Streaming computation of Delaunay triangulations

Abstract

Figure 1: Streaming computation of Delaunay triangulations in 2D (Neuse River) and 3D. Blue quadrants or octants are unfinalized space where future points will arrive. Purple triangles and tetrahedra are in memory. Black points and their triangles and tetrahedra have already been written to disk or piped to the next application. AbstractWe show how to greatly accelerate algorithms that compute Delaunay triangulations of huge, well-distributed point sets in 2D and 3D by exploiting the natural spatial coherence in a stream of points. We achieve large performance gains by introducing spatial finalization into point streams: we partition space into regions, and augment a stream of input points with finalization tags that indicate when a point is the last in its region. By extending an incremental algorithm for Delaunay triangulation to use finalization tags and produce streaming mesh output, we compute a billion-triangle terrain representation for the Neuse River system from 11.2 GB of LIDAR data in 48 minutes using only 70 MB of memory on a laptop with two hard drives. This is a factor of twelve faster than the previous fastest out-of-core Delaunay triangulation software.

A Stream Tilling Approach to Surface Area Estimation for Large Scale Spatial Data in a Shared Memory System

“…Isenburg et al used stream computing to redesign the existing incremental Delaunay triangulation implementations [15]. Before triangulating the huge data set of points, the space was previously decomposed into small regions.…”

“…Then a stream of input points with finalization tags was augmented, and each finalization tag indicated whether a topological point in the last region could be used for the future computation. Furthermore, the TIN (Triangulated Irregular Network) Streaming was also used in Digital Elevation Model (DEM) generation [16]. In addition, Wu et al further optimized the streaming triangulation by partitioning the input points into non-overlapped blocks and then triangulating each block with divide and conquer Delaunay triangulation, instead of the incremental algorithm [13].…”

Surface reconstruction by layer peeling

“…With the current personal computers or workstations having dual or quad cores CPUs, we should fully utilize all the available computing power. In some of the newer works in out-of-core surface reconstruction [21,40,7], they make use of incremental local refinements to a coarse representation of the final reconstructed surface, making it suitable for out-of-core implementation. The layer peeling algorithm is in general a local algorithm and we hope to develop the algorithm further for adaptation to large point sets.…”

Comparative Analysis of Triangulation Libraries for Modeling Large Point Clouds from Land and Their Infrastructures

“…The merge of subsets and the modification of overlap areas is the most crucial step in the process [16]; (ii) Cache-efficient strategies, which act directly in the hardware memory (caches and virtual memory) [17]. These strategies can respond to optimized software for a particular cache architecture or software designed to cooperate well with any cache or virtual memory, regardless of the details of its architecture [18]; (iii) External memory strategies, which outsource the calculation through data structures stored on a disk [19]. These strategies explicitly manage the contents of each level of the memory hierarchy directly in the triangulation algorithm, passing through the virtual memory system [20]; (iv) Streaming strategies, which sequentially read a stream of data and retain only a small portion of the information in the memory [21].…”