Rendering kaleidoscopic scenes using orbifold theory

Kaleidoscopes create fascinating visual effects due to the presence of multiple mirrors placed at carefully designed distances and angles. These effects, such as infinite repeating copies of a single object, are difficult to capture. Moreover, lighting and shadow effects in kaleidoscopic scenes are highly impacted by the interaction between lights and mirrors. Such effects pose challenges to existing rendering techniques such as ray tracing and photon mapping. In this paper, we present a unified framework to render scenes from the perspective of a viewer inside a kaleidoscope based on Orbifold theory, which provides the mathematical foundation to describe the position and orientation of reflected objects (including light sources). Our framework is able to accurately capture the global illumination effects inside a kaleidoscope. We demonstrate the power of our technique with the rendering of a number of scenes including animation.