Unistable polyhedra are in equilibrium on only one of their faces. The smallest known homogeneous unistable polyhedron to date has 18 faces. Using a new optimization algorithm, we have found a unistable polyhedron with only 14 faces, which we believe to be a lower bound. Despite the simplicity of the formulation, computers were never successfully used for solving this problem due to the seemingly insurmountable dimensionality of the underlying mathematical apparatus.

We propose a new texture sampling approach that preserves crisp
silhouette edges when magnifying during close-up viewing, and benefits
from image pre-filtering when minifying for viewing at farther
distances.
During a pre-processing step, we extract curved silhouette edges from
the underlying images. These edges are used to adjust the texture
coordinates of the requested samples during magnification. The
original image is then sampled -- only once!

Translucent objects such as fog, clouds, smoke, glass, ice, and liquids are pervasive in cinematic environments because they frame scenes in depth and create visually-compelling shots.

Renderers apply alpha testing to mask out complex silhouettes using alpha textures on simple proxy geometry. While widely used, alpha testing has a long-standing problem that is underreported in the literature, but observable in commercial games: geometry can entirely disappear as alpha mapped polygons recede with distance.

We introduce a new data structure and algorithms that employ it to compute real-time global illumination from static environments. Light field probes encode a scene’s full light field and internal visibility. They extend current radiance and irradiance probe structures with per-texel visibility information similar to a G-buffer and variance shadow map. We apply ideas from screen-space and voxel cone tracing techniques to this data structure to efficiently sample radiance on world space rays, with correct visibility information, directly within pixel and compute shaders.