Molecular mechanics and dynamics simulations use distance based cutoff approximations for faster computation of pairwise van der Waals and electrostatic energy terms. These approximations traditionally use a precalculated and periodically updated list of interacting atom pairs, known as the "nonbonded neighborhood lists" or nblists, in order to reduce the overhead of finding atom pairs that are...

In a current research project, our group is developing a 3D Spatial Query Language for Building Information Models. Among other features, the spatial language includes metric operators, i.e. operators that depend on the distance between 3D spatial objects. To implement these operators, a fast and well-scaling algorithm based on the octree-encoded discretized geometry for computing the distance ...

The accurate matching of 3D anatomical surfaces with sensory data such as 2D X-ray projections is a basic problem in Computer and Robot Assisted Surgery. In model-based vision, this problem can be formulated as the estimation of the spatial pose (position and orientation) of a 3D smooth object from 2D video images. We present a new method for determining the rigid body transformation that descr...

We present scalable algorithms for parallel adaptive mesh refinement and coarsening (AMR), partitioning, and 2:1 balancing on computational domains composed of multiple connected two-dimensional quadtrees or three-dimensional octrees, referred to as a forest of octrees. By distributing the union of octants from all octrees in parallel, we combine the high scalability proven previously for adapt...

This work emerged from the following observation: usual search procedures for octrees start from the root to retrieve the data stored at the leaves. But since the leaves are the farthest nodes to the root, why start from the root? With usual octree representations, there is no other way to access a leaf. However, hashed octrees allow direct access to any node, given its position in space and it...

An algorithm is described that updates an object's octree representation as the object is linearly translated through space. This is accomplished by performing simple arithmetic on the path representations of the nodes to be translated. Among others, one advantage of the algorithm is in devising collision-free and efficient trajectories of moving objects in robotics.

IN [1], in Figs. 1, 2, 3, and 4, all occurrences of “-” between words and all occurrences of a space between words are gone; as a result, some words are also not aligned with the boxes and some occurrences of “)” also do not appear in the right places. Corrections: Figs. 1, 2, 3, and 4 in [1] should have appeared as follows (the correct version of [1] is available from the author’s Web site: ht...