Fast Generation of Pointerless Octree Duals

Geometry processing applications frequently rely on octree structures, since they provide simple and efficient hierarchies for discrete data. However, octrees do not guarantee direct continuous interpolation of this data inside its nodes. This motivates the use of the octree's dual structure, which is one of the simplest continuous hierarchical structures. With the emergence of pointerless representations, with their ability to reduce memory footprint and adapt to parallel architectures, the generation of duals of pointerless octrees becomes a natural challenge. This work proposes strategies for dual generation of static or dynamic pointerless octrees. Experimentally, those methods enjoy the memory reduction of pointerless representations and speed up the execution by several factors compared to the usual recursive generation.