The rules of 4-dimensional perspective: How to implement Lorentz transformations in relativistic visualization

TL;DR

This paper introduces an efficient method using geometric algebra and complex quaternions to implement Lorentz transformations for relativistic visualization, demonstrated through an interactive black hole simulator.

Contribution

It presents a novel, efficient approach to applying Lorentz transformations in relativistic visualization using geometric algebra and complex quaternions, integrated into a black hole simulation.

Findings

Efficient implementation of Lorentz transformations using geometric algebra.

Integration into an interactive black hole flight simulator.

Robust and straightforward composition and interpolation of transformations.

Abstract

This paper presents a pedagogical introduction to the issue of how to implement Lorentz transformations in relativistic visualization. The most efficient approach is to use the even geometric algebra in 3+1 spacetime dimensions, or equivalently complex quaternions, which are fast, compact, and robust, and straightforward to compose, interpolate, and spline. The approach has been incorporated into the Black Hole Flight Simulator, an interactive general relativistic ray-tracing program developed by the author.