Tetrahedron, octahedron and rhombohedron

Aluminum-Centered Tetrahedron-Octahedron Transition in Advancing Al-Sb-Te Phase Change Properties

Group IIIA elements, Al, Ga, or In, etc., doped Sb-Te materials have proven good phase change properties, especially the superior data retention ability over popular Ge2Sb2Te5, while their phase transition mechanisms are rarely investigated. In this paper, aiming at the phase transition of Al-Sb-Te materials, we reveal a dominant rule of local structure changes around the Al atoms based on ab i...

Fast Tetrahedron-Tetrahedron Overlap Algorithm

We present an algorithm to test two tetrahedra for overlap. The algorithm is based on a dimension reduction technique that allows to apply the Separating Axis Theorem avoiding part of the computation needed to perform the Separating Axis Test. Source code is available online.

The Octahedron Abstract Domain

An interesting area in static analysis is the study of numerical properties. Complex properties can be analyzed using abstract interpretation, provided that an adequate abstract domain is defined. Each domain can represent and manipulate a family of properties, providing a different trade-off between the precision and complexity of the analysis. The contribution of this paper is a new numerical...

Octahedron Environment Maps

In this paper, we examine the octahedron as a parameterization scheme to represent environment maps in real-time rendering applications. We discuss two projection schemes and show two convenient unfold mappings to pack the platonic solid into quadratic or rectangular textures. We carry out an analysis and consider rendering performance for interactive applications as well as the quality of repr...

Arrays and the Octahedron Recurrence