paper, we present a complete derivation of the apparent position of a point and some more complex geometric objects for general parameter settings (configurations). We implemented our results in python and asymptote and used these tools to generate scripts that create the figures in this paper. These scripts are directly applicable in an undergraduate course to special relativity and can also serve as the basis for student projects with the aim to study more complex sceneries.