Relativity
Lorentz Transformation
\begin{bmatrix}
x'\\
t'\\
\end{bmatrix} = \begin{bmatrix}
\frac{1}{\sqrt{1 - \beta^2}} & -\frac{\beta}{\sqrt{1 - \beta^2}}\\
-\frac{\beta}{\sqrt{1 - \beta^2}} & \frac{1}{\sqrt{1 - \beta^2}}\\
\end{bmatrix}\begin{bmatrix}
x\\
t\\
\end{bmatrix}
where \beta \in [0, 1] is fraction of speed of light.
Relativistic Rendering
Strategies:
-
polygon rendering: Hsiung et al 1990, Gekelman 1991
-
4D ray tracing: Hsiung & Dunn 1989, Hsiung & Thibadeau 1990
-
image-based: fast observer, static environment - Weiskopf 2000, Savage 2007
-
local GPU ray tracing: Gumhold 2003, Reina&Erti 2005, Gascuel et al 2008
we would like to have interactive, multiple objects, different direction of motion
Keep in mind:
-
apparent bending and rotating of object
-
doppler shift
Table of Content