Geometric algebra, an up-and-coming field of mathematics, has
found its way into video games thanks to Geomerics, a British startup.
Although the company has yet to release details of their products, they've recently published some information on
technology advances made possible by geometric algebra which help add further realism into gaming.
Currently, lighting in games is a toss-up between three elements: in real life, light often changes position (e.g. as the sun moves across the sky); objects cast shadows, which are often quite subtle; and depending on your viewpoint, you can sometimes see light sources reflected in other objects. The usual method is to pre-calculate the shadows in a scene and paint them on the ground, but this means the light source must stay fixed. Thanks to next-gen computing power, spherical harmonic lighting can be used to generate soft, lifelike shadows from moving light sources, but without any of the shiny surface effects that complete the picture and add realism.
Geomerics' development, using geometric algebra and wavelet technologies, allows all three elements to be computed in realtime: moving light sources, soft shadows and glossy surfaces. Hopefully this means that next-gen graphics can get even better.