Searchlight and Doppler effects in the visualization of special relativity: a corrected derivation of the transformation of radiance

ABSTRACT

We demonstrate that a photo-realistic image of a rapidly moving object is dominated by the searchlight and Doppler effects. Using a photon-counting technique, we derive expressions for the relativistic transformation of radiance. We show how to incorportate the Doppler and searchlight effects in the two common techniques of special relativistic visualization, namely ray tracing and polygon rendering. Most authors consider geometrical appearance only and neglect relativistic effects on the lighting model. Chang et al. [1996] present an incorrect derivation of the searchlight effect, which we compare to our results. Some examples are given to show the results of image synthesis with relativistic effects taken into account.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS

Additional Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.7 Three-Dimensional Graphics and Realism
          Subjects: Color, shading, shadowing, and texture

  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Physics

General Terms:
Algorithms, Theory

Keywords:
Doppler effect, Lorentz transformation, aberration of light, illumination, searchlight effect, special relativity