Relativity for games
Abstract
We present how to implement special relativity in computer games. The resultant relativistic world shows the time dilation and Lorentz contraction exactly, not only for the player but also for all the nonplayer characters, who obey the correct relativistic equation of motion according to their own accelerations. Causality is explicitly maintained in our formulation by use of the covariant velocities, proper times, worldlines, and light cones. Faraway relativistic scenes can be accurately projected onto the skydome. We show how to approximate a rigid body consisting of polygons, which is ubiquitous in computer games but itself is not a relativistically invariant object. We also give a simple idea to mimic the Doppler effect within the RGB color scheme.
Cite
@article{arxiv.1703.07063,
title = {Relativity for games},
author = {Daiju Nakayama and Kin-ya Oda},
journal= {arXiv preprint arXiv:1703.07063},
year = {2017}
}
Comments
Version appearing in PTEP; 48 pages, 8 figures including new Figs. 1 and 2 for sample game screens according to Referee's request; part of results presented in 2015 Annual (70th) Meeting, Physics Society of Japan (JPS) and in invited talk at 2015 Summer Conference, Digital Games Research Association (DiGRA) JAPAN