Recursive Algorithms for Distributed Forests of Octrees

The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based applications. Although linear octrees, which store only leaf octants, have an underlying tree structure by definition, it is not often exploited in previously published mesh-related algorithms. This is because the branches are not explicitly stored, and because the topological relationships in meshes, such as the adjacency between cells, introduce dependencies that do not respect the octree hierarchy. In this work we combine hierarchical and topological relationships between octree branches to design efficient recursive algorithms. We present three important algorithms with recursive implementations. The first is a parallel search for leaves matching any of a set of multiple search criteria. The second is a ghost layer construction algorithm that handles arbitrarily refined octrees that are not covered by previous algorithms, which require a 2:1 condition between neighboring leaves. The third is a universal mesh topology iterator. This iterator visits every cell in a domain partition, as well as every interface (face, edge and corner) between these cells. The iterator calculates the local topological information for every interface that it visits, taking into account the nonconforming interfaces that increase the complexity of describing the local topology. To demonstrate the utility of the topology iterator, we use it to compute the numbering and encoding of higher-order $C^0$ nodal basis functions. We analyze the complexity of the new recursive algorithms theoretically, and assess their performance, both in terms of single-processor efficiency and in terms of parallel scalability, demonstrating good weak and strong scaling up to 458k cores of the JUQUEEN supercomputer.Comment: 35 pages, 15 figures, 3 table

3D Reconstruction & Assessment Framework based on affordable 2D Lidar

Lidar is extensively used in the industry and mass-market. Due to its measurement accuracy and insensitivity to illumination compared to cameras, It is applied onto a broad range of applications, like geodetic engineering, self driving cars or virtual reality. But the 3D Lidar with multi-beam is very expensive, and the massive measurements data can not be fully leveraged on some constrained platforms. The purpose of this paper is to explore the possibility of using cheap 2D Lidar off-the-shelf, to preform complex 3D Reconstruction, moreover, the generated 3D map quality is evaluated by our proposed metrics at the end. The 3D map is constructed in two ways, one way in which the scan is performed at known positions with an external rotary axis at another plane. The other way, in which the 2D Lidar for mapping and another 2D Lidar for localization are placed on a trolley, the trolley is pushed on the ground arbitrarily. The generated maps by different approaches are converted to octomaps uniformly before the evaluation. The similarity and difference between two maps will be evaluated by the proposed metrics thoroughly. The whole mapping system is composed of several modular components. A 3D bracket was made for assembling of the Lidar with a long range, the driver and the motor together. A cover platform made for the IMU and 2D Lidar with a shorter range but high accuracy. The software is stacked up in different ROS packages.Comment: 7 pages, 9 Postscript figures. Accepted by 2018 IEEE International Conference on Advanced Intelligent Mechatronic

Path-tracing Monte Carlo Library for 3D Radiative Transfer in Highly Resolved Cloudy Atmospheres

Interactions between clouds and radiation are at the root of many difficulties in numerically predicting future weather and climate and in retrieving the state of the atmosphere from remote sensing observations. The large range of issues related to these interactions, and in particular to three-dimensional interactions, motivated the development of accurate radiative tools able to compute all types of radiative metrics, from monochromatic, local and directional observables, to integrated energetic quantities. In the continuity of this community effort, we propose here an open-source library for general use in Monte Carlo algorithms. This library is devoted to the acceleration of path-tracing in complex data, typically high-resolution large-domain grounds and clouds. The main algorithmic advances embedded in the library are those related to the construction and traversal of hierarchical grids accelerating the tracing of paths through heterogeneous fields in null-collision (maximum cross-section) algorithms. We show that with these hierarchical grids, the computing time is only weakly sensitivive to the refinement of the volumetric data. The library is tested with a rendering algorithm that produces synthetic images of cloud radiances. Two other examples are given as illustrations, that are respectively used to analyse the transmission of solar radiation under a cloud together with its sensitivity to an optical parameter, and to assess a parametrization of 3D radiative effects of clouds.Comment: Submitted to JAMES, revised and submitted again (this is v2

The Skip Quadtree: A Simple Dynamic Data Structure for Multidimensional Data

We present a new multi-dimensional data structure, which we call the skip quadtree (for point data in R^2) or the skip octree (for point data in R^d, with constant d>2). Our data structure combines the best features of two well-known data structures, in that it has the well-defined "box"-shaped regions of region quadtrees and the logarithmic-height search and update hierarchical structure of skip lists. Indeed, the bottom level of our structure is exactly a region quadtree (or octree for higher dimensional data). We describe efficient algorithms for inserting and deleting points in a skip quadtree, as well as fast methods for performing point location and approximate range queries.Comment: 12 pages, 3 figures. A preliminary version of this paper appeared in the 21st ACM Symp. Comp. Geom., Pisa, 2005, pp. 296-30